Title: Fourth Grade Math
Course: BPSS (MAT) Mathematics Standards > Section: Standards

MAT-04.OA.01

Under Development

MAT-04 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Use the four operations with whole numbers to solve problems.

MAT-04.OA.01 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.OA.02

Under Development

MAT-04 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Use the four operations with whole numbers to solve problems.

MAT-04.OA.02 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.OA.03

MAT-04 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Use the four operations with whole numbers to solve problems.

MAT-04.OA.03 Solve multistep word problems posed with whole numbers and having whole-numbers answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

- I can interpret the meanings of remainders.
- I can decide if my answer makes sense using mental math, estimation, and rounding strategies.

Skills (Performance) Targets

- I can solve multistep word problems using the four operations.
- I can represent problems using equations with a letter standing for the unknown quantity.

Product Targets

Rubric / Proficiency Scale

Score |  | Description | Sample Activity
4.0 | Advanced Criteria is Under Development In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0
Student is able to use the four operations to solve multi-step word problems, write equations using a symbol for the unknown, interpret remainders, and use estimation strategies to assess the reasonableness of the answer, without error.

I can use any of the four operations to solve two-step word problems.

I can represent the problem using an equation with a letter for the unknown.

I can use mental math, estimation strategies, and rounding to decide in my answer makes sense.

I can interpret remainders in problems with division.
Student is able to do all tasks without error.
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0
Student is able to use the four operations to solve multi-step word problems, write equations using a symbol for the unknown, interpret remainders, and use estimation strategies to assess the reasonableness of the answers.  Student work contains some errors.

I can use any of the four operations to solve two-step word problems, with few mistakes.

I can represent the problem using an equation with a letter for the unknown, with few mistakes.

I can use mental math, estimation strategies, and rounding to decide in my answer makes sense, with few mistakes.

I can interpret remainders in problems with division, with few mistakes.
Student has 2 errors in a single problem or has the same error among all problems.
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to demonstrate understanding of solving word problems, but there are multiple errors on more than one problem. I can solve word problems using the four operations, but I may have mistakes. I can write equations that represent the problem, but I may have mistakes. | Student shows some understanding of solving problems and writing equations, but strategies lead to incorrect answers. Student is unable to assess the reasonableness of their answers.
 | 0.5 | Limited or no understanding of the skill is demonstrated.

Resources

Websites

- Learnzillion 1
- Learnzillion 2
- Learnzillion 3
- Learnzillion 4
- Learnzillion 5

Vocabulary

- multiplication / multiply
- division / divide
- addition / add
- subtraction / subtract
- equations
- unknown variable
- remainders
- reasonableness
- mental computation
- estimation strategies
- rounding
- operations

MAT-04.OA.04

Under Development

MAT-04 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Gain familiarity with factors and multiples.

MAT-04.OA.04 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.OA.05

Under Development

MAT-04 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Generate and analyze patterns.

MAT-04.OA.05 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NBT.01

Under Development

MAT-04 Targeted Standards
(NBT) Domain: Number and Operations in Base Ten
Cluster: Generalize place value understanding for multidigit whole numbers. Limited to whole numbers less than or equal to 1,000,000.

MAT-04.NBT.01 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NBT.02

MAT-04 Targeted Standards
(NBT) Domain: Number and Operations in Base Ten
Cluster: Generalize place value understanding for multidigit whole numbers. Limited to whole numbers less than or equal to 1,000,000.

MAT-04.NBT.02 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

- I can compare numbers to 1,000,000 and decide if a number is greater than, less than, or equal to another.

Skills (Performance) Targets

- I can read numbers to 1,000,000.
- I can write numbers to 1,000,000 in standard form, word form, and expanded form.
- I can use the symbols >, <, and = to compare numbers.

Product Targets

Rubric / Proficiency Scale

Score |  | Description | Sample Activity
4.0
Student is able to demonstrate understanding of place value concepts and skills to read and write multi-digit decimal numbers to the thousandths place.

I can read decimal numbers to the thousandths place.

I can write decimal numbers to the thousandths in standard form, word form, or expanded form.

I can compare decimal numbers to the thousandths using >, <, = symbols.
Student completes all tasks for decimal numbers without error.
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0
Student is able to demonstrate understanding of place value concepts and skills to read and write multi-digit whole numbers.

Skill Set A: Read Numbers within 10,000; 100,000; 1,000,000.

Skill Set B: Write Numbers in Standard Form within 10,000; 100,000; 1,000,000.

Skill Set C: Compare Numbers (>,<,=) within 10,000; 100,000; 1,000,000.

Skill Set D: Write Numbers in Word Form within 10,000; 100,000; 1,000,000.

Skill Set E: Write Numbers in Expanded Form within 10,000; 100,000; 1,000,000.

I can read numbers 1,000,000.

I can write numbers to 1,000,000 in standard form, word form, or expanded form.

I can compare numbers to 1,000,000 using >, <, = symbols.
e.g. Student is able to complete tasks for numbers to 1,000,000 with minimal error.
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0
Student is able to demonstrate partial understanding of place value concepts and skills to read and write multi-digit numbers.

Skill Set A: Read Numbers within 10,000; 100,000; 1,000,000.

Skill Set B: Write Numbers in Standard Form within 10,000; 100,000; 1,000,000.

Skill Set C: Compare Numbers (>,<,=) within 10,000; 100,000; 1,000,000.

Skill Set D: Write Numbers in Word Form within 10,000; 100,000; 1,000,000.

Skill Set E: Write Numbers in Expanded Form within 10,000; 100,000; 1,000,000.

I can read numbers 100,000.

I can write numbers to 100,000 in standard form, word form, or expanded form.

I can compare numbers to 100,000 using >, <, = symbols.
e.g. Student is able to complete tasks for numbers to 10,000 and 100,000 with minimal error within each level.

or

Student is able to complete at least two tasks within 4 skill sets for numbers to 1,000,000.
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0
Student is able to demonstrate beginning understanding of place value concepts and skills to read and write multi-digit numbers.

Skill Set A: Read Numbers within 10,000; 100,000; 1,000,000.

Skill Set B: Write Numbers in Standard Form within 10,000; 100,000; 1,000,000.

Skill Set C: Compare Numbers (>,<,=) within 10,000; 100,000; 1,000,000.

Skill Set D: Write Numbers in Word Form within 10,000; 100,000; 1,000,000.

Skill Set E: Write Numbers in Expanded Form within 10,000; 100,000; 1,000,000.

I can read numbers 10,000.

I can write numbers to 10,000 in standard form, word form, or expanded form.

I can compare numbers to 10,000 using >, <, = symbols.
Student has at least two correct responses in one skill set. Either within the specific type of skill or within the level of the numbers.

e.g. Student is able to complete some tasks for numbers within 10,000 only.

or

Student is able to complete tasks for one skill (e.g. compare numbers) to 1,000,000 but is not able to complete other tasks.
 | 0.5 | Limited or no understanding of the skill is demonstrated.

Resources

Websites

- Learnzillion 1
- Learnzillion 2
- Learnzillion 3

Vocabulary

- place value
- greater than
- less than
- equal to
- < , >, =
- number names (1000 - 1,000,000)
- word form
- standard form
- expanded form

MAT-04.NBT.03

Under Development

MAT-04 Targeted Standards
(NBT) Domain: Number and Operations in Base Ten
Cluster: Generalize place value understanding for multidigit whole numbers.

MAT-04.NBT.03 Use place value understanding to round multi-digit whole numbers to any place.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NBT.04

MAT-04 Targeted Standards
(NBT) Domain: Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to perform multidigit arithmetic.

MAT-04.NBT.04 Add and subtract whole numbers to 1,000,000 - Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

- I can choose a strategy with a reasonable amount of steps to solve a problem.
- I can understand when I need to regroup in my strategy.

Skills (Performance) Targets

- I can use the standard algorithm to add whole numbers to 1,000,000.
- I can use the standard algorithm to subtract numbers to 1,000,000.

Product Targets

Rubric / Proficiency Scale

Score |  | Description | Sample Activity
4.0 | There are no advanced criteria as this standard is foundational in the application and use of the standard algorithm to add and subtract whole numbers within 1,000,000. | -
 | 3.5 |
3.0 | Student is able to fluently add and subtract multi-digit whole numbers to 1,000,000 using the U.S. standard algorithm. I can add whole numbers to 1,000,000 using the standard algorithm without error. I can subtract whole numbers to 1,000,000 using the standard algorithm without error. | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to add and subtract whole numbers to 10,000. I can add whole numbers to 10,000 using the standard algorithm without error. I can subtract whole numbers to 10,000 using the standard algorithm without error. | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0
Student is able to add and subtract whole numbers to 1000 using place value strategies but may have a simple error.

I can add and subtract numbers within 1000.

I can choose a strategy that has a reasonable amount of steps to solve a problem.

I can understand when I need to regroup/trade ones or tens in my strategy.

I can break numbers into place value parts to solve problems.
-
 | 0.5 | Limited or no understanding of the skill is demonstrated.

Resources

Websites

- Learnzillion

Vocabulary

- add
- addend
- addition
- sum
- subtract
- subtraction
- difference
- equation
- strategy
- standard algorithm

MAT-04.NBT.05

MAT-04 Targeted Standards
(NBT) Domain: Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to perform multidigit arithmetic.

MAT-04.NBT.05 (Multiply whole numbers) Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

- I can understand the distributive property.
- I can understand the connection between place value (base ten) and the distributive property.

Skills (Performance) Targets

- I can multiply a number that has four digits by a one-digit number.
- I can multiply a two-digit number by a two-digit number.
- I can show and explain my work using equations, rectangular arrays, and area models.
- I can multiply one-digit numbers by multiples of 10.
- I can multiply two-digit numbers by one-digit numbers.

Product Targets

Rubric / Proficiency Scale

Score |  | Description | Sample Activity
4.0 | Advanced Criteria is under Development. In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0
Student is able to multiply a whole number of up to four digits by a one-digit number and two two-digit numbers using strategies based on place value and the properties of operations.

and

Student is able to illustrate and explain the calculation using equations, rectangular arrays, and/or area.

I can multiply four-digit numbers by one-digit numbers.

I can multiply two-digit numbers by two-digit numbers.

I can show and explain my work using equations, rectangular arrays, and area models.
Student uses understandings about base ten, distributive property, arrays, etc. to multiply numbers.

For 27 x 18, a student might use an partial products to represent the base ten parts

20 x 10 = 200

20 x 8   = 160

7 x 10   =  70

7 x 8     =  56

               486
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0
Student is able to multiply a two-digit whole number by a one-digit whole number.

and

Student is able to illustrate and explain the calculation using equations, rectangular arrays, and/or area.

I can multiply two-digit numbers by one-digit numbers.

I can show and explain my work using equations, rectangular arrays, and area models.
Student uses understandings about base ten, distributive property, arrays, etc. to multiply numbers.

For 37 x 5, a student might think:

(30 x 5) + (7 x 5)=

   150   +     35   =185
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to multiply one-digit whole numbers by multiples of 10 in the range of 10-90 (e.g. 9 x 80) using strategies based on place value and the properties of operations. I can multiply multiples of 10 (10,20,30...90) by one-digit numbers using place value strategies. | Student uses understandings about multiplication and base ten to multiply numbers. For 40x3, a student might think: I know 4x3=12, so 40x3 is 120 because it is 10x more
 | 0.5 | Limited or no understanding of the skill is demonstrated.

Resources

Websites

- Learnzillion 1
- Learnzillion 2

Vocabulary

- equation
- strategies
- properties - rules about how numbers work
- rectangular arrays
- area model
- multiply
- factor
- product
- place value
- base ten
- decompose

MAT-04.NBT.06

MAT-04 Targeted Standards
(NBT) Domain: Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to perform multidigit arithmetic.

MAT-04.NBT.06 (Dividing whole numbers) Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

- I can understand the relationship between multiplication and division.
- I can understand the connection between place value (base ten) and area models when dividing.

Skills (Performance) Targets

- I can divide a four-digit number by a one-digit number with and without remainders.
- I can show and explain my work using equations, rectangular arrays, an area models.
- I can divide numbers within 100 by one-digit numbers (known dividends/divisors 64 ÷ 8).
- I can divide three-digit numbers by a one-digit number with and without remainders..

Product Targets

Rubric / Proficiency Scale

Score |  | Description | Sample Activity
4.0
Student is able to find whole number quotients and remainders with up to four-digit dividends and two-digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

and

Student is able to illustrate and explain the calculations by using equations, rectangular arrays, and/or area models.

I can divide four-digit numbers by two-digit numbers with and without remainders.

I can show and explain my work using equations, arrays, and area models.
Problems such as

8172 ÷ 34
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0
Student is able to find whole number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

and

Student is able to illustrate and explain the calculations by using equations, rectangular arrays, and/or area models.

I can divide four-digit numbers by one-digit numbers with and without remainders.

I can show and explain my work using equations, arrays, and area models.
Problems such as

3172 ÷ 6
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0
Student is able to find whole number quotients and remainders with up to three-digit dividends and one-digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

and

Student is able to illustrate and explain the calculations by using equations, rectangular arrays, and/or area models.

I can divide three-digit numbers by one-digit numbers with and without remainders.

I can show and explain my work using equations, arrays, and area models.
Problems such as

172 ÷ 5
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to fluently divide within 100 without remainders using strategies such as the relationships between multiplication and division or the properties of operations, I can divide numbers within 100. I can show my work using representations such as arrays, equations, and groups of. | Problems such as 27 ÷ 9; 56 ÷ 8; etc.
 | 0.5 | Limited or no understanding of the skill is demonstrated.

Resources

Websites

- Learnzillion 1

Vocabulary

- equation
- strategies
- properties - rules about how numbers work
- rectangular arrays
- area model
- divide
- quotient
- divisor
- dividend
- remainder

MAT-04.NF.01

Under Development

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Extend understanding of fraction equivalence and ordering.

MAT-04.NF.01 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NF.02

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Extend understanding of fraction equivalence and ordering.

MAT-04.NF.02 Comparing Fractions s with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, and < and justify the conclusions, e.g., by using a visual fraction model.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

- I can compare fractions with different numerators and different denominators.
- I can understand in order to compare fractions, I need to use the same whole.
- I can justify and explain why my answer is reasonable.

Skills (Performance) Targets

- I can use fraction models and pictures to compare fractions.
- I can order fractions on a number line.
- I can use the >,<, and = symbols to compare fractions.

Product Targets

Rubric / Proficiency Scale

Score |  | Description | Sample Activity
4.0 | Advanced Criteria is Under Development. In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content. | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0
Student is able to compare two fractions with different numerators and denominators, recognize comparisons are only valid when the fractions refer to the same whole, record results using >,<,= symbols, order fractions on a number line, and justify the conclusions using a visual fraction model and explanation.

I can understand in order to compare fractions, I need to use the same whole.

I can justify and explain why my answer is reasonable.

I can order fractions on a number line.
Students compare fractions using >,<,=.

Students justify answers using fraction models and explanations.

Students order fractions with unlike numerators and denominators on a number line.
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0
Student is able to compare two fractions with different numerators and denominators using >,<,= symbols and justify answers using a visual fraction model.

I can compare fraction pictures using >,<, and = symbols.

I can use fraction models and pictures to justify my answers.

I can compare fractions with unlike denominators and numerators.
Students compare fractions using >,<,=.

Students use given wholes to draw/show fractions.
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to compare two fractions with like numerators and like denominators using >,<,= symbols to record the results. I can compare fraction pictures using >,<, and = symbols. | Students use >,<, = symbols to compare fractions with like denominators or numerators, given a picture representation of the fractions.
 | 0.5 | Limited or no understanding of the skill is demonstrated.

Resources

Websites

- Learnzillion 1
- Learnzillion 2
- Learnzillion 3
- Learnzillion 4

Vocabulary

- fraction
- unit fraction
- equivalent
- numerator
- denominator
- benchmark fraction
- >,<,= symbols
- compare
- common denominators
- fraction model

MAT-04.NF.03

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MAT-04.NF.03 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

a) Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

b) Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

c) Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

- I can understand adding and subtracting fractions involves joining and separating parts of the same whole.

Skills (Performance) Targets

- I can decompose a fraction in more than one way and represent each with an
equation.
- I can use visual fraction models to justify and explain my thinking.
- I can write equations when adding and subtracting fractions.
- I can add and subtract fractions <1 with like denominators.
- I can solve word problems involving fractions and mixed numbers with like denominators.

Product Targets

Rubric / Proficiency Scale

Score |  | Description | Sample Activity
4.0 | Student is able to add and subtract mixed numbers with unlike denominators to solve word problems. | Traveled 5 1/4 miles + 1 3/8 miles. If traveling 10 miles in all, how much farther?
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0
Student is able to demonstrate understanding of fraction concepts involving decomposing fractions, using fraction models, and can solve word problems involving addition and subtraction of mixed numbers  having like denominators.

I can use visual fraction models to justify and explain my thinking.

I can write equations when adding and subtracting fractions.

I can solve word problems involving fractions and mixed numbers with like denominators.
2 1/3 cups of sugar - 2/3 cups of sugar
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0
Student is able add fractions <1 with like denominators to solve word problems in which the sum results in a mixed number , use visual models to support thinking, and write equations.

I can use visual fraction models to justify and explain my thinking.

I can write equations when adding and subtracting fractions.

I can solve word problems involving fractions and mixed numbers with like denominators.
5/8 of a pie + 4/8 of a pie
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to add and subtracts fractions <1 with like denominators. I can understand adding and subtracting fractions involves joining and separating parts of the same whole. I can add and subtract fractions <1 with like denominators. | 1/4+ 2/4 5/6 - 3/6
 | 0.5 | Limited or no understanding of the skill is demonstrated.

Resources

Websites

- Learnzillion 1  (Add/Subtract Fractions Using Visual Models)
- Learnzillion 2  (Add/Subtract Fractions by Joining Parts)
- Learnzillion 3  (Add/Subtract & Compare Fractions Using Models/Symbols)
- Learnzillion 4  (Add/Subtract & Decompose Fractions)
- Learnzillion 5  (Mixed Numbers with Like Denominators Using Models)
- Learnzillion 6  (Add/Subtract Mixed Numbers Using Equivalent Fractions)
- Learnzillion 7  (Solve Word Problems)

Vocabulary

- operations
- addition
- subtraction
- fraction
- unit fraction
- equivalent
- denominator
- numerator
- decompose
- fraction model
- mixed number
- equations
- properties (rules about how numbers work)

MAT-04.NF.03.a

Under Development

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MAT-04.NF.03.a Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NF.03.b

Under Development

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MAT-04.NF.03.b Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NF.03.c

Under Development

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MAT-04.NF.03.c Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NF.03.d

Under Development

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MAT-04.NF.03.d Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NF.04

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MAT-04.NF.04 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

a) Understand a fraction a/b as a multiple of 1/b. For example use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4).

b) Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b).

c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example: If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Student Learning Targets:

Knowledge Targets

Reasoning Targets

- I can understand a fraction is the product of a number of groups times a unit fraction (5/4 = 5 x 1/4 or 5 groups of 1/4).
- I can understand a multiple of a fraction is also the multiple of a unit fraction with the same denominator (6/5 is a multiple of both 3/5 and 1/5 because when counting by 3/5 we say 3/5, 6/5 and for 1/5 we say 1/5, 2/5, 3/5, 4/5, 5/5, 6/5.

Skills (Performance) Targets

- I can multiply a unit fraction by a whole number.
- I can solve word problems using multiplication of a fraction by a whole number.
- I can use visual fraction models and equations to represent my understanding.

Product Targets

Rubric / Proficiency Scale

Score |  | Description | Sample Activity
4.0 | Student is able to solve real world problems involving multiplication of fractions and mixed numbers using fractions models and equations to represent the problem. | Find the area of a rug that is 3 1/2 feet by 6 1/3 feet long.
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0
Student is able to apply and extend understandings of multiplication concepts (multiples, repeated addition, area models) to multiply fractions by a whole number in which the product result in mixed numbers.

I can solve word problems using multiplication of a fraction by a whole number.

I can use visual fraction models and equations to represent my understanding.

I can understand a multiple of a fraction is also the multiple of a unit fraction with the same denominator.
There are 5 bags of grapes. Each way 2/3 of a pound. How many pounds total?
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to solve word problems using multiplication of a fraction by a whole number in which the product does not result in mixed numbers. I can solve word problems using multiplication of a fraction by a whole number. I can use visual fraction models and equations to represent my understanding. | 4 pieces of ribbon. Each piece was 1/6 of a yard in length.  How many yards in all?
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to multiply a fraction by a whole number. I can understand a fraction is the product of a number of groups times a unit fraction (5/4 = 5 x 1/4 or 5 groups of 1/4). I can multiply a unit fraction by a whole number. | 3 x 1/6 = 5/8 = ____ x ____
 | 0.5 | Limited or no understanding of the skill is demonstrated.

Resources

Websites

- Learnzillion 1  (Multiplication of Fractions by Whole Numbers)
- Learnzillion 2  (Compose/Decompose Fractions)
- Learnzillion 3  (Solve Word Problems Involving Multiplication of Fractions)
- Learnzillion 4  (Word Problems / Fraction Models)

Vocabulary

- operations
- multiplication
- multiply
- repeated addition
- multiple
- product
- fraction
- unit fraction
- mixed number
- numerator
- denominator
- fraction model
- equation
- properties - rules about how numbers work

MAT-04.NF.04.a

Under Development

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MAT-04.NF.04 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4).

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NF.04.b

Under Development

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MAT-04.NF.04.b Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b).

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NF.04.c

Under Development

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MAT-04.NF.04.c Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example: If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NF.05

Under Development

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Understand decimal notation for fractions, and compare decimal fraction.

MAT-04.NF.05 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 and add 3/10 + 4/100 = 34/100.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NF.06

Under Development

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Understand decimal notation for fractions, and compare decimal fractions.

MAT-04.NF.06 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NF.07

MAT-04 Targeted Standards
(NF) Domain: Number and Operations - Fractions
Cluster: Understand decimal notation for fractions, and compare decimal fractions.

MAT-04.NF.07 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, and < and justify the conclusions, e.g., by using a visual model.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

- I can compare two decimals to hundredths by reasoning about their size.
- I can understand in order to compare decimals, I need to use the same whole.
- I can justify and explain why my answer is reasonable.

Skills (Performance) Targets

- I can use visual models to compare decimals and justify my reasoning.
- I can use the >,<, and = symbols to compare decimals.

Product Targets

Rubric / Proficiency Scale

Score |  | Description | Sample Activity
4.0 | Advanced Criteria is Under Development In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content. | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0
Student is able to compare decimals and use visual models and explanations to justify reasoning without error.

I can justify and explain why my answer is reasonable.

I can use >,<,= symbols to compare two decimals, with no mistakes.

I can use a visual model to compare decimals, with no mistakes

I can compare decimals to hundredths by reasoning about their size.

I can understand in order to compare decimals, I need to use the same whole.
Given two decimals, students use symbols to compare their size and justify reasoning with explanations and/or visual models.
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0
Student is able to compare decimals given a grid as a visual model without error.

I can use >,<,= symbols to compare two decimals, with no mistakes.

I can use a visual model to compare decimals, with no mistakes.

I can compare decimals to hundredths by reasoning about their size.
Given decimal grids, students compare two decimals using symbols and shading in the grids to represent decimal size.
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0
Student is able to demonstrate understanding of comparing decimals, given a grid as a visual model, but may have an error in representing the size of the decimal within the grid.

I can use >,<,= symbols to compare two decimals.

I can use a visual model to compare decimals, but I may have mistakes.

I can compare decimals to hundredths by reasoning about their size.
Given decimal grids, students compare two decimals using symbols and shading in the grids to represent decimal size.
 | 0.5 | Limited or no understanding of the skill is demonstrated.

Resources

Websites

- Learnzillion

Vocabulary

- fraction
- numerator
- denominator
- decimal
- equivalent
- tenths
- hundredths
- compare
- >, <, = symbols
- justify
- reasoning
- visual model

MAT-04.MD.01

Under Development

MAT-04 Targeted Standards
(MD) Domain: Measurement and Data
Cluster: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

MAT-04.MD.01 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.MD.02

Under Development

MAT-04 Targeted Standards
(MD) Domain: Measurement and Data
Cluster: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

MAT-04.MD.02 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.MD.03

Under Development

MAT-04 Targeted Standards
(MD) Domain: Measurement and Data
Cluster: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

MAT-04.MD.03 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.MD.04

Under Development

MAT-04 Targeted Standards
(MD) Domain: Measurement and Data
Cluster: Represent and interpret data.

MAT-04.MD.04 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.MD.05

Under Development

MAT-04 Targeted Standards
(MD) Domain: Measurement and Data
Cluster: Geometric measurement: understand concepts of angle and measure angles.

MAT-04.MD.05 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.MD.05.a

Under Development

MAT-04 Targeted Standards
(MD) Domain: Measurement and Data
Cluster: Geometric measurement: understand concepts of angle and measure angles.

MAT-04.MD.05.a Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure angles.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.MD.05.b

Under Development

MAT-04 Targeted Standards
(MD) Domain: Measurement and Data
Cluster: Geometric measurement: understand concepts of angle and measure angles.

MAT-04.MD.05.b Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.MD.06

MAT-04 Targeted Standards
(MD) Domain: Measurement and Data
Cluster: Geometric measurement: understand concepts of angle and measure angles.

MAT-04.MD.06 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

- I can reason about angle measurements using my understanding of benchmark angles.

Skills (Performance) Targets

- I can measure angles using a protractor.
- I can sketch angles of a given measurement.

Product Targets

Rubric / Proficiency Scale

Score |  | Description | Sample Activity
4.0 | Advanced Criteria is Under Development. In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content. | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0
Student is able to measure angles in whole number degrees using a protractor and sketch angles of a given measurement without error.

I can measure angles using a protractor without errors.

I can sketch angles of a given measurement without errors.

I can reason about angle measurements using my understanding of benchmark angles.
-
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to measure angles in whole number degrees using a protractor, without error. I can measure angles using a protractor with no mistakes. I can reason about angle measurements using my understanding of benchmark angles. | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to measure angles in whole number degrees using a protractor, but may demonstrate errors. I can measure angles using a protractor, but I make some mistakes. | -
 | 0.5 | Limited or no understanding of the skill is demonstrated.

Resources

Websites

- Learnzillion

Vocabulary

- angles
- degrees
- measure
- protractor
- point
- end point
- vertex
- ray
- acute angle
- right angle
- obtuse angle
- straight angle
- sketch
- benchmark angles (eg. 90°)

MAT-04.MD.07

Under Development

MAT-04 Targeted Standards
(MD) Domain: Measurement and Data
Cluster: Geometric measurement: understand concepts of angle and measure angles.

MAT-04.MD.07 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.G.01

Under Development

MAT-04 Targeted Standards
(G) Domain: Geometry
Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

MAT-04.G.01 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.G.02

Under Development

MAT-04 Targeted Standards
(G) Domain: Geometry
Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

MAT-04.G.02 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of specified size. Recognize right triangles as a category, and identify right triangles.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.G.03

Under Development

MAT-04 Targeted Standards
(G) Domain: Geometry
Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

MAT-04.G.03 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Student Learning Targets:

Knowledge Targets

- I can

Reasoning Targets

- I can

Skills (Performance) Targets

- I can

Product Targets

- I can

Proficiency (Rubric) Scale

Score |  | Description | Sample Activity
4.0 | Student is able to | -
 | 3.5 | In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 | “The Standard.” Student is able to | -
 | 2.5 | No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.
2.0 | Student is able to | -
 | 1.5 | In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0 | Student is able to | -
 | 0.5 | Limited or no understanding of the skill id demonstrated.

Resources

Websites

- Add resources with links, youtube or PDF

Vocabulary

- List

MAT-04.NBT

Domain (NBT)

Number and Operation in Base Ten

Narrative for the (NBT) Number and Operation in Base Ten

At Grade 4, students extend their work in the base-ten system. They use standard algorithms to fluently add and subtract. They use methods based on place value and properties of operations supported by suitable representations to multiply and divide with multi-digit numbers. Visual representations such as area and array diagrams that students draw and connect to equations and other written numerical work are useful for this purpose. By reasoning repeatedly about the connection between math drawings and written numerical work, students can come to see multiplication and division algorithms as abbreviations or summaries of their reasoning about quantities.

Building on earlier work, students generalize place value understanding for multi-digit whole numbers to read, write, and compare whole numerals between 1,000 and 1,000,000. They also extend understanding of place value to include decimals to hundredths and fractional quantities 1/10 and 1/100.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-04.OA

Domain (OA)

Operations and Algebraic Thinking

 Narrative for the (OA) Operations and Algebraic Thinking

Algebraic thinking is about generalizing arithmetic operations and operating on unknown quantities.  It involves recognizing and analyzing patterns and developing generalizations about these patterns.  In algebra, symbols can be used to represent generalizations. Operations and Algebraic Thinking deals with the basic operations - addition, subtraction, multiplication, and division - the relationships they model, the kinds of problems they can be used to solve, as well as, their mathematical properties and relationships.

Fourth graders extend problem solving to multi-step word problems using the four operations posed with whole numbers.  Some problems might easily be represented with a single equation, and others will be more sensibly represented by more than one equation or a diagram and one or more equations. Consider two diving boards, one 40 feet high, the other 8 feet high. Students in earlier grades learned to compare these heights in an additive sense—“This one is 32 feet higher than that one”—using addition and subtraction to solve word problems. Students in Grade 4 learn to compare these quantities multiplicatively as well: “This one is 5 times as high as that one.”

Students reason about number or shape patterns, connecting a rule for a given pattern with its sequence of numbers or shapes. In examining numerical sequences and patterns, fourth graders can explore rules of repeatedly adding the same whole number or repeatedly multiplying by the same whole number.

Fourth graders also build upon earlier understandings about multiplication and division. Students examine various patterns in factor pairs by finding factor pairs for all numbers 1 to 100, and extend the idea of decomposition to multiplication and learn to use the terms multiple, prime number, composite number.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-04.NF

Domain (NF)

Number and Operations - Fraction

Narrative for (NF) Number and Operations - Fractions

Grade 4 students learn a fundamental property of equivalent fractions: multiplying the numerator and denominator of a fraction by the same non-zero whole number results in a fraction that represents the same number as the original fraction. This property forms the basis for much of their other work in Grade 4, including the comparison, addition, and subtraction of fractions and the introduction of decimals.

Grade 4 students use their understanding of equivalent fractions to compare fractions with different numerators and different denominators. Students use area models and number line diagrams to reason about equivalence.  Students also compare decimals using the meaning of a decimal as a fraction, making sure to compare fractions with the same denominator. For example, to compare 0.2 and 0.09, students think of them as 0.20 and 0:09 and see that 0.20>0.09 because 20/100 > 9/100.

Using the understanding gained from work with whole numbers of the relationship between addition and subtraction, students add and subtract fractions with the same denominator. Students also compute sums of whole numbers and fractions, by representing the whole number as an equivalent fraction with the same denominator as the fraction. Grade 4 students also solve word problems involving multiplication of a fraction by a whole number.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-04.MD

Domain (MD)

Measurement and Data

Narrative for the (MD) Measurement and Data

In Grade 4, students build on competencies in measurement and in building and relating units and units of units that they have developed in number, geometry, and geometric measurement.

Fourth graders learn the relative sizes of measurement units within a system of measurement4.MD.1 including: length: meter (m), kilometer (km), centimeter (cm), millimeter (mm); volume: liter (l), milliliter (ml, 1 cubic centimeter of water; a liter, then, is 1000 ml); mass: gram (g, about the weight of a cc of water), kilogram (kg); time: hour (hr), minute (min), second (sec).

Students learn to consider perimeter and area of rectangles, begun in Grade 3, more abstractly. Based on work in previous grades with multiplication, spatially structuring arrays, and area, they abstract the formula for the area of a rectangle.Students learn to apply these understandings and formulas to the solution of real-world and mathematical problems.

Students can use these skills to solve problems, including problems that arise from analyzing line plots. For example, with reference to the line plot above, students might find the difference between the greatest and least values in the data.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-04.G

Domain (G)

Geometry

Narrative for the (G) Geometry

Grade 4 students describe, analyze, compare, and classify two-dimensional shapes by their properties, including explicit use of angle sizes and the related geometric properties of perpendicularity and parallelism.

By the end of Grade 4, students develop explicit awareness of and vocabulary for many concepts they have been developing, including points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Such mathematical terms are useful in communicating geometric ideas, but more important is that constructing examples of these concepts, such as drawing angles and triangles that are acute, obtuse, and right, help students form richer concept images connected to verbal definitions.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.