Second Grade Math


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MAT-02.G

BPSS-MAT logoDomain (G)

Geometry

Narrative for the (G) Geometry

Grade 2 students learn to name and describe the defining attributes of categories of two-dimensional shapes, including circles, triangles, squares, rectangles, rhombuses, trapezoids, and the general category of quadrilateral. They describe pentagons, hexagons, octagons, and other polygons by the number of sides. Because they have developed both verbal descriptions of these shapes and their defining attributes and a rich store of associated mental images, they are able to draw shapes with specified attributes, such as a shape with five sides or a shape with six angles.

Students in Grade 2 also explore decompositions of shapes into regions that are congruent or have equal area. For example, two squares can be partitioned into fourths in different ways. Any of these fourths represents an equal share of the shape (e.g., “the same amount of cake”) even though they have different shapes.

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-02.G.03

MAT-02 Targeted Standards
(G) Domain: Geometry
Cluster: Reason with shapes and their attributes.

MAT-02.G.03 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Partition: Divide into pieces. (ND)

Student Learning Targets:

Knowledge Targets

  • I can identify one-half, one-fourth, and one-third shaded parts.

Reasoning Targets

  • I can understand that the same shape can be divided into equal parts in different ways.

Skills (Performance) Targets

  • I can divide circles and rectangles into 2,3,and 4 equal parts in different ways.
  • I can use the words halves, thirds, fourths, and half of to describe the equal parts.
  • I can describe one whole as being 2 halves, 3 thirds, and 4 fourths.

Product Targets

 

Rubric / Proficiency Scale

Score   Description Sample Activity
4.0

Student is able to partition shapes into parts with equal areas; express the area of each part as a unit fraction of the whole; determine if fractions are equivalent; and use models to prove if fractions are greater than/less than another.

I can write a fraction to represent the shaded portion of a shape.

I can represent a fraction using models or pictures.

I can explain why fractions are equivalent.

I can use pictures/models to prove if a fraction is greater than/less than another fraction.

-
  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 partition circles and rectangles into two, three, and four equal parts without error; use the words halves, thirds, fourths; and recognize equal shares of identical wholes can have different shapes.

I can divide shapes into 2, 3, and 4 equal parts in more than one way with no mistakes.

I can use the words halves, thirds, and fourths to describe the equal parts.

-
  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 divide shapes/pictures into halves and fourths in more than one way without error.

I can divide shapes into 2 and 4 equal parts in different ways with no mistakes.

I can use the words halves and fourths to describe the equal parts.

-
  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 identify shapes that have 1/2 and 1/4 parts shaded without error.

I can identify shapes/pictures that show 1/2 and 1/4 with no mistakes.

-
  0.5 Limited or no understanding of the skill is demonstrated.

Resources

Websites

Vocabulary

  • partition / divide
  • equal shares / parts
  • whole
  • one half
  • one fourth
  • one third
  • half of
  • third of
  • fourth of
  • halves
  • thirds
  • fourths
  • two halves
  • three thirds
  • four fourths

 


MAT-02.MD

BPSS-MAT logoDomain (MD)

Measurement and Data

Narrative for the (MD) Measurement and Data

Second graders learn to measure length with a variety of tools, such as rulers, meter sticks, and measuring tapes. To learn measurement concepts and skills, students might use both simple rulers (e.g., having only whole units such as centimeters or inches) and physical units (e.g., manipulatives that are centimeter or inch lengths). Second graders also learn the concept of the inverse relationship between the size of the unit of length and the number of units required to cover a specific length or distance. For example, it will take more centimeter lengths to cover a certain distance than inch lengths because inches are the larger unit.

In Grade 2, students learn to combine and compare lengths using arithmetic operations to solve word problems. That is, they can add two lengths to obtain the length of the whole and subtract one length from another to find out the difference in lengths.

After experience with measuring, second graders learn to estimate lengths. Real-world applications of length often involve estimation. Skilled estimators move fluently back and forth between written or verbal length measurements and representations of their corresponding magnitudes on a mental ruler (also called the “mental number line”).

As students work with data in Grades K–5, they build foundations for their study of statistics and probability in Grades 6 and beyond, and they strengthen and apply what they are learning in arithmetic. Kindergarten work with data uses counting and order relations. First- and second-graders solve addition and subtraction problems in a data context.  Students in Grade 2 draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. They solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

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-02.MD.07

MAT-02 Targeted Standards
(MD) Domain: Measurement and Data
Cluster: Work with time and money.

MAT-02.MD.07 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

  • I can decide if the time of an activity would happen during the a.m. or p.m. based on words such as morning, afternoon, evening, breakfast, supper, etc.

Skills (Performance) Targets

  • I can read/tell the time up to 5 minute intervals using analog and digital clocks.
  • I can write the time shown on an analog clock up to 5 minute intervals.
  • I can draw the hands on an analog clock to match the time on a digital clock.

Product Targets

 

Rubric / Proficiency Scale

Score   Description Sample Activity
4.0

Student is able to tell and write time to the nearest minute; measure time intervals in minutes; and solves word problems involving elapsed time situations for intervals in minutes without error.

I can tell and write time to the minute.

I can solve word problems about elapsed time.

-
  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 all time concepts without error/one minor error (identify am/pm situations, write time shown on analog clocks, draw hands to match a digital time).

I can answer questions about a.m. and p.m. without mistakes.

I can write the time shown on an analog clock without mistakes.

I can draw hands on a clock to match a digital time without mistakes.

-
  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 understanding of at least 2 out of 3 time concepts without error (identify am/pm situations, write time shown on analog clocks, draw hands to match a digital time).

I can answer questions about a.m. and p.m. without mistakes.

I can write the time shown on an analog clock without mistakes.

I can draw hands on a clock to match a digital time without mistakes.

-
  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 time concepts but has multiple errors.

I can answer some questions about a.m. and p.m.

I can sometimes tell the time shown on an analog clock.

I can sometimes write the time shown on an analog clock.

-
  0.5 Limited or no understanding of the skill is demonstrated.

Resources

Websites

Vocabulary

  • clocks
  • minute hand
  • hour hand
  • hour
  • minute
  • count by fives
  • a.m.
  • p.m.
  • o'clock
  • analog clock
  • digital clock
  • half hour
  • thirty minutes before/after/past/until
  • fifteen minutes before/after/past/until
  • quarter past / 'til
  • half past / 'til

 


MAT-02.NBT

BPSS-MAT logoDomain (NBT)

Number and Operation in Base Ten

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

At Grade 2, students extend their base-ten understanding to hundreds. They now add and subtract within 1000, with composing and decomposing, and they understand and explain the reasoning of the processes they use. They become fluent with addition and subtraction within 100.

Students extend their understanding of the base-ten system by viewing 10 tens as forming a new unit called a “hundred.” This lays the groundwork for understanding the structure of the base-ten system as based in repeated bundling in groups of 10 and understanding that the unit associated with each place is 10 of the unit associated with the place to its right.

Students also begin to work towards multiplication when they skip count by 5s, by 10s, and by 100s. This skip counting is not yet true multiplication because students don’t keep track of the number of groups they have counted.

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-02.NBT.01

BPSS-MAT logoMAT-02 Targeted Standards
(NBT) Domain: Number and Operations in Base Ten
Cluster: Understand place value.

MAT-02.NBT.01 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

a) 100 can be thought of as a bundle of ten tens - called a "hundred";
b)The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

Student Learning Targets:

Knowledge Targets

  • I can identify the place value for each digit in a three-digit number.
  • I can identify which digits are in the hundreds', tens', and ones, place.

Reasoning Targets

  • I can understand which digit of a three-digit number shows the amount of hundreds, tens, and ones.
  • I can understand one hundred is made of ten bundles of ten.
  • I can understand numbers such as 200 are the same as two hundreds, 0 tens, and 0 ones.

Skills (Performance) Targets

  • I can write the three-digit number represented by base ten blocks.
  • I can tell/show the value of a digit in a three-digit number.

Product Targets

 

Rubric / Proficiency Scale

Score   Description Sample Activity
4.0

Student is able to demonstrate understanding of the relationship between hundreds, tens, and ones in order to regroup the amount of tens and ones to identify a number and write a number in expanded form.

I can write three-digit numbers in expanded form.

I can write numbers represented by hundreds, tens, and ones that require me to regroup / bundle.

Given 267, student is able to write 200+60+7 to represent the number.

Given 1 hundred 12 tens and 4 ones, student identifies the number as 224.

  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 all place value concepts for three-digit numbers without error.

I can write the three-digit number represented by the base ten blocks.

I can identify the place value each digit holds in a three-digit number.

I can identify which digits are in the hundreds', tens' and ones' place.

I can tell/show the value a digit has in a three-digit number.

 
  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 for three-digit numbers by writing the three-digit number represented by base ten blocks, with minor error.

I can identify the place value each digit holds in a three-digit number.

I can identify which digits are in the hundreds', tens' and ones' place.

 
  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 for three-digit numbers by writing the three-digit number represented by base ten blocks, but may exhibit errors.

and

Student is able correctly identify at least two place value concepts for two-digit numbers: the place value for tens and ones digits, how many tens and ones are in a number; and the value of a digit in a two-digit number.

I can tell/show which digit is in the ten's and one's place.

I can tell/show how many tens and ones are in a number.

I can tell/show the value a digit has in a two-digit number.

I can write the three-digit number represented by the base ten blocks, but I may have mistakes.

 
  0.5

Limited or no understanding of the skill is demonstrated.

Student is unable to correctly identify at least two place value concepts for two-digit numbers: the place value for tens and ones digits, how many tens and ones are in a number; and the value of a digit in a two-digit number. (1st grade target)

Resources

Websites

Vocabulary

  • hundreds
  • tens
  • ones
  • base-ten
  • number names (1-1000)
  • bundles / groups of
  • equal to / the same as
  • digit
  • hundreds' place
  • tens' place
  • ones' place
  • value

MAT-02.NBT.02

 

MAT-02 Targeted Standards
(NBT) Domain: Number and Operations in Base Ten
Cluster: Understand place value.

MAT-02.NBT.02 Count within 1000; skip-count by 5s, 10s, and 100s.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

Skills (Performance) Targets

  • I can count on by 1s from any number within 1000.
  • I can count on by 10s from any number within 1000.
  • I can count on by 5s from any number within 1000.
  • I can count on by 100s from any number within 1000.

Product Targets

 

Rubric / Proficiency Scale

Score   Description Sample Activity
4.0 Student is able to count beyond 1000; Skip count by 5s, 10s, and 100s beyond 1000 including counting on from numbers that are not multiples of 5.
-
  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 accurately complete sequences counting on from any number by 1s and skip counting by 5s, 10s, and 100s within 1000 with no more than 1 error among all sequences.

I can count on by 1s from any number within 1000 without mistakes.

I can skip count by 5s, 10s, and 100s from any number within 1000 without mistakes.

-
  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 complete three sequences counting on by 1s within 1000 without error.

and

Student is able to complete at least 2 out of 3 sequences skip counting by each - 5s, 10s, and 100s - but may make an error within each number type.

I can count on by 1s from any number within 1000 without mistakes.

I can skip count  by 5s, 10s, and 100s from any number within 1000 but I may have mistakes.

-
  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 count on by 1s within 1000, but may have errors.

I can count on by 1s from any number within 1000, but I may have mistakes.

-
  0.5

Limited or no understanding of the skill is demonstrated.

Student demonstrates very little skill in counting by ones above 120. (1st Grade)

Student demonstrates very little skill in skip counting by tens to 100. (Kindergarten)

Resources

Websites

Vocabulary

  • count
  • count on
  • skip count
  • number pattern
  • number names (1-1000)

 


MAT-02.NBT.03

 

MAT-02 Targeted Standards
(NBT) Domain: Number and Operations in Base Ten
Cluster: Understand place value.

MAT-02.NBT.03 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

Skills (Performance) Targets

  • I can read numbers to 1000.
  • I can write numbers to 1000 in standard form (47).
  • I can write numbers in word form (forty-seven).
  • I can write numbers in expanded form (40+7).

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 read and write numbers to 1000 using base ten numerals, number names, and expanded form with minor error.

I can read numbers to 1000.

I can write numbers to 1000 in standard form.

I can write numbers to 1000 in expanded form.

I can write numbers to 1000 in word form.

Given three different numbers for each concept, student has no more than 1 error overall.
  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 read three numbers and write three numbers to 1000 in standard form with no more than one error.

I can read numbers to 1000.

I can write numbers to 1000 in standard form.

Given three different numbers for each concept, student has no more than one error in each skill.
  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 reading and writing numbers to 1000, but exhibits errors.

I can read numbers to 100.

I can write numbers to 100.

Given three different numbers for each concept, student is able to complete  some of the activities for numbers to 100.
  0.5 Limited or no understanding of the skill is demonstrated.

Resources

Websites

Vocabulary

  • base ten numeral / number
  • standard form
  • word form
  • expanded form
  • number names (1-1000)
  • number words (one - one thousand)

 


MAT-02.NBT.05

MAT-02 Targeted Standards
(NBT) Domain: Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to add and subtract.

MAT-02.NBT.05 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction

Student Learning Targets:

Knowledge Targets

Reasoning Targets

  • I can choose efficient strategies based on the numbers in a problem.

Skills (Performance) Targets

  • I can add and subtract numbers up to100 using efficient strategies.
  • I can add and subtract numbers using strategies such as breaking numbers into place value parts.
  • I can add and subtract numbers using strategies such as counting on by 10s and 100s and using landmark numbers.
  • I can use base ten drawings to show how numbers are composed and decomposed.

Product Targets

 

Rubric / Proficiency Scale

Score   Description Sample Activity
4.0

Student is able to accurately and fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

I can accurately add and subtract numbers within 1000 using efficient strategies.

I can choose efficient strategies based on the numbers in a problem.

 
  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 fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.  Student uses efficient strategies that lead to correct answers.

I can accurately add and subtract numbers up to 100 using efficient strategies.

I can choose efficient strategies based on the numbers in a problem.

Student completes four problems accurately and efficiently.
  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 problems using strategies such a counting on, base ten drawings, landmark numbers, decomposing into place value parts, etc., but may have errors. 

I can add and subtract numbers using strategies such as breaking numbers into place value parts.

I can add and subtract numbers using strategies such as counting on by 10s and 100s and using landmark numbers.

I can use base ten drawings to show how numbers are composed and decomposed.

Student completes four problems with no more than 2 errors.
  1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.
1.0

Student solves problems by "counting all" by ones using concrete models/counters, tallies, pictures, etc. to add within 100 and subtract multiples of 10 from numbers 10-90.  Student attempts may or may not result in correct answers.

I can solve problems using counting tools.

 
  0.5 Limited or no understanding of the skill is demonstrated.

Resources

Websites

Vocabulary

  • fluent
  • compose
  • decompose
  • place value
  • digit
  • add
  • subtract
  • sum
  • equal
  • difference
  • landmark numbers
  • place value parts
  • addition
  • subtraction
  • base ten
  • ten more/less
  • 100 more/less
  • number line
  • base ten blocks
  • 100 chart

 


MAT-02.NBT.08

MAT-02 Targeted Standards
(NBT) Domain: Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to add and subtract.

MAT-02.NBT.08 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

Skills (Performance) Targets

  • I can mentally add 10 and 100 to any number 100-900.
  • I can mentally subtract 10 or 100 from any number 100-900.

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 mentally add and subtract 10 and 100 from any number 100-900 without error.

I can answer what is 10 more and 10 less than any number 100-900 with no mistakes.

I can answer what is 100 more and 100 less than any number 100-900 with no mistakes.

-
  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 mentally add and subtract 10 and 100 from any number 100-900 that is a multiple of 5 without error.

I can answer what is 10 more and 10 less than a number that ends with five.

I can answer what is 100 more and 100 less than a number that ends with five.

-
  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 mentally add and subtract 10 and 100 from any number 100-900 that is a multiple of 10, but may exhibit a minor error.

I can answer what is 10 more and 10 less than a number that ends with  zero.

I can answer what is 100 more and 100 less than a number that ends with zero.

-
  0.5 Limited or no understanding of the skill is demonstrated.

Resources

Websites

Vocabulary

  • add
  • subtract
  • ten more
  • ten less
  • one hundred more
  • one hundred less
  • mental math

 



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