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# Geometry

## Narrative for the (G) Geometry Domain

Grade 3 students analyze, compare, and classify two-dimensional shapes by their properties. They explicitly relate and combine these classifications. Because they have built a firm foundation of several shape categories, these categories can be the foundation for thinking about the relationships between classes.

Students investigate, describe, and reason about decomposing and composing polygons to make other polygons. Problems such as finding all the possible different compositions of a set of shapes involve geometric problem solving and understanding of congruence and symmetry

Students in Grade 3 also develop more competence in the composition and decomposition of rectangular regions, spatially structuring rectangular arrays.  They count by the number of columns or rows, or use multiplication to determine the number of squares in the array.

## 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-03.G.01

3rd Grade (MAT) Targeted Standard
(G) Geometry
Cluster: Reason with shapes and their attributes.

#### MAT-03.G.02

Under Development

 MAT-03 Targeted Standards(G) Domain: GeometryCluster: Reason with shapes and their attributes. MAT-03.G.02 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

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## 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.

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# Measurement and Data

## Narrative for (MD) Measurement and Data

Students in Grade 3 learn to solve a variety of problems involving measurement and such attributes as length and area, liquid volume, mass, and time.They focus on solving real-world and mathematical problems involving perimeters of polygons. Third graders also focus on learning area. Students learn formulas to compute area, with those formulas based on, and summarizing, a firm conceptual foundation about what area is.

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. In Grades 3–5, work with data is closely related to the number line, fraction concepts, fraction arithmetic, and solving problems that involve the four operations.

In Grade 3, the most important development in data representation for categorical data is that students now draw picture graphs in which each picture represents more than one object, and they draw bar graphs in which the height of a given bar in tick marks must be multiplied by the scale factor in order to yield the number of objects in the given category. These developments connect with the emphasis on multiplication in this grade. At the end of Grade 3, students can draw a scaled picture graph or a scaled bar graph to represent a data set with several categories (six or fewer categories).

## Calculation Method for Domains

Domains are larger groups of related standards. So the DomainGrade is a calculation of all the related standards. So click on the standard name below each Domain to access the learning targets and proficiency scales for each Domain's related standards.

#### MAT-03.MD.01

3rd Grade (MAT) Targeted Standard
(MD) Measurement and Data
Cluster: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

#### MAT-03.MD.02

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. MAT-03.MD.02 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

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## 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.

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#### MAT-03.MD.03

3rd Grade (MAT) Targeted Standard
(MD) Measurement and Data
Cluster: Represent and interpret data.

#### MAT-03.MD.04

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Represent and interpret data. MAT-03.MD.04 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters

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## 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.

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#### MAT-03.MD.05

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. MAT-03.MD.05 Recognize area as an attribute of plane figures and understand concepts of area measurement.

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## 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.

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#### MAT-03.MD.05.a

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. MAT-03.MD.05.a Recognize area as an attribute of plane figures and understand concepts of area measurement. -A square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area.

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## 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.

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#### MAT-03.MD.05.b

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. MAT-03.MD.05.b Recognize area as an attribute of plane figures and understand concepts of area measurement. -A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

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## 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

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#### MAT-03.MD.06

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. MAT-03.MD.06 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

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## 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

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#### MAT-03.MD.07

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. MAT-03.MD.07 Relate area to the operations of multiplication and addition:

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## 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.

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#### MAT-03.MD.07.a

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. MAT-03.MD.07.a Relate area to the operations of multiplication and addition: Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

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## 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.

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#### MAT-03.MD.07.b

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. MAT-03.MD.07.b Relate area to the operations of multiplication and addition: Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

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## 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.

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#### MAT-03.MD.07.c

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. MAT-03.MD.07.c Relate area to the operations of multiplication and addition: Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning.

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## 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.

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#### MAT-03.MD.07.d

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. MAT-03.MD.07.d Relate area to the operations of multiplication and addition: Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.

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## 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

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#### MAT-03.MD.08

3rd Grade (MAT) Targeted Standard
(MD) Measurement and Data
Cluster: Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

# Number and Operation in Base Ten

## Narrative for (NBT) Number and Operations in Base Ten

At Grade 3, the major focus is multiplication, so students’ work with addition and subtraction is limited to maintenance of fluency within 1000 for some students and building fluency to within 1000 for others.  They achieve fluency with strategies and algorithms that are based on place value, properties of operations, and/or the relationship between addition and subtraction. Such fluency can serve as preparation for learning standard algorithms in Grade 4, if the computational methods used can be connected with those algorithms.

For students in grade 3, the special role of 10 in the base-ten system is important in understanding multiplication of one-digit numbers with multiples of 10. For example, the product of 3 x 50 can be represented as 3 groups of 5 tens, which is 15 tens, which is 150.

## 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-03.NBT.01

Under Development

 MAT-03 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Use place value understanding and properties of operations to perform multi­digit arithmetic. MAT-03.NBT.01 Use place value understanding to round whole numbers to the nearest 10 or 100.

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## 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.

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#### MAT-03.NBT.02

3rd Grade (MAT) Targeted Standard
(NBT) Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to perform multi­digit arithmetic.

#### MAT-03.NBT.03

 MAT-03 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Use place value understanding and properties of operations to perform multi­digit arithmetic. MAT-03.NBT.03 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.

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## Rubric / Proficiency 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 is demonstrated.

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# Number and Operations - Fraction

## Narrative for (NF) Number and Operations - Fractions

In Grades 1 and 2, students use fraction language to describe partitions of shapes into equal shares. In Grade 3, they start to develop the idea of a fraction more formally, building on the idea of partitioning a whole into equal parts. The whole can be a shape such as a circle or rectangle, a line segment, or any one finite entity susceptible to subdivision and measurement. In Grade 4, this is extended to include wholes that are collections of objects.

Grade 3 students do some preliminary reasoning about equivalent fractions, in preparation for work in Grade4. As students experiment on number line diagrams they discover that many fractions label the same point on the number line, and are therefore equal; that is, they are equivalent fractions.

Previously, in Grade 2, students compared lengths using a standard measurement unit. In Grade 3 they build on this idea to compare fractions with the same denominator. They see that for fractions that have the same denominator, the underlying unit fractions (fractions with numerator1) are the same size, so the fraction with the greater numerator is greater because it is made of more unit fractions.

## 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-03.NF.01

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.01 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

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## 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

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#### MAT-03.NF.02

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.02 Understand a fraction as a number on the number line; represent fractions on a number line diagram:

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## 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

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#### MAT-03.NF.02.a

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.02.a Understand a fraction as a number on the number line; represent fractions on a number line diagram: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

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## 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.

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#### MAT-03.NF.02.b

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.02.b Understand a fraction as a number on the number line; represent fractions on a number line diagram: Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

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## 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

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#### MAT-03.NF.03

3rd Grade (MAT) Targeted Standard
(NF) Number and Operations - Fractions
Cluster: Develop understanding of fractions as numbers.

##### MAT-03.NF.03 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
b. Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent using a visual fraction model.
c. Recognize fractions, a/1 or a/a, that are equivalent to whole numbers. Express whole numbers as fractions, a/1 or a/a.
d. Compare two fractions with the same numerator or the same denominator by reasoning about their size.
e. Recognize that comparisons are valid only when the two fractions refer to the same whole.
f. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions by using a visual fraction model.

#### MAT-03.NF.03.a

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.03.a Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size: Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

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## 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.

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#### MAT-03.NF.03.b

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.03.b Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size: Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

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## 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

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#### MAT-03.NF.03.c

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.03.c Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

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## 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.

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#### MAT-03.NF.03.d

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.03.d Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size: Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

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## 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

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# 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 analysing 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.

Students in Grade 3 begin the step to formal algebraic language by using a letter for the unknown quantity in expressions or equations for one and two-step problems. As with two-step problems at Grade 2, which involve only addition and subtraction, the Grade 3 two-step word problems vary greatly in difficulty and ease of representation. More difficult problems may require two steps of representation and solution rather than one

Students focus on understanding the meaning and properties of multiplication and division and on finding products of single-digit multiplying and related quotients.  These skills and understandings are crucial; students will rely on them for years to come as they learn to multiply and divide with multi-digit whole number and to add, subtract, multiply and divide with fractions and with decimals.

All of the understandings of multiplication and division situations, of the levels of representation and solving, and of patterns culminate by the end of Grade 3 in fluent multiplying and dividing all single-digit numbers and 10. This is the outcome of a carefully designed learning process that heavily involves the interplay of practice and reasoning about the relationship between multiplication and division facts.

## 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 proficiency scales for individual standards within the Domain.

#### MAT-03.OA.01

Under Development

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Represent and solve problems involving multiplication and division. MAT-03.OA.01 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7.

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## 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

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#### MAT-03.OA.02

Under Development

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Represent and solve problems involving multiplication and division. MAT-03.OA.02 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

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## 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

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#### MAT-03.OA.03

3rd Grade (MAT) Targeted Standard
(OA) Operations and Algebraic Thinking
Cluster: Represent and solve problems involving multiplication and division.

#### MAT-03.OA.04

Under Development

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Represent and solve problems involving multiplication and division. MAT-03.OA.04 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = [ ] ÷ 3, 6 x 6 = ?.

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## 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

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#### MAT-03.OA.05

Under Development

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Understand properties of multiplication and the relationship between multiplication and division. MAT-03.OA.05 Apply properties of operations as strategies to multiply and divide

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## 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

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#### MAT-03.OA.06

Under Development

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Understand properties of multiplication and the relationship between multiplication and division. MAT-03.OA.06 Understand division as an unknown-factor problem.

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## 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

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#### MAT-03.OA.07

3rd Grade (MAT) Targeted Standard
(OA) Operations and Algebraic Thinking
Cluster: Represent and solve problems involving multiplication and division.

##### MAT-03.OA.07 Using mental strategies, fluently multiply and divide within 100.
Use multiple strategies such as count-by/skip counting, doubles, double/doubles, double/double/doubles, derived facts, benchmark numbers, decomposition.

#### MAT-03.OA.07.a

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Multiply and divide within 100. MAT-03.OA.07.a Fluently multiply within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40/5 = 8) or properties of operations. By end of Grade 3, know from memory all products of two one-digit numbers. (Fluently multiply basic facts within 100)

## Student Learning Targets:

### Knowledge Targets

• I can recall from memory the products of multiplication facts up to 10 x 10.

### Reasoning Targets

• I can think about the facts I know to help me find the answers to the facts I need to learn

## Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 There are no advanced criteria for this task as this skill is foundational.  Application of this standard will occur in solving word problems. - 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 answer multiplication and division facts with at least 90% accuracy given 5 seconds per fact. I can answer almost all / all multiplication facts quickly. - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. Student is able to answer multiplication with at least 85% accuracy given 5 seconds per fact. 2.0 Student is able to answer multiplication facts with at least 75% accuracy given 5 seconds per fact. I can answer many multiplication facts quickly. - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. Student is able to answer multiplication facts with at least 50% accuracy given 5 seconds per fact. 1.0 Student is able to answer multiplication facts with at least 25% accuracy given 5 seconds per fact. I can answer some multiplication facts quickly. - 0.5 Limited or no understanding of the skill is demonstrated.

## Resources

### Vocabulary

• factor
• product
• unknown
• strategies
• mental computation
• know from memory
• multiplication facts
• properties of operations - how numbers work

#### MAT-03.OA.07.b

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Multiply and divide within 100. MAT-03.OA.07.b Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40/5 = 8) or properties of operations. By end of Grade 3, know from memory all products of two one-digit numbers. (Fluently divide basic facts within 100)

## Student Learning Targets:

### Knowledge Targets

• I can recall from memory the quotients of division facts to 100.

### Reasoning Targets

• I can think about the facts I know to help me find the answers to the facts I need to learn.

## Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 There are no advanced criteria for this task as this skill is foundational.  Application of this standard will occur in solving word problems. - 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 answer division facts with at least 90% accuracy given 5 seconds per fact. I can answer almost all / all division facts quickly. - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. Student is able to answer division facts with at least 85% accuracy given 5 seconds per fact. 2.0 Student is able to answer division facts with at least 75% accuracy given 5 seconds per fact. I can answer many division facts quickly. - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. Student is able to answer division facts with at least 50% accuracy given 5 seconds per fact. 1.0 Student is able to answer division facts with at least 25% accuracy given 5 seconds per fact. I can answer some division facts quickly. - 0.5 Limited or no understanding of the skill is demonstrated.

## Resources

### Vocabulary

• divide
• quotient
• unknown
• strategies
• mental computation
• know from memory
• division facts
• properties of operations - how numbers work

#### MAT-03.OA.08

3rd Grade (MAT) Targeted Standard
(OA) Operations and Algebraic Thinking
Cluster: Solve problems involving the four operations, and identify and explain patterns in arithmetic. Multiply and divide within 100.

#### MAT-03.OA.09

Under Development

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Solve problems involving the four operations, and identify and explain patterns in arithmetic. Multiply and divide within 100. MAT-03.OA.09 Standard Text

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## 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

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