Prioritized Categories All categories Not categorized Prioritized (G) Geometry (MD) Measurement and Data (NBT) Number and Operations in Base Ten (NF) Number and Operations - Fractions (OA) Operations and Algebraic Thinking

# 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

(G) Geometry
Cluster: Reason with shapes and their attributes.

# 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

(MD) Measurement and Data
Cluster: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

#### MAT-03.MD.03

(MD) Measurement and Data
Cluster: Represent and interpret data.

#### MAT-03.MD.08

(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.02

(NBT) Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to perform multi­digit arithmetic.

# 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.03

(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.

# 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.03

(OA) Operations and Algebraic Thinking
Cluster: Represent and solve problems involving multiplication and division.