3.OA.1 - About the Math, Learning Targets, and Rigor

Grade 3 Multiplication and Division

3.OA.A.1

Full Standard

Interpret products of whole numbers, e.g., interpret 5 × 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 × 7.

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

3rd Grade Students Learning 3rd Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

Report Card Measurement Topic: Demonstrates understanding of multiplication.

Report Card Measurement Topic: Demonstrates understanding of multiplication.

 

 

Learning Target

  • Represent multiplication with equal groups.
  • Represent multiplication with arrays.
  • Relate repeated addition to representations of multiplication.
  • Represent multiplication as equal jumps on a number line.
  • Describe how a multiplication chart relates to these representations.
  • Write an equation for a multiplication situation.
  • Represent multiplication with an area model (3rd quarter after the concept of area is taught).

 

About the Math

Multiplication is a major third-grade concept. Students must understand it deeply. 

  • Represent multiplication with equal groups.

An equal group situation might be something like baskets of apples. Here, there are groups of apples. We can find the number in all by multiplying the number of groups by the number of things in each group. Students should use physical models to show equal groups and connect them to drawings and equations. Looking at a problem such as, "How many apples in 4 baskets of 8 apples each?", students need to think multiplicatively about this problem. They need to think there are four sets of eight. Children conceptualize each group of eight as a single item to be counted. 

  • Represent multiplication with arrays.

Tesselaar Tulip Festival Arrays are arranged in rows and columns of things. One can find the total number of objects by multiplying the number in each row by the number of rows. The difference between an array and area is clear. An array can be an arrangement of any shape or thing in rows or columns. For example, an array could be rows of flowers in a garden. Area is an array of squares with no gaps or spaces. If color tiles are all connected they are an area model. If they are separated by space they are an array.

  • Relate repeated addition to representations of multiplication.

A product can be found with repeated addition. Repeated addition can represent the action of adding equal groups or rows/columns. However, it is critical that students do not overly rely on repeated addition. 

  • Represent multiplication as equal jumps on a number line.

Multiplication can be represented on a number line to find a product. Multiplication on a number line should be connected to other representations and equations.

  • Describe how a multiplication chart relates to these representations.

Students should be able to explain how a multiplication chart works and how it can be used for division (see 3.OA.2). Students should connect representations to equations and the multiplication chart. Students should use the chart consistently so that students find the correct products. 

  • Write an equation for a multiplication situation.

Multiplication can be represented with equations. Students should connect multiplication equations to representations beginning with their first experiences with multiplication. In context, 5 x 7 refers to 5 groups of 7. For example, if asked how many cookies are in 5 bags of 7 cookies, a student's representation/reasoning should show 5 groups of 7 in each. However, in situations without context, overemphasis on the order of factors is not necessary because the commutative property tells us that 5 x 7 = 7 x 5. "Naked numbers" are examples of situations without context. In these cases, students could show either order of factors to represent their understanding. 

  • Represent multiplication with an area model (3rd quarter after the concept of area is taught).

Understanding multiplication as it relates to area is a critical understanding in mathematics. This understanding should be developed after students understand what area is. Students are not to learn the formula for area. Instead, students should understand area as lenghth x length regardless of a rectangle's orientation. Also, students should connect decomposing of area to the distributive property.

 

Essential vocabulary for this standard includes multiplication, factor, product, array, equal group, groups of, areaand repeated addition.

 

Progression of Standard within Grade 3

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Represent multiplication with equal groups.
  • Represent multiplication with arrays.
  • Relate repeated addition to representations of multiplication.
  • Represent multiplication as equal jumps on a number line.
  • Describe how a multiplication chart relates to these representations.
  • Write an equation for a multiplication situation.
  • Represent multiplication with equal group with an area model (3rd quarter after the concept of area is taught).

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 2 Grade 4
  • Work with equal groups of objects and arrays (2.OA.4)
  • Determine whether a group of objects (up to 20) has an odd or even number of members ( 2.OA.3 )
  • Multiplicative Comparison (4.OA.1)
  • Multiply a fraction by a whole number (4.NF.4)

 

 

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