Unit Overview
Unit learning goals
- Students represent and solve multiplication problems through the context of picture and bar graphs that represent categorical data.
Unit at-a-Glance
Total Lessons: 21
Required: 20
Optional lessons: 1
Assessments: 1
End-of-unit assessment
Section Goals:
Section A Goals
- Interpret scaled picture and bar graphs.
- Represent data using scaled picture and bar graphs.
- Solve one- and two-step story problems using addition and subtraction.
Section B Goals
- Represent and solve multiplication problems involving equal groups.
- Understand multiplication in terms of equal groups.
Section C Goals
- Represent and solve multiplication problems involving arrays.
Standards Addressed:
3.OA.A.13.OA.A.33.OA.A.43.OA.B.53.OA.C.73.OA.D.93.MD.B.3
Lesson learning goals
Full unit narrative
In this unit, students interpret and represent data on scaled picture graphs and scaled bar graphs. Then, they learn the concept of multiplication.
This is the first of four units that focus on multiplication. In this unit, students explore scaled picture graphs and bar graphs as an entry point for learning about equal-size groups and multiplication.
In grade 2, students analyzed picture graphs in which one picture represented one object and bar graphs that were scaled by single units. Here, students encounter picture graphs in which each picture represents more than one object and bar graphs that were scaled by 2 or 5 units. The idea that one picture can represent multiple objects helps to introduce the idea of equal-size groups.
Students learn that multiplication can mean finding the total number of objects in groups of objects each, and can be represented by . They then relate the idea of equal groups and the expression to the rows and columns of an array. In working with arrays, students begin to notice the commutative property of multiplication.
In all cases, students make sense of the meaning of multiplication expressions before finding their value, and before writing equations that relate two factors and a product.
Later in the unit, students see situations in which the total number of objects is known but either the number of groups or the size of each group is not known. Problems with a missing factor offer students a preview to division.
Throughout the unit, provide access to connecting cubes or counters, as students may choose to use them to represent and solve problems.
Throughout the unit
Students work toward fluency in multiplying by 2, 5, and 10. The How Many Do You See routine is used to encourage students to look for equal groups. It prompts students to subitize a group of dots as one unit, see the iterations of the groups, and skip-count to say the total number of dots they see in the image. This routine progresses from dots to drawings of equal groups to array formations.
Here is a sampling of the How Many Do You See warm-ups in the unit.
| lesson 4 | lesson 18 |
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Number Talks are likewise designed to help students build fluency with equal groups and multiplication expressions. The sequence of expressions encourages students to relate multiplication to skip-counting. For example, in the sequence , , , , students can discover that the products increase in the same way as in skip-counting by 10. Some Number Talks elicit students' understanding of addition and subtraction within 100 in preparation for the work in an upcoming unit.
Here is a sampling of the Number Talk warm-ups in the unit.
| lesson 5 | lesson 15 | lesson 19 | lesson 20 |
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Unit assessments
You can find the unit materials list, family letter, support for distance and unfinished learning, and print versions of the student workbook and teacher guide in the Additional resources section of this page.
Section and lesson materials
Unit Materials
Support for distance and unfinished learning
Home Connection
Home Connection includes Family Support Materials such as videos to provide the background a family may need to support student learning at home and access to key concepts and ideas in both English and Spanish.
Student and Teacher Books
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