Students deepen their understanding of multiplication and division, including their properties and extending their study of factors to include all units from 0 to 10, as well as multiples of 10 within 100.
Math
Unit 3
3rd Grade
Unit 3 extends the study of factors from 2, 3, 4, 5, and 10, which students explored in Unit 2, to include all units from 0 to 10, as well as multiples of 10 within 100. To work with these more challenging units, students will rely on skip-counting (a Level 2 strategy) and converting to an easier problem (a Level 3 strategy dependent on the properties of operations). They then will apply their understanding of all four operations to two-step word problems as well as arithmetic patterns. Finally, the unit culminates with a focus on categorical data, where students draw and solve problems involving scaled picture graphs and scaled bar graphs, a nice application of the major work of multiplication and division.
Topic A begins by reminding students of the commutative property they learned in Unit 2, as well as introducing them to the distributive and associative properties, upon which they will rely for many of the strategies they learn for the larger factors. In order to be able to use these properties, they need to understand how to compute with a factor of 1, which they explore along with 0, as well as understand how to use parentheses. They’ll then explore the factors of 6, 7, 8, and 9 in Topics B and C. Because of the increased difficulty of these facts, students will rely on both skip-counting (a Level 2 strategy) as well as converting to an easier problem (a Level 3 strategy). Converting to an easier problem is dependent on the properties of operations (e.g., to find 6 x 7, think of 5 x 7 and add a group of 7 is dependent on the distributive property). Thus, students will work with the properties extensively throughout the unit, with their understanding of them and notation related to them growing more complex and abstract throughout the unit. In Topic D, students will multiply one-digit numbers by multiples of 10 and by two-digit numbers using the associative property. Then, students solve two-step word problems involving all four operations, assessing the reasonableness of their answer, and identify arithmetic patterns and explain them using the properties of operations. Finally, students explore picture graphs in which each picture represents more than one object and bar graphs where the scale on the axis is more than 1, a key development from Grade 2 (3.MD.3). As the Progressions note, “these developments connect with the emphasis on multiplication in this grade” (MD Progression, p. 7). Students also solve one- and two-step word problems related to the data in these plots, relying on the extensive work students have done with word problems throughout the year. Thus, this supporting cluster standard nicely enhances the major work they’ve been working on throughout this and the previous unit.
In Unit 3, students deepen their understanding of multiplication and division, including their properties. “Mathematically proficient students at the elementary grades use structures such as…the properties of operations…to solve problems” (MP.7) (Standards for Mathematical Practice: Commentary and Elaborations for K–5, p. 9). Students use the properties of operations to convert computations to an easier problem (a Level 3 strategy), as well as construct and critique the reasoning of others regarding the properties of operations (MP.3). Lastly, students model with mathematics with these new operations, solving one- and two-step equations using them (MP.4).
Students’ understanding of multiplication and division will further develop in Unit 4, when students study area. Students will also use their understanding of these operations in Unit 7 when they apply them in the context of measurement word problems. In subsequent years, students’ understanding will be entirely dependent on their conceptual understanding and fluency with these operations—everything from multi-step multiplicative comparison words problems in Grade 4 to polynomial multiplication and division in Algebra 2, and lots in between. Thus, this unit culminates major work of Grade 3 as well as deeply important foundational work upon which students will rely for years to come.
Pacing: 31 instructional days (28 lessons, 2 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 2021-2022 school year, see our 3rd Grade Scope and Sequence Recommended Adjustments.
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This assessment accompanies Unit 3 and should be given on the suggested assessment day or after completing the unit.
Read the following table that includes models used throughout the unit.
Equal groups |
Example: 4 equal groups of 3 stars |
Array |
Example: 4 rows of 3 |
Tape diagram |
Example: There are 4 bags with 3 plums in each bag. How many plums are there in all? |
Concrete or pictorial base ten blocks |
Example: Find $$2 \times 60$$ using base ten blocks. |
Picture graph | |
Bar graph |
distributive property
associative property
scale
key
parentheses
To see all the vocabulary for this course, view our 3rd Grade Vocabulary Glossary.
Word Problems and Fluency Activities
Access daily word problem practice and our content-aligned fluency activities created to help students strengthen their application and fluency skills.
Topic A: Introduction to The Properties of Operations
Topic B: Multiplication and Division by 6 and 7
Topic C: Multiplication and Division by 8 and 9
Topic D: Multiplication and Division by Values Greater than 10
Topic E: Two-Step Word Problems and Patterns in Arithmetic
Topic F: Scaled Picture and Bar Graphs
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 2
Multiplication and Division, Part 1
Unit 4
Area