Multiplication Equations

10 min

Narrative

This Warm-up prompts students to carefully analyze and compare features of expressions and equations. When students compare the drawing, expression, and equations, they must use language precisely to describe how the representations are alike (MP6). Listen to the language students use to describe the different characteristics of the multiplication expression and equation. After the new terms "factor" and "product" are introduced in the Synthesis, connect students' descriptions to those terms.

This is the first time students experience the Which Three Go Together? routine in IM Grade 3. Students should be familiar with this routine from a previous grade. However, they may benefit from a brief review of the steps involved.

Launch

  • Groups of 2
  • Display the image, expression, and equations.
  • "Pick 3 that go together. Be ready to share why they go together."
  • 1 minute: quiet think time
Teacher Instructions
  • "Discuss your thinking with your partner."
  • 2–3 minutes: partner discussion
  • Share and record responses.

Student Task

Which 3 go together?

A

3 groups of 5 dots.

B

3×53\times5

C

2×5=102\times5 =10

D

7+8=157 + 8 = 15

Solution Steps (4)
  1. 1
    Analyze each representation
    →A = drawing (3 groups of 5), B = expression (3×5), C = equation (2×5=10), D = addition equation (7+8=15)
  2. 2
    Identify multiplication representations
    →A, B, and C all represent multiplication with equal groups of 5
  3. 3
    Distinguish expression from equation
    →B is an expression (no =), C is an equation (has = and product)
  4. 4
    Learn vocabulary
    →Factors = numbers being multiplied (2 and 5 in C), Product = result (10 in C)

Sample Response

Sample responses:

A, B, and C go together because:
  • They show equal groups.
  • They represent multiplication.
  • They show groups of 5.
A, B, and D go together because:
  • They represent a total of 15.
A, C, and D go together because:
  • They show the total.
B, C, and D go together because:
  • They use numbers in expressions or equations.
Activity Synthesis (Teacher Notes)
  • "How is C different from the other ways we've represented equal groups before?" (It has an equal sign. It's an equation.)
  • "C is a multiplication equation because it contains a multiplication symbol and the equal sign."
  • "There are words that help us talk about different parts of the multiplication equation. The factors are the numbers being multiplied. The product is the result of multiplying some numbers. In the equation in C, the numbers 2 and 5 are the factors. The product is 10. Keep these words in mind today as we work with other multiplication equations."
Standards
Addressing
  • 3.OA.1·Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. <em>For example, describe a context in which a total number of objects can be expressed as 5 × 7.</em>
  • 3.OA.3·Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
  • 3.OA.A.1·Interpret products of whole numbers, e.g., interpret <span class="math">\(5 \times 7\)</span> as the total number of objects in 5 groups of 7 objects each. <span>For example, describe a context in which a total number of objects can be expressed as <span class="math">\(5 \times 7\)</span>.</span>
  • 3.OA.A.3·Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.<span>See Glossary, Table 2.</span>

20 min

15 min