# Multi-Digit Multiplication

## Objective

Multiply two-digit multiples of 10 by two-digit multiples of 10. Estimate multi-digit products by rounding numbers to their largest place value.

## Common Core Standards

### Core Standards

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• 4.NBT.B.5 — Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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• 3.NBT.A.3

• 4.NBT.A.1

• 3.OA.C.7

## Criteria for Success

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1. Multiply multiples of 10 by multiples of 10.
2. Identify patterns in multiplication of multiples of 10 by multiples of 10.
3. Estimate products of two-digit by two-digit multiplication by rounding the multi-digit values to their largest place value.

## Tips for Teachers

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• The following material is needed for today's lesson: base ten blocks
• Throughout this topic and then next one, “when students decompose numbers into sums of multiples of base-ten units to multiply them, they are seeing and making use of structure (MP.7). As they illustrate and explain the calculation by using physical or drawn models, they are using appropriate drawn tools strategically (MP.5) and attending to precision (MP.6) as they use base-ten units in the appropriate places” (PARCC Model Content Frameworks, Mathematics, Grades 3–11).
• Further, it is important to preserve place value when talking about products of multi-digit numbers. For example, when discussing the computation 1,768 x 4, the partial product of the 6 digit and the 4 digit should be referenced as “six tens times four” or “sixty times four” rather than “six times four.”
• In Lessons 16—20, students estimate products of a whole number of up to four digits by a one-digit whole number by rounding the largest factor, thus connecting the work of 4.NBT.3 across clusters to the work of 4.NBT.4, as well as preparing students to assess reasonableness in the context of multi-step word problems (4.OA.3).

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 1 and Anchor Task 3 (benefit from worked examples). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

1. Solve.

a. 6 x 3

b. 60 x 3

c. 60 x 30

2. What do you notice about #1? What do you wonder?

### Problem 2

1. Kristen and Rajiv are finding the product 80 x 50. Kristen says to find 8 x 50, then multiply by 10. Rajiv says to find 80 x 5, then multiply by 10.
1. Will both Kristen and Rajiv’s method give the correct product? Why?
2. Write expressions to represent Kristen and Rajiv’s methods.
2. Find the product 80 x 50.

### Problem 3

Estimate the following products.

a. 64 x 32

b. 57 x 45

c. 24 x 77

## Problem Set & Homework

#### Discussion of Problem Set

• What pattern did you notice while solving #1?
• What made #2(d) and #2(h) particularly more challenging?
• Think about the problems we solved during the lesson and the problems you solved in the Problem Set. When does the number of zeros in the factors not equal the number of zeros in the product?
• For each problem in #4, would you expect the actual product to be greater or less than your estimate? Why?
• How can you tell, just by looking at the size of the factors and the size of the product Josh found, that his answer is unreasonable?

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### Problem 1

Find the following products.

 a.   20 x 40 b.   60 x 70 c.   20 x 50

### Problem 2

Estimate the following products.

 a.   32 x 81 b.   48 x 59 c.   25 x 73

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