Learn on PengiSaxon Math, Intermediate 4Chapter 5: Lessons 41–50, Investigation 5

Lesson 49: Word Problems About Equal Groups, Part 1

In this Grade 4 Saxon Math lesson, students learn to solve equal groups word problems using the multiplication formula: Number of groups × Number in each group = Total. They practice identifying clue words like "in each," setting up and solving multiplication equations, and applying division when the total or group size is the unknown. The lesson also introduces estimation as a strategy for checking reasonableness of answers.

Section 1

📘 Word Problems About Equal Groups, Part 1

New Concept

Number of groups ×\times Number in each group = Total

What’s next

Next, you’ll use this formula to translate word problems into equations and find the total in different scenarios.

Section 2

Formula

Property

Number of groups × Number in each group = Total

Example

Example 1: 6 flocks with 8 birds each is 6×8=486 \times 8 = 48 birds in all.
Example 2: 9 cars with 6 people in each is 9×6=549 \times 6 = 54 people in all.
Example 3: 3 cartons with 12 eggs in each is 3×12=363 \times 12 = 36 eggs total.

Explanation

When you have several groups that are all the same size, don't count one by one! Just multiply the number of groups by the number of items in a single group to find your grand total. It’s a fantastic shortcut for organized counting and works every single time.

Section 3

Spotting the clues

Property

The words in each are a clue to this problem. The words in each usually mean that the problem has an "equal groups" plot.

Example

Problem: 5 cans with 3 balls in each can. Solution: 5 cans×3 balls in each can=15 tennis balls5 \text{ cans} \times 3 \text{ balls in each can} = 15 \text{ tennis balls}.
Problem: 4 dozen muffins. Solution: 4 dozen×12 muffins in each dozen=48 muffins4 \text{ dozen} \times 12 \text{ muffins in each dozen} = 48 \text{ muffins}.

Explanation

Think of the words 'in each' as a secret signal that it's time to multiply! Once you spot them, you know you're dealing with equal groups. Just identify the number of groups and the amount 'in each' one, then multiply them together to find the total. Easy peasy!

Book overview

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Continue this chapter

Chapter 5: Lessons 41–50, Investigation 5

  1. Lesson 1

    Lesson 41: Subtracting Across Zero, Missing Factors

  2. Lesson 2

    Lesson 42: Rounding Numbers to Estimate

  3. Lesson 3

    Lesson 43: Adding and Subtracting Decimal Numbers, Part 1, Activity Adding and Subtracting Decimals

  4. Lesson 4

    Lesson 44: Multiplying Two-Digit Numbers, Part 1

  5. Lesson 5

    Lesson 45: Parentheses and the Associative Property, Naming Lines and Segments

  6. Lesson 6

    Lesson 46: Relating Multiplication and Division, Part 1, Activity Using a Multiplication Table to Divide

  7. Lesson 7

    Lesson 47: Relating Multiplication and Division, Part 2

  8. Lesson 8

    Lesson 48: Multiplying Two-Digit Numbers, Part 2

  9. Lesson 9Current

    Lesson 49: Word Problems About Equal Groups, Part 1

  10. Lesson 10

    Lesson 50: Adding and Subtracting Decimal Numbers, Part 2, Activity Adding and Subtracting Decimals

  11. Lesson 11

    Investigation 5: Percents, Activity Percent

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Word Problems About Equal Groups, Part 1

New Concept

Number of groups ×\times Number in each group = Total

What’s next

Next, you’ll use this formula to translate word problems into equations and find the total in different scenarios.

Section 2

Formula

Property

Number of groups × Number in each group = Total

Example

Example 1: 6 flocks with 8 birds each is 6×8=486 \times 8 = 48 birds in all.
Example 2: 9 cars with 6 people in each is 9×6=549 \times 6 = 54 people in all.
Example 3: 3 cartons with 12 eggs in each is 3×12=363 \times 12 = 36 eggs total.

Explanation

When you have several groups that are all the same size, don't count one by one! Just multiply the number of groups by the number of items in a single group to find your grand total. It’s a fantastic shortcut for organized counting and works every single time.

Section 3

Spotting the clues

Property

The words in each are a clue to this problem. The words in each usually mean that the problem has an "equal groups" plot.

Example

Problem: 5 cans with 3 balls in each can. Solution: 5 cans×3 balls in each can=15 tennis balls5 \text{ cans} \times 3 \text{ balls in each can} = 15 \text{ tennis balls}.
Problem: 4 dozen muffins. Solution: 4 dozen×12 muffins in each dozen=48 muffins4 \text{ dozen} \times 12 \text{ muffins in each dozen} = 48 \text{ muffins}.

Explanation

Think of the words 'in each' as a secret signal that it's time to multiply! Once you spot them, you know you're dealing with equal groups. Just identify the number of groups and the amount 'in each' one, then multiply them together to find the total. Easy peasy!

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 5: Lessons 41–50, Investigation 5

  1. Lesson 1

    Lesson 41: Subtracting Across Zero, Missing Factors

  2. Lesson 2

    Lesson 42: Rounding Numbers to Estimate

  3. Lesson 3

    Lesson 43: Adding and Subtracting Decimal Numbers, Part 1, Activity Adding and Subtracting Decimals

  4. Lesson 4

    Lesson 44: Multiplying Two-Digit Numbers, Part 1

  5. Lesson 5

    Lesson 45: Parentheses and the Associative Property, Naming Lines and Segments

  6. Lesson 6

    Lesson 46: Relating Multiplication and Division, Part 1, Activity Using a Multiplication Table to Divide

  7. Lesson 7

    Lesson 47: Relating Multiplication and Division, Part 2

  8. Lesson 8

    Lesson 48: Multiplying Two-Digit Numbers, Part 2

  9. Lesson 9Current

    Lesson 49: Word Problems About Equal Groups, Part 1

  10. Lesson 10

    Lesson 50: Adding and Subtracting Decimal Numbers, Part 2, Activity Adding and Subtracting Decimals

  11. Lesson 11

    Investigation 5: Percents, Activity Percent