We included HMH Into Math Grade 4 Answer Key PDF Module 10 Lesson 1 Investigate Factors to make students experts in learning maths.
HMH Into Math Grade 4 Module 10 Lesson 1 Answer Key Investigate Factors
I Can use visual models and equations to find all the factor pairs of a number.
Spark Your Learning
Fiona has these pictures of her favorite flowers. She wants to hang all of them in equal rows on a wall.
Show how many different ways Fiona can arrange the pictures.
Answer:
Explanation:
Number of flowers she has = 12.
Multiples of 12:
1 × 12 = 12.
2 × 6 = 12.
3 × 4 = 12.
Turn and Talk How are all of the arrangements alike? How are they different?
Answer:
They are different in their patterns of arrangement. They are alike with the total number of flowers.
Explanation:
They are alike with the total number of flowers.
They are different in their patterns of arrangement.
Build Understanding
1. Ichiro has 18 flowers to plant. How many different ways can he plant all the flowers in equal rows?
Use 18 square tiles to make as many different arrays as you can. Show all the arrays.
A. Write a multiplication equation on the grid to model each array.
B. How can you use the equations to identify all the factors of 18?
C. What are all the factors of 18?
D. Ichiro can plant 18 flowers ____ in different ways.
Answer:
Factors of 18: 1,2,3,9,18.
Ichiro can plant 18 flowers 6 in different ways.
Explanation:
Number of flowers to plant Ichiro has =18.
Multiples of 18:
1 × 18 = 18.
18 × 1 = 18.
2 × 9 = 18.
9 × 2 = 18.
3 × 6 = 18.
6 × 3 = 18.
Connect to Vocabulary
A factor is a number that is multiplied by another number to find a product.
factor × factor — product.
Turn and Talk How is the number of factors related to the number of different ways?
Answer:
The number of factors related to the number of different ways as they divide the total number of flowers.
Explanation:
The number of factors related to the number of different ways because they are divide the number of flowers.
2. A rectangular garden has an area of 8 square meters.
Show all the area models you can make for the number 8.
A. Write a multiplication equation for each area model.
B. How can you use the equations to identify all the factor pairs for 8?
C. What are all the factor pairs for 8?
Answer:
All the factor pairs for 8:
1 × 8 = 8.
8 × 1 = 8.
2 × 4 = 8.
4 × 2 = 8.
Explanation:
Area of the rectangular garden = 8 square meters.
Multiples of 8:
1 × 8 = 8.
8 × 1 = 8.
2 × 4 = 8.
4 × 2 = 8.
Factors of 8: 1,2, 4,8.
Turn and Talk How does making arrays or area models help you find all the factor pairs for a number?
Answer:
Making arrays or area models help you find all the factor pairs for a number as when using arrays in multiplication, the symbol × can also be read “rows of”.
Explanation:
An array is when objects or symbols are organized into rows and columns. Another way you can make an array is to color in a grid. Th is special type of array is called an area model. An area model is made of shaded squares organized into rows and columns.
Check Understanding Math Board
Question 1.
Blake has 20 of these square mosaics. What are all the different ways he can place the mosaics in equal rows?
- Draw arrays or area models on grid paper to show all the ways. Then describe the visual models.
_______________________ - List all the factor pairs for 20. ___________
Answer:
All the different ways he can place the mosaics in equal rows = 6.Explanation:
Number of square mosaics Blake has = 20.
The factor pairs for 20:
1 × 20 = 20.
2 × 10 = 20.
4 × 5 = 20.
5 × 4 = 20.
10 × 2 = 20.
20 × 1 = 20.
All the different ways he can place the mosaics in equal rows = 6.
On Your Own
Question 2.
Use Tools A gardener has 30 potted plants to place in equal rows in a plaza. Use square tiles to show all of the arrays for 30.
- What are all the factor pairs for 30?
______________________ - What are all the factors of 30?
______________________ - How many different ways can the gardener arrange the plants in equal rows? ____
Answer:
8 different ways the gardener can arrange the plants in equal rows.Explanation:
Number of potted plants to place in equal rows in a plaza gardener has = 30.
The factor pairs for 30:
1 × 30 = 30.
30 × 1 = 30.
2 × 15 = 30.
15 × 2 = 30.
3 × 10 = 30.
10 × 3 = 30.
5 × 6 = 30.
6 × 5 = 30.
Question 3.
Draw area models on the grid to show all the factors of 9.
- Write all the factor pairs for 9. ____
- List all the factors of 9. _____
Answer:
Explanation:
Factors pairs of 9:
1 × 9 = 9.
3 × 3 = 9.
All the factors of 9:
1,3,9.
Question 4.
Critique Reasoning Devin draws arrays to show all the ways to put 24 stamps into equal rows. Then she writes these equations to model the arrays. Since she can write 8 equations,
Devin says that 24 has 8 factor pairs. Do you agree? Why or why not?
Answer:
Yes, Devin says that 24 has 8 factor pairs.
Explanation:
Factors pairs of 24:
1 × 24 = 24.
24 × 1 = 24.
2× 12 = 24.
12 × 2 = 24.
3 × 8 = 24.
8 × 3 = 24.
4 × 6 = 24.
6 × 4 = 24.
All the factors of 9:
1,2,3,4,6,8,12,24.
I’m in a Learning Mindset!
What strategies for finding factor pairs can I share with my classmates?
________________________________
Answer:
Strategy for finding factor pairs I share with my classmates is that use division method and mutliplication method.
Explanation:
I tell my students that while multiples are many, factors are few! With a little concentration and a bit of practice, they can find those few factors of any number. Multiples are many, factors are few.