Into Math Grade 4 Module 10 Answer Key Algebraic Thinking: Number Theory

We included HMH Into Math Grade 4 Answer Key PDF Module 10 Algebraic Thinking: Number Theory to make students experts in learning maths.

HMH Into Math Grade 4 Module 10 Answer Key Algebraic Thinking: Number Theory

HMH Into Math Grade 4 Module 10 Answer Key Algebraic Thinking Number Theory 1
Engineer
Engineers are problem solvers. They apply their knowledge of science and math to analyze, test, and construct solutions. In fact, the word engineer comes from the Latin words for “devise” and “cleverness.”

Most engineers focus on solving problems in a particular area. Civil engineers, for example, design the infrastructure of places. They figure out how to build roads, bridges, dams, and buildings. Mechanical engineers deal with machines. They might design robots or entire factories. Chemical engineers come up with all kinds of useful products, such as medicines, processed foods, paper, and fuels.

Stem Task:
Build a three- or four- story tower using only index cards. Imagine your building will be in
an earthquake zone, so it must be as sturdy as possible. You may fold the index cards but do not cut them. When you are finished, shake your desk a little to see if your tower can withstand an ‘earthquake.” Were you successful? Talk about it with your classmates. Did their buildings survive? Determine what features resulted in the sturdiest buildings.

Learning Mindset
Perseverance Collects and Tries
Multiple Strategies
HMH Into Math Grade 4 Module 10 Answer Key Algebraic Thinking Number Theory 2
There is usually more than one way to solve a problem. Different problems require different strategies. For the STEM task, you may have tried different strategies by experimenting with what worked and what did not work. When you compare fractions, being flexible and trying different strategies may keep you from getting stuck. For example, a comparison that is difficult to make using the numerators or denominators of fractions may be simpler to make using visual models.

Reflect

Question
What strategies did you try for the STEM task? Which strategy was most successful?
Answer:
For the STEM task, you may have tried different strategies by experimenting with what worked and what did not work. Build a three- or four- story tower using only index cards strategy was most successful.

Explanation:
STEM initiatives consultant, asserts that “Developing these skills is a natural outcome of a STEM curriculum and perhaps the best reason to engage students in these experiences.”

Question
What did you learn from other students who shared their strategies? What would you change if you were to do the activity again?
Answer:
For the STEM task, you may have tried different strategies by experimenting with what worked and what did not work. When you compare fractions, being flexible and trying different strategies may keep you from getting stuck. For example, a comparison that is difficult to make using the numerators or denominators of fractions may be simpler to make using visual models.

Explanation:
For the STEM task, you may have tried different strategies by experimenting with what worked and what did not work. When you compare fractions, being flexible and trying different strategies may keep you from getting stuck. For example, a comparison that is difficult to make using the numerators or denominators of fractions may be simpler to make using visual models.

Where does each factor go?

  • Write the numbers from 1 to 10 in the boxes. Use each as a factor one time to make all of the equations true.
    HMH Into Math Grade 4 Module 10 Answer Key Algebraic Thinking Number Theory 3
    Answer:
    HMH-Into-Math-Grade-4-Module-10-Answer-Key-Algebraic-Thinking-Number-Theory-Where does each factor goExplanation:
    4 × 10 = 40.
    6 × 5 = 30.
    3 × 7 = 21.
    2 × 9 = 18.
    1 × 8 = 8.

Turn and Talk

  • How is the product 21 different from the other products?
    Answer:
    The product 21 different from the other products as odd number multiplied by odd number gives the product odd number.Explanation:
    Multiples of 21:
    1 × 21 = 21.
    3 × 7 = 21.
    Product of 21: odd × odd = odd.
  • Which products have a factor of 5? a factor of 3? a factor of 2? a factor of 4?
    Answer:
  • Products have a factor of 5: 25,10,105 …
    Products have a factor of 3: 6,84,114  …
    Products have a factor of 2: 6,20,100 …
    Products have a factor of 4: 16,88,200 …Explanation:
    Products have a factor of 5: 25,10,105 …
    Products have a factor of 3: 6,84,114  …
    Products have a factor of 2: 6,20,100 …
    Products have a factor of 4: 16,88,200 …

Are You Ready?
complete these problems to review prior concepts and skills you will need for this module.
Count by Fives and Tens
Question 1.
Start at 45 and count by fives. Write the unknown numbers.
HMH Into Math Grade 4 Module 10 Answer Key Algebraic Thinking Number Theory 4
45, ___, ___ 60
Answer:
The unknown numbers: 45,50,55,60.
HMH-Into-Math-Grade-4-Module-10-Answer-Key-Algebraic-Thinking-Number-Theory-Are You Ready

Explanation:
45 + count by fives = 45 + 5 = 50
50 + count by fives = 50 + 5 = 55.
55 + count by fives = 55 + 5 = 60.

Arrays
Use the array to find the product.
Question 2.
HMH Into Math Grade 4 Module 10 Answer Key Algebraic Thinking Number Theory 5
Answer:
HMH-Into-Math-Grade-4-Module-10-Answer-Key-Algebraic-Thinking-Number-Theory-Arrays-2

Explanation:
4 rows of 3
= 4 × 3
= 12.

Question 3.
HMH Into Math Grade 4 Module 10 Answer Key Algebraic Thinking Number Theory 6
Answer:
HMH-Into-Math-Grade-4-Module-10-Answer-Key-Algebraic-Thinking-Number-Theory-Arrays-3

Explanation:
5 rows of 2
= 5 × 2
= 10.

Unknown Factors
Find the unknown factor.

Question 4.
____ × 7 = 42
Answer:
6 × 7 = 42.

Explanation:
____ × 7 = 42
=> ?? = 42 ÷ 7
=> ?? = 6.

Question 5.
8 × ___ = 40
Answer:
8 × 5 = 40.

Explanation:
8 × ___ = 40
=> ?? = 40 ÷ 8
=> ?? = 5.

Question 6.
5 × ___ = 45
Answer:
5 × 9 = 45.

Explanation:
5 × ___ = 45.
=> ?? = 45 ÷ 5
=> ?? = 9.

Question 7.
___ × 6 = 60
Answer:
10 × 6 = 60.

Explanation:
___ × 6 = 60
=> ?? = 60 ÷ 6
=> ?? = 10.

Question 8.
7 × ___ = 49
Answer:
7 × 7 = 49.

Explanation:
7 × ___ = 49.
=> ?? = 49 ÷ 7
=> ?? = 7.

Question 9.
___ × 8 = 72
Answer:
___ × 8 = 72.

Explanation:
___ × 8 = 72.
=> ?? = 72 ÷ 8
=> ?? = 9.

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