We includedHMH Into Math Grade 7 Answer KeyPDFModule 7 Solve Problems Using Expressions and Equations to make students experts in learning maths.
Model with Expressions, Equations, and Inequalities.
Archaeologist
An archaeologist collects and analyzes data about past civilizations in order to learn about human life and cultures. Sarah Parcak is a space archaeologist who uses satellite images to identify ancient sites. Her wish is “for us to discover the millions of unknown archaeological sites acrossthe globe” and to “find and protect the world’s heritage”
STEM Task:
Volunteers often help archaeologists at excavation sites. At one excavation site, there can be no more than 8 volunteers for every field guide. If a total of 50 people are working at the site, what is the greatest possible number of volunteers? Explain your thinking.
Learning Mindset Resilience Identifies Obstacles
Resilience is the acuity to recover from a setoack. Everyone encounters challenges or obstacles at some point. Resilience allows you to overcome them and continue moving forward. Next time you run into some difficulty completing a task or reaching a goal, try following these steps.
- Identify the problem or obstacle. What is holding you back from moving ahead?
- Develop a list of ideas for overcoming the obstacle. Visualize strategies you can apply to the problem and ways you can break the problem down into smaller steps. If you’re still not sure what to do, think about where you can look for help.
- Choose an idea from your list and give it a try.
- Did you successfully overcome the obstacle? If not, try a different approach. And if that one does not work, try another one. Ask for help if you need it, but don’t give up.
Reflect
Question 1.
What challenges or problems did you encounter as you worked on the STEM Task? How did you address them?
Answer:
Question 2.
Have you given up in the past when you encountered an obstacle or difficulty? What can you do to improve your resilience?
Answer:
BALANCE Mystery
Jada has set up several balance mysteries for her friends. She has made stacks of 1, 2, or 3 blocks and hidden some blocks in cups. She is challenging her friends to figure out how many blocks are in each cup. If more than one cup is on a balance, there is an equal number of blocks in each cup. The cups are light enough that their mass does not impact the balance.
Write and solve an equation for each balance.
A.
Answer:
B.
Answer:
C.
Answer:
D.
Answer:
Turn and Talk
Darius says, “Balances A and D are both solved with the same operation.” What pattern did Darius notice? Explain.
Answer:
Are You Ready?
Complete these problems to review prior concepts and skills you will need for this module.
Solve One-Step Equations
Solve the equation.
Question 1.
c + 27 = 68 _________
Answer:
41
Explanation:
Let us solve the given equations
c + 27 = 68
c = 68 -27
c = 41
Question 2.
t – 1.5 = 7.9 __________
Answer:
5.6
Explanation:
Let us solve the given equation
t – 1.5 = 7.9
t = 7.9 – 1.5
t = 5.6
Question 3.
\(\frac{a}{3}\) = 21 __________
Answer:
a = 63
Explanation:
Let us solve the given equation
\(\frac{a}{3}\) = 21
a = 21 × 3
a = 63
Question 4.
r + \(\frac{3}{4}\) = \(\frac{7}{8}\) _____________
Answer:
r = \(\frac{1}{8}\)
Explanation:
Let us solve the given equation.
r + \(\frac{3}{4}\) = \(\frac{7}{8}\)
r = \(\frac{7}{8}\) – \(\frac{3}{4}\)
r = \(\frac{7}{8}\) – \(\frac{6}{4}\)
r = \(\frac{1}{8}\)
Question 5.
4.2x = 25.2 _____________
Answer:
6
Explanation:
Let us solve the given equation
4.2x = 25.2
x = \(\frac{25.2}{4.2}\)
x = 6
Question 6.
15b = 75 ___________
Answer:
5
Explanations:
Let us solve the given equation
15b = 75
b = \(\frac{75}{15}\)
b = 5
Question 7.
All tickets to a play have the same cost. A group bought 6 tickets and paid a total of $99.
A. Write a multiplication equation that can be used to determine cost c in dollars for each ticket.
Answer:
99 × c = 6
c = \(\frac{99}{6}\)
Explanation:
Let us assume the cost of each ticket as c.
A group bought 6 tickets
Now calculate the cost of each ticket.
99 × c = 6
c = \(\frac{99}{6}\)
B. Solve the equation and tell what the solution represents.
Answer:
c = 16.5
Explanation:
99 × c = 6
c = \(\frac{99}{6}\)
c = 16.5
Apply Properties of Operations
Use the given property to write an equivalent expression.
Question 8.
Commutative Property of Addition
4(3x + 10) ________________
Answer:
2(6x + 20)
Explanation:
An equivalent expression for the given question is 2(6x + 20)
Question 9.
Associative Property of Addition
(16 + 4n) + 2 n _______________
Answer:
16 + ( 4n + 2n)
Explanation:
An equivalent expression for the given question is 16 + ( 4n + 2n).
(16 + 4n) + 2 n = 16 + ( 4n + 2n)
Question 10.
Distributive Property
2 (a – b) _______________
Answer:
2a – 2b
Explanation:
An equivalent expression for the given question is 2a – 2b.
2 (a – b) = 2a – 2b
Question 11.
Associative Property of Multiplication
\(\frac{1}{4}\) (12P) _________________
Answer:
\(\frac{1}{(2 × 2)}\) (3×4P)
Explanation:
The Associative Property of Multiplication for the given expression is \(\frac{1}{(2 × 2)}\) (3×4P)
