We included **HMH Into Math Grade 6 Answer Key PDF** **Module 8 Numerical and Algebraic Expression **to make students experts in learning maths.

## HMH Into Math Grade 6 Module 8 Answer Key Numerical and Algebraic Expression

**Visual Artist**

Edna Andrade was an American artist and educator. She began her teaching career as an elementary school art teacher in Virginia. She later taught at the University of the Arts in Philadelphia and Tulane University in New Orleans. As an artist, Andrade was an early pioneer in the op art movement. Op art features geometric patterns that create optical illusions such as a sense of motion, flashing, or vibration.

**Stem Task:**

Visual artists may mix paints to match a colour they used before or to create new colours. Matthew is an artist. He mixes 4 parts of blue paint with 2 parts of yellow paint to make a pint of green paint. After he uses all of the green paint, he wants to make 3 more pints of the same shade. How much blue and yellow paint should he mix? Explain.

Answer:

The artist mixed 4 parts blue and 2 parts yellow and then he makes a pint of green paint. Later he needs same shade of 3 more pints then he mixed 4 x 3 = 12 parts of blue and 2 x 3 = 6 parts of yellow.

**Learning Mindset**

**Resiliance Monitors Emotions**

Artists may be frustrated as they strive to achieve a particular result, or sad when their work receives negative criticism. What emotions do you experience when you are learning something new? Do you feel excited, or do you feel discouraged and want to give up? It’s normal to experience negative emotions at times, but learning to recognize and address these feelings will help prevent them from being obstacles to learning. As you work, monitor your thoughts and feelings by asking yourself these questions.

- How am I feeling about this task? Am I frustrated, bored, or tired? Am I worried or embarrassed about how others perceive my work?
- Is there a fixed-mindset voice in my head that is contributing to my negative feelings? If so, what is that voice telling me? What is triggering that voice?
- How can I activate my growth-mindset voice to counter messages from the fixed-mindset voice?

Remember, feelings often shift and change. If you find yourself struggling with negative emotions, take a few deep breaths. You may also want to take a short break or talk to someone about your feelings.

**Reflect**

Question.

As you worked on the STEM Task, how did you feel about your learning?

Answer:

Question.

Did any part of the STEM Task trigger a fixed-mindset voice in your head? If so, what part? How did you use self-talk to activate a growth-mindset voice?

Answer:

**Guess the Number**

Follow the directions to see if the number game is true for any number.

Ethan discovered a number game. See if it works for any number.

A. Try Ethan’s number game.

Think of a number. ___________

Add 5. ___________

Double the result. ___________

Subtract 4. ___________

Divide by 2. ___________

Subtract the original number. ___________

Answer:

We go by step-by-step:

Step 1: The number is 5

Step 2: and then add 5 that means we need to add 5 to the 5

Thus, 5 + 5 = 10

Step 3: Double the number which we got which is 10

10 + 10 = 20

Step 4: Now subtract it from 4; 20 – 4 = 16

Step 5: the result will be divided by 2

16/2 = 8

Step 6: Now subtract the original number which means the above-given number.

8 – 5 = 3

B. How does your final number compare with Ethan’s prediction?

Answer:

according to the instructions we solved the problem.

And finally when we subtract the original number and the result we got.

We got 3 and Ethan’s prediction is also 3.

C. Use your original number to write a single numerical expression that represents the steps of the game.

Answer:

The order of operations gives us a consistent sequence for computation. Without the order of operations, we could come up with different answers to the same computation problem.

The numerical expression will be:

(5 + 5)+10 – 4 ÷ 2 – 5

(5 + 5) = 10

Add and subtract (left to right)

10 +10= 20

20 – 4 = 16/2 =8

8-5 =3

**Turn and Talk**

Question 1.

How does your expression show the order in which the operations should be performed?

Answer:

It is one of the ways to remember the order of the operations is PEMDAS, where each letter stands in mathematical order.

Order of operations math is given below in the expanded form:

– P: P stands for parenthesis. First solve the calculation or equation which is present in the parentheses or brackets like small brackets( ), curly brackets{ } or big brackets. Priority is given to brackets first.

– E: E stands for exponential. These expressions should be calculated first before the operations of multiplication, division, addition and subtraction. Usually, they are expressed in power or roots, like 2² or the square root of 4

– MD: MD stands for multiplication and division. Then perform multiplication or division from left to right order, whichever comes first in the equation.

-AS: AS stands for Addition and Subtraction. At last, perform addition or subtraction whichever comes first moving from left to right order.

We have to follow the rules of the order of operations to solve expressions so that everyone arrives at the same answer.

Question 2.

How could you change your expression so that it would model the game no matter which number you start with?

Answer:

The order of operations gives us a consistent sequence for computation. Without the order of operations, we could come up with different answers to the same computation problem.

When we have to evaluate arithmetic expressions, the order of operations that should be followed are:

– First, simplify all operations inside parentheses.

– Then perform all multiplications and divisions, moving from left to right.

– After that perform all additions and subtractions, moving from left to right.

If the question contains a fraction bar, then we have to perform all calculations above and below the fraction bar before dividing the numerator by the denominator.

**Are You Ready?**

Complete these problems to review prior concepts and skills you will need for this module.

**Write and Interpret Numerical Expressions**

**Write the expression.**

Question 1.

3 times the sum of 4 and 9: _____________

Answer:

First of all the sum of 4 and 9 is 13

This can be written in algebraic expression:

The expression is 3 ( 4 + 9 )

= 3 ( 13)

= 39

Therefore, the answer for the algebraic expression is 39.

Question 2.

Divide 12 by 4 and add 5: _____________

Answer:

First divide the given numbers.

12/4 = 3

Now we have to add 5 to the result we got after division operation performed.

3 + 5 = 8

Therefore, the answer is 8

Question 3.

Subtract 6 from 13, then multiply by 2: _____________

Answer:

In this problem, the expression will be:

= (13 – 6) x 2

= (7) x 2

= 14

Therefore, the answer is 14 for the above expression.

Question 4.

The quantity 12 times 5 divided by 7: _____________

Answer:

The expression for this problem is

= 12(5)/7

= 60/7

= 8.57

Therefore, the answer for the above expression is 8.57

Question 5.

The quantity 32 minus 16 multiplied by 9: _____________

Answer:

The expression for this problem is:

= (32 – 16) x 9

= (16) x 9

= 144

Therefore, the answer is 144.

**Write a statement to represent each expression.**

Question 6.

3 × 2 + 5: _____________

Answer:

Follow the PEMDAS order of operations:

Multiply and divide (left to right):

3 x 2 = 6

Add and subtract from left to right:

6 + 5 = 11

Therefore, the answer for the above-given expression is 11

Question 7.

6(5 + 7): _____________

Answer:

Follow the PEMDAS order of operations:

First, calculate within the parentheses:

= (5 + 7)

= 12.

Multiply and divide (left to right):

= 6. 12

= 72

therefore, the answer for the above-given expression is 72

Question 8.

24 – 8 ÷ 4: _____________

Answer:

Follow the PEMDAS order of operations:

Multiply and divide (left to right):

= 8 ÷ 4

= 2

Add and subtract (left to right):

= 24 – 2

= 22

Therefore, the answer for the above-given expression is 22.

Question 9.

(9 + 5) ÷ 7: _____________

Answer:

Follow the PEMDAS order of operations:

First, calculate within the parentheses:

= (9 + 5)

= 14

Multiply and divide (left to right):

= 14 ÷ 7

= 2

Therefore, the answer for the above-given expression is 2

**Evaluate Simple Numerical Expressions**

**Find the value of each expression.**

Question 10.

4 × (3 + 5) = _____________

Answer:

Follow the PEMDAS order of operations:

First, calculate within the parentheses:

= (3 + 5)

= 8

Multiply and divide (left to right):

= 4 x 8

= 32

Therefore, the answer for the above-given expression is 32.

Question 11.

7 + (3 × 2) = _____________

Answer:

Follow the PEMDAS order of operations:

First, calculate within the parentheses:

= (3 x 2)

= 6

Add and subtract (left to right):

= 7 + 6

= 13

Therefore, the answer for the above-given expression is 13.

Question 12.

(45 ÷ 9) × 2 = _____________

Answer:

Follow the PEMDAS order of operations:

First, calculate within the parentheses:

= (45 ÷ 9)

= 5

Multiply and divide (left to right):

= 5 x 2

= 10

Therefore, the answer for the above-given expression is 10.

Question 13.

(3 + 9) ÷ 3 = _____________

Answer:

Follow the PEMDAS order of operations:

First, calculate within the parentheses:

= (3 + 9)

= 12

Divide and multiply (left to right):

= 12 ÷ 3

= 4

Therefore, the answer for the above-given expression is 4

Question 14.

(12 + 6) ÷ 2 + 4 = _____________

Answer:

Follow the PEMDAS order of operations:

First, calculate within the parentheses:

= (12 + 6)

= 18

Multiply and divide (left to right):

= 18 ÷ 2

= 9

Add and subtract (left to right):

= 9 + 4

= 13

Therefore, the answer for the above-given expression is 13.

Question 15.

(20 – 11) × 5 + 1 = _____________

Answer:

Follow the PEMDAS order of operations:

First, calculate within the parentheses:

= (20 – 11)

= 9

Multiply and divide (left to right):

= 9 x 5

= 45

Add and subtract(left to right)

= 45 + 1

= 46

Therefore, the answer for the above-given expression is 46.