Refer to our Texas Go Math Grade 5 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 5 Lesson 8.1 Answer Key Equations.

Investigate

Materials: a pan balance, connecting cubes

A pan balance weighs objects whose weights are unknown by balancing them with objects whose weights are known. When the two pans are balanced, the objects have the same weight.

You can use a pan balance to model and solve an equation. An equation is a mathematical sentence that shows that two amounts are equal.

A. Use a pan balance to model and solve the equation 11 = 8 + x. Place 11 connecting cubes in the left pan of a pan balance. Place 8 connecting cubes in the right pan. Are the pans balanced? Explain.
In the left pan there are 11 connecting cubes and in the right pan there are 8 connecting cubes. The pans is not balanced because more cubes are there in left pan compared to right pan.

B. Use your pan balance to find the value of x in the equation. Add cubes to the right pan, one at a time, until the pans are balanced. What is the value of x?
11 = 8 + x
11 = 8 + 3
The value of X is 3.
Explanation:
In the left pan there are 11 connecting cubes and in the right pan there are 8 connecting cubes. Add 1 cube to the right pan the pans are not balanced. Now the right pan contains 9 connecting cubes. Add 1 more cube to the right pan again the pans are not balanced. Now the right pan contains 10 connecting cubes. Add 1 more cube to the right pan the pans are balanced. The right pan contains 11 connecting cubes. So, the value of x is 3.

Complete the picture of the pan balance below by drawing blocks to show how you balanced the equation.

11 = 8 + x
11 = 8 + 3
11 = 11
The pans are balanced.

Example

Use the pan balance to solve 4 + 2 × 3 = 7 + y.
STEP 1: Use the order of operations to simplify the equation.
4 + 2 × 3 = 7 + y Multiply first.
4 + 6 = 7 + y Then add.

STEP 2: Model the equation.

STEP 3: Solve the equation. Complete the pan balance picture by drawing squares to balance the equation.

The pans are balanced.
Explanation:
The equation is 4 + 2 × 3 = 7 + y. In first step we have to multiply the 2 with 3. Now the equation is 4 + 6 = 7 + y. Next we have to add 4 with 6 the sum is 10. The equation is 10 = 7 + y. In the above image we can observe 10 squares in left pan and 7 + y squares in right pan. To balance the pans we have to add three squares to the right pan. Add 7 squares with 3 squares the sum is 10. Now both pans have equal squares. So both pans are balanced.

Mathematical Processes

How can you tell that your solution to an equation is correct?
10 = 7 + y
10 = 7 + 3
10 = 10
The solution to the equation is correct because both pans are balanced.

Share and Show

Use the pan balance to model and solve the equation.

Question 1.
1 + b = 3 + 8

b = ___________

1 + b = 3 + 8
1 + b = 11
1 + 10 = 11
b = 10
The pans are balanced by adding 10 squares to the left pan.
Explanation:
The equation is 1 + b = 3 + 8. First we have to add squares in the right pan. Add 3 squares with 8 squares the sum is 11 squares. In right pan there are 11 squares. In right pan there are 1 + b squares. We have to calculate the b value. Add 1 with 10 the sum is 11. The value of b is 10. In left pan there are 11 squares. Now the pans are balanced.

Question 2.
7 + 6 = B + k

____________ = k

7 + 6 = B + K
13 = B + K
13 = 8 + K
13 = 8 + 5
The pans are balanced by adding 5 squares to the right pan.
Explanation:
The equation is 7 + 6 = B + k. First add 7 squares with 6 squares in the left pan. The total squares in right pan are 13. In the above image we can observe 8 + K squares in right pan. So B value is 8. We have to find out the K value. Add 5 squares to the 8 squares the sum is 13 squares. The value of K is 5. In left pan there are 13 squares. Now the pans are balanced.

Which value of m, 4, 8, or 10, makes the equation true?

Question 3.
5 + 4 + 4 = 9 + m
_________ = m
5 + 4 + 4 = 9 + m
13 = 9 + m
13 = 9 + 4
m = 4
The value m = 4 makes the equation true.
Explanation:
The equation is 5 + 4 + 4 = 9 + m. We can make the equation true by calculating m value. First add 5 with 4 and 4 the sum is 13. The equation is 13 = 9 + m. Add 4 to the 9 the sum is 13. So m is equal to 4. The value m = 4 makes the equation true.

Question 4.
3 + m + 2 = 7 + 4 + 2
m = _________
3 + m + 2 = 7 + 4 + 2
5 + m = 13
5 + 8 = 13
m = 8
The value m= 8 makes the equation true.
Explanation:
The equation is 3 + m + 2 = 7 + 4 + 2. We can make the equation true by calculating m value. First add right side values. Add 7 with 4 and 2 the sum is 13. The equation is 5 + m = 13. Add 8 to the 5 the sum is 13. So m is equal to 8. The value m = 8 makes the equation true.

Question 5.
H.O.T. Explain why there is only one solution to the equation 8 = w + 5.
8 = w + 5
8 = 3 + 5
w = 3
The value w = 3 makes the equation true.
Explanation:
There is only one solution to the above equation because we have to calculate only w value.

Problem Solving

When two pans are balanced, the objects on the pans have the same weight. Use the pan balances to solve 6-8.

Question 6.
H.O.T. Multi-Step Zane found the weight of 6 blocks on the first pan balance. He wants to find the weight of the green cylinder on the second pan balance. How can Zane find the weight of the green cylinder? What is the weight of the green cylinder? Explain.

1 block is equal to 5 grams.
4 blocks is equal to 20 grams.
The weight of the green cylinder is 20 grams.
Explanation:
Zane found the weight of 6 blocks on the first pan balance. The weight of 6 blocks is 30 grams as we can observe in the above image. He wants to find the weight of the green cylinder on the second pan balance. Here 1 block is equal to 5 grams there are total 4 blocks as we can observe in the below pan balance. Multiply 4 blocks with 5 grams the product is 20 grams. So, the weight of the green cylinder is 20 grams.

Question 7.
Write Math what If a pyramid and a block together have the same weight as 2 cylinders? How could Zane use the information from Problem 6 to find the weight of 1 pyramid? Explain.

Question 8.
What if the weight on the right side of the first balance weighed the same as 3 blocks? What is the weight of one block? Of one green cylinder?

Question 9.
H.O.T. Multi-Step Lucia placed 12 spheres on one side of a pan balance and 10 triangular prisms on the other side. Each side weighs 60 grams. What is the weight of one sphere? One triangular prism?
Each side weighs 60 grams.
12 spheres on one side of a pan balance.
12 spheres x X = 60 grams
12 spheres x 5 grams = 60 grams
1 sphere = 5 grams
10 triangular prisms on the other side.
10 triangular prisms x Y = 60 grams
10 triangular prisms x 6 grams = 60 grams
1 triangular prism = 6 grams
Explanation:
Lucia placed 12 spheres on one side of a pan balance and 10 triangular prisms on the other side. Each side weighs 60 grams. To calculate the weight of one sphere we have to divide 60 grams by 12 spheres the result is 5 grams. The weight of one sphere is equal to 5 grams. To calculate the weight of one triangular prism we have to divide 60 grams by 10 triangular prism the result is 6 grams. The weight of one triangular prism is equal to 6 grams.

Question 10.
Reasoning On the right side of a balance, there are two birds that each weigh 12 ounces. On the left side, there is a bird that weighs 14 ounces, and a bird with an unknown weight. If both sides of the balance have the same weight, how much does the unknown bird weigh?
(A) 5 oz
(B) 48 oz
(C) 10 oz
(D) 12 oz

On the right side of a balance, there are two birds that each weigh 12 ounces.
12 ounces + 12 ounces = 24 ounces
On right side the weight of two birds is 24 ounces.
On the left side, there is a bird that weighs 14 ounces, and a bird with an unknown weight.
14 ounces + X = 24 ounces
14 ounces + 10 ounces = 24 ounces
The bird with an unknown weight is 10 ounces.
So option C is correct.
Explanation:
On the right side of a balance, there are two birds that each weigh 12 ounces. Add 12 ounces with 12 ounces the sum is 24 ounces. On right side the weight of two birds is 24 ounces. On the left side, there is a bird that weighs 14 ounces, and a bird with an unknown weight. Both sides of the balance have the same weight. Add 14 ounces with 10 ounces the sum is 24 ounces. The bird with an unknown weight is 10 ounces. So, option C is correct.

Question 11.
Use Tools How would you balance the pan balance?

(A) Take away 8 cubes from the left side of the balance.
(B) Add 11 more cubes to the right side of the balance.
(C) Add 27 more cubes to the right side of the balance.

So, option B is correct.
Explanation:
In the above pans balance we can observe that cubes are in both left pan and right pan. We can see 19 cubes in the left pan of a pan balance. We can see 8 cubes in the right pan of a pan balance. To balance the pan we need to add 11 more cubes to the right side of the balance. So option B is correct.

Question 12.
Multi-Step Kevin placed 10 cubes on the right side of a pan balance. He placed 4 cubes on the left side. Then he doubled the number of cubes on the right side. Find the number of cubes that he must add to the left side to balance the pans.
(A) 14
(B) 6
(C) 16
(D) 24

on right side
10 cubes + 10 cubes = 20 cubes
On left side
4 cubes + X = 20 cubes
4 cubes + 16 cubes = 20 cubes
So, option C is correct.
Explanation:
Kevin placed 10 cubes on the right side of a pan balance. He placed 4 cubes on the left side. Then he doubled the number of cubes on the right side. Add 10 cubes with 10 cubes the sum is 20 cubes. We have to calculate the number of cubes that he must add to the left side to balance the pans. We have add 16 cubes to balance the pans. So, option C is correct.

Texas Test Prep

Question 13.
What is the weight of 1 cube?

(A) 28 ounces
(B) 10 ounces
(C) 14 ounces
(D) 7 ounces

The weight one sphere is 7 ounces
The weight one cube
7 ounces x 4 spheres = 28 ounces
So, option A is correct.
Explanation:
There are pans balance in the above images. In right side image we can see that one sphere is equal to 7 ounces. In left side image there are four spheres in left side pan balance and 1 cube in right side pan balance. Multiply 4 spheres with 7 ounces the product is 28 ounces. One cube is equal to 28 ounces. So, option A is correct.

### Texas Go Math Grade 5 Lesson 8.1 Homework and Practice Answer Key

Use the pan balance to model and solve the equation.

Question 1.
8 + 7 = 5 + x

___________ = x
8 + 7 = 5 + x
15 = 5 + x
15 = 5 + 10
The value of x is 10.
Explanation:
The equation is 8 + 7 = 5 + x. In the above image we can observe left side pan and right side pan. In left side pan 15 cubes. In right side pan 5 + x cubes. We have to calculate the x value. Add 10 cubes to the right side pan to balance the pans. The value of x is 10.

Question 2.
2 + z = 4 + 10

z = ___________
2 + z = 4 + 10
2 + z = 14
2 + 12 = 14
The value of z is 12.
Explanation:
The equation is 2 + z = 4 + 10. In the above image we can observe left side pan and right side pan. In left side pan 2 + z cubes. In right side pan 14 cubes. We have to calculate the z value. Add 12 cubes to the left side pan to balance the pans. The value of x is 12.

Which value of p, 4, 6, or 8, makes the equation true?

Question 3.
6 + 4 + 3 = 7 + p
_________ = p
6 + 4 + 3 = 7 + p
13 = 7 + p
13 = 7 + 6
The value p = 6 makes the equation true.
Explanation:
The equation is 6 + 4 + 3 = 7 + p. We can make the equation true by calculating p value. First add left side values. Add 6 with 4 and 3 the sum is 13. The equation is 13 = 7 + 6. Add 6 to the 7 the sum is 13. So p is equal to 6. The value p = 6 makes the equation true.

Question 4.
5 + p + 7 = 5 + 6 + 5
p = __________
5 + p + 7 = 5 + 6 + 5
12 + p = 16
12 + 4 = 16
The value p = 4 makes the equation true.
Explanation:
The equation is 5 + p + 7 = 5 + 6 + 5. We can make the equation true by calculating p value. First add right side values. Add 5 with 6 and 5 the sum is 16. The equation is 12 + p = 16. Add 4 to the 12 the sum is 16. So p is equal to 4. The value p = 4 makes the equation true.

Which value of g, 8, 9, or 10, makes the equation true?

Question 5.
3 × 2 + 4 = 2 + g
_________ = g
3 × 2 + 4 = 2 + g
6 + 4 = 2 + g
10 = 2 + 8
The value g = 8 makes the equation true.
Explanation:
The equation is 3 x 2 + 4 = 2 + g. We can make the equation true by calculating g value. First add left side values. First perform multiplication operation with the values 3 and 2. Multiply 3 with 2 the product is 6. Next add 6 with with 4 the sum is 10. The equation is 10 = 2 + g. Add 8 to the 2 the sum is 10. So, the value g is equal to 8 makes the equation true.

Question 6.
3 + 2 × 6 = g + 5
g = _________
3 + 2 × 6 = g + 5
3 + 12 = g + 5
15 = 10 + 5
The value g = 10 makes the equation true.
Explanation:
The equation is3 + 2 × 6 = g + 5. We can make the equation true by calculating g value. First add left side values. First perform multiplication operation with the values 2 and 6. Multiply 2 with 6 the product is 12. Next add 3 with with 12 the sum is 15. The equation is 15 = g + 5. Add 10 to the 5 the sum is 15. So, the value g is equal to 10 makes the equation true.

Problem Solving

Question 7.
Carlo places 8 apple slices on one side of a pan balance and 12 orange slices on the other side. Each side weighs 48 grams. What is the weight of one apple slice? One orange slice?
Carlo places 8 apple slices on one side of a pan balance.
1 apple slice = ?
8 apple slices = 48 grams
48 grams / 8 = 6 grams
1 apple slice is equal to 6 grams.
Carlo places 12 orange slices on the other side.
1 orange slice = ?
12 orange slices = 48 grams
48 grams / 12 = 4 grams
1 orange slice is equal to 4 grams.
Explanation:
Carlo places 8 apple slices on one side of a pan balance and 12 orange slices on the other side. Each side weighs 48 grams. Divide 48 grams by 8 apple slices the result is 6 grams. 1 apple slice weight is equal to 6 grams. Divide 48 grams by 12 orange slices the result is equal to 4 grams. one orange slice is equal to 4 grams.

Question 8.
On another pan balance, Carlo places 3 of the apple slices and 4 of the orange slices on the left side. He places I apple slice on the right side. How many orange slices will Carlo need to place on the right side so that pans are balanced?
Carlo places 3 of the apple slices and 4 of the orange slices on the left side.
1 apple slice is equal to 6 grams.
3 x 6 = 18
3 apple slices is equal to 18 grams.
1 orange slice is equal to 4 grams.
4 x 4 = 16
4 orange slices is equal to 16 grams.
18 grams+ 16 grams = 34 grams
On left side of the pan balance the weight of apple slices and oranges are 34 grams.
Carlos places 1 apple slice on the right side.
1 x 6 = 6
1 apple slice is equal to 6 grams.
7 x 4 = 28
7 oranges is equal to 28 grams.
Carlo need to place 7 oranges on the right side so that pans are balanced.
On right side of the pan balance the weight of apple slices and oranges are 34 grams.
Explanation:
On another pan balance, Carlo places 3 of the apple slices and 4 of the orange slices on the left side. He places I apple slice on the right side. He needs to place 7 orange slices on the right side so that pans are balanced.

Lesson Check

Question 9.
How would you balance the pan balance?

(A) Add 4 cubes to the left side of the balance.
(B) Take away 4 cubes from the right side of the balance.
(C) Move 4 cubes from the right side of the balance to the left side of the balance.
(D) Move 8 cubes from the right side of the balance to the left side of the balance.

So, option C is correct.
Explanation:
In the above image we can observe the pans balance. In left side pan balance there are only 4 cubes. In right side pan balance there are 12 cubes. The pans are balanced by moving 4 cubes from the right side of the balance to the left side of the balance. Now in left side pan balance 8 cubes and in right side pan balance 8 cubes. Both the pans are balanced. So, option C is correct.

Question 10.
Brandy places weights measuring 1 gram, 5 grams, and 10 grams on the right side of a pan balance. She has a box of 2-gram weights and a box of 4-gram weights. Which combination of weights cannot be placed on the left side if Brandy wants the pans to balance?
(A) four 4-gram weights
(B) eight 2 – gram weights
(C) two 4-gram weights and four 2-gram weights
(D) three 4-gram weights and one 2-gram weight

So, option D is correct.
Explanation:
Brandy places weights measuring 1 gram, 5 grams, and 10 grams on the right side of a pan balance. Add 1 gram with 5 grams and 10 grams then the sum is 15 grams. She has a box of 2-gram weights and a box of 4-gram weights. we have to calculate the unbalanced weight. Three 4 grams weight is 12 grams and one 2 grams weight is 2 grams. Add 12 grams with 2 grams the sum is 14 grams. To balance the pans 14 grams weight cannot be placed on the left side. So option D is correct.

Question 11.
On the left side of a pan balance, there are two model cars that each weigh 8 ounces. On the right side, there is a model truck that weighs 12 ounces and a model car with an unknown weight. If both sides of the balance have the same weight, how much does the unknown model car weigh?
(A) 28 oz
(B) 4 oz
(C) 20 oz
(D) 8 oz

On left side, there are two model cars that each weigh 8 ounces.
8 ounces + 8 ounces = 16 ounces
on right side, there is a model truck that weighs 12 ounces and a model car with an unknown weight.
12 ounces + unknown weight = 16 ounces
12 ounces + 4 ounces = 16 ounces
The unknown model car weight is 4 ounces.
So, option B is correct.
Explanation:
On the left side of a pan balance, there are two model cars that each weigh 8 ounces. On the right side, there is a model truck that weighs 12 ounces and a model car with an unknown weight. If both sides of the balance have the same weight, then we have to calculate the unknown weight. Add 4 ounces to the 12 ounces the sum is 16 ounces. The unknown model car weight is 4 ounces. So, option B is correct.

Question 12.
Multi-Step Casey placed 14 cubes on the right side of a pan balance. She placed 5 cubes on the left side. Then she removed half the cubes on the right side. Find the number of cubes that Casey must add to the left side to balance the pans.
(A) 9
(B) 7
(C) 5
(D) 2

So, option D is correct.
Explanation:
Casey placed 14 cubes on the right side of a pan balance. She placed 5 cubes on the left side. Then she removed half the cubes on the right side. The number of cubes left on the right side is 7 cubes. We have to calculate the number of cubes that Casey must add to the left side to balance the pans. Casey need to add 2 cubes on the left side to balance the pans. So, option D is correct.

Question 13.
Multi-Step The total weight of the shape blocks on both sides of Michael’s pan balance equals 30 grams. Circles weigh 5 grams, squares weigh 10 grams, and triangles weigh 3 grams. The right side has a circle and a square. How many triangles are on the left side?
(A) 5
(B) 4
(D) 6
(D) 10

On right side a circle and a square.
5 grams + 10 grams = 15grams
On left side triangles.
3 grams + 3 grams + 3 grams + 3 grams + 3 grams = 15grams
There are 5 triangles on the left side.
So, option A is correct.
Explanation:
The total weight of the shape blocks on both sides of Michael’s pan balance equals 30 grams. Circles weigh 5 grams, squares weigh 10 grams, and triangles weigh 3 grams. The right side has a circle and a square. Add 5 grams with 10 grams the sum is 15 grams. To balance the pans we need to keep 5 triangles on left side. Add triangles weight. Add 3 grams as 5 times the sum is 15 grams. So, option A is correct.

Question 14.
Multi-Step Will placed 12 cubes on the right side of a pan balance. He placed 3 cubes on the left side. Then he added 14 cubes on the left side. Find the number of cubes he must add to the right side to balance the pans.
(A) 5
(B) 9
(C) 23
(D) 3