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## Texas Go Math Grade 5 Lesson 10.3 Answer Key Number Patterns in Graphs

**Unlock the Problem**

Sona has some dimes. Adil offers to give her nickels for her dimes.

The graph shows the relationship between the number of dimes Sona gives to

Adil and the number of nickels she receives in exchange. Find a rule to describe the pattern.

STEP 1: Write number pairs that relate the number of dimes to the number of nickels

STEP 2 Describe the relationship between the number of dimes and the number of nickels.

The output is __________ times the input. The pattern uses multiplication.

STEP 3 Write the rule. Let n stand for number of nickels, and d stand for the number of dimes.

n = __________ × ___________

Think: The relationship is multiplicative. Use multiplication to write the rule.

Answer:

Step 1:

Pairs that relate between Sona and Adil the number of dimes to the

number of nickels are (1,2), (2,4), (3,6), (4,8),

Step 2:

The output is 2 times the input,

Step 3:

Rule: n = d X 2,

Explanation:

Step 1:

As the number of dimes is the input, the horizontal distance from

0 for the first point is 1 and the number of nickels is output the vertical distance

for the first point is 2, So the pairs that relate between Sona and Adil

the number of dimes to the number of nickels are (1,2), (2,4), (3,6), (4,8),

Step 2:

By seeing the pairs the relationship between the number of dimes is

twice the number of nickels. so the output is two times the input.

The pattern uses multiplication,

Step 3:

Let n stand for number of nickels, and d stand for the number of dimes.

as the relationship is multiplicative. Using multiplication to write the rule as

n = d X 2.

**Math Idea**

An additive pattern uses addition ¡n its rule. A multiplicative pattern uses multiplication in its rule.

**Example**

Find the rule for the pattern shown in the graph.

Jack mails some magazines in a box. The graph shows the relationship between

the number of magazines and the total weight of the magazines and the box.

STEP 1: Write number pairs that relate the number of magazines and the total weight.

(1, ______)

(2, ______)

(3, ______)

(4, ______)

STEP 2: Describe the relationship between the number of magazines and the weight.

The output is the sum of the number of magazines and __________.

The pattern uses addition.

STEP 3: Write the rule. Let w stand for total weight, and m stand for the number of magazines.

w = __________ + __________

Answer:

Pairs are (1,3), (2,4), (3,5), (4,6),

The output total weight is the sum of the number of magazines and 2,

rule is w = m + 2,

Explanation:

Step 1: Number pairs that relate the number of magazines and the total weight is

(1,3), (2,4), (3,5), (4,6),

Step 2: By seeing the graph The output is the sum of the number of magazines and 2

the relationship between the number of magazines and the weight.

The output is the sum of the number of magazines and 2 by using

addition pattern and let w stand for total weight, and

m stand for the number of magazines the rule is w = m + 2.

**Math Talk**

**Mathematical Processes**

Explain what the 2 stands for in w = m + 2.

Answer:

2 stands for adding 2 more plus number of magazines we get the weight,

Explanation:

As w = m + 2 here 2 stands we are adding 2 more to the

number of magazines we will get the weight.

**Share and Show**

**Is the pattern additive or multiplicative? Find the rule for the pattern.**

Question 1.

Answer:

Pattern is multiplicative,

Rule : t = s X 3,

Explanation:

Step 1: Number pairs that relate input s and output t we see

(1,3),(2,6), (3,6),

Step 2: By seeing the graph the relationship between the input and output is

the output t is multiplication of 3 times with input s by using

multiplication pattern rule is t = s X 3.

Question 2.

Answer:

Pattern is additive,

Rule : t = s + 3,

Explanation:

Step 1: Number pairs that relate input s and output t we see

(1,4),(2,5), (3,6),

Step 2: By seeing the graph the relationship between the input and output is

the output t is addition of 3 more with input s by using

addition pattern rule is t = s + 3.

**Problem Solving**

Question 3.

**H.O.T. Write Math** Explain the differences between the graphs in Exercises 1 and 2.

Answer:

One is multiplicative pattern and other is additive pattern,

Explanation:

The main difference between the graphs in Exercise 1 and 2 is

the first 1 is multiplicative pattern with steeper(larger) slope and linear and

seeing relations between input and output,

In the second graph it is additive pattern with linear and deeper(closer) slope

and seeing relations between input and output.

Question 4.

**Write Math** Explain how you can tell whether a pattern shown in a graph is additive or multiplicative.

Answer:

By seeing the graph and points

origin, slope is deeper or steeper, linear

and relations between input and outputs,

Explanation:

In additive graph it will not start from origin and slope

will be deeper(closer) and it will be linear and we see the

relationship between input and output,

In multiplicative graph it can will start from origin and slope

will be steeper(increases) and it will be linear and we see the

relationship between input and output.

**Problem Solving**

**Use the graph for 5-6.**

Question 5.

**H.O.T. Multi-Step** Maryanne’s map uses a scale to show how many miles each inch on the map represents.

Use the pattern shown in the graph to find the rule for calculating the actual distance.

Use in for number of miles and j for number of inches.

Answer:

Rule in = j X 10,

Explanation:

Given Maryanne’s map uses a scale to show how many miles each inch on the map represents.

Step 1: Number pairs that relate input and output is

(1,0),(2,20), (3,30),(4,40),

Step 2: By seeing the graph the relationship between

in for number of miles and j for number of inches on map rule is

the number of miles is multiplication of 10 times with number of inches on the map

using multiplication pattern rule is (actual distance) in = j X 10

Used the pattern shown in the graph to find the rule for calculating the actual distance.

Question 6.

**H.O.T.** If the distance on the map is 2.5 inches, how many miles is the actual distance?

Explain how you calculated the actual distance.

Answer:

The actual distance is 25 miles,

Explanation:

Given the distance on the map is 2.5inches to calculate

the actual distance by using the graph and rule of question 5 we have

(actual distance) in = j X 10(where j is number of inches on the map)

substituting j = 2.5 we get in = 2.5 X 10 = 25 miles the actual distance.

Question 7.

**H.O.T.** Apply Olivia uses 1 red button for the nose and 2 blue buttons

for the eyes for each rag doll she makes.

Would the pattern comparing the number of nose buttons to

the total number of buttons be multiplicative or additive? Explain.

Answer:

The number of nose buttons to total number of buttons

will be multiplicative,

Explanation:

Given Olivia uses 1 red button for the nose and 2 blue buttons

for the eyes for each rag doll she makes. If n is the total number of buttons

let r is red button for the nose and b for blue button we have

1 rag doll = 3 buttons = 1 red button + 2 blue buttons

means the total number of buttons is

depending upon number of red buttons and also on

blue buttons which means it is multiplicative

if 2 rag dolls = 3 x 2 = 6 buttons = (2 X 1r + 2 X 2b) = 2 + 4 = 6.

**Daily Assessment Task**

**Fill in the bubble completely to show your answer. Use the graph.**

Question 8.

The graph shows the number of pounds of fish the seals at an aquarium eat each day.

Which statement and equation about the relationship is true?

(A) additive pattern, d = p + 3

(B) addition pattern, p = d + 3

(C) multiplicative pattern, p = 10 × d

(D) multiplicative pattern, d = 3 × p

Answer:

(C) multiplicative pattern, p = 10 × d is true,

Explanation:

Given the graph shows the number of pounds of fish the seals

at an aquarium eat each day the pattern is if

p is the number of pounds of fish the seals and d is number of days

Step 1: Number pairs that relate input d and output p we see

(1,10),(2,20), (3,30),(4,40),

Step 2: By seeing the graph the relationship between the input and output is

multiplicative of 10 times with input d is output p by using

multiplicative pattern rule is p = 10 X d which exactly matches with (C).

**Use the graph for 9-10.**

Question 9.

The graph shows the relationship between the number of days and

the amount of food that a bottlenose dolphin eats.

Which point on the graph shows the amount of food that the dolphin consumes in two days?

(A) point A

(B) point B

(C) point C

(D) point D

Answer:

(C) point C,

Explanation:

Given the graph shows the relationship between the number of days and

the amount of food that a bottlenose dolphin eats. If we see points on the

graph Point A is day 0, Point B is day 1, Point C is day 2 and Point D is day 3,

So point on the graph that shows the amount of food that the

dolphin consumes in two days is Point C matches with (C).

Question 10.

**Multi-Step** If s is the amount of food a bottlenose dolphin cats in a

day and n is the number of days, which of the following describes the

rule for the pattern shown in the graph?

(A) s = n + 23

(B) s = n × 23

(C) n = s × 23

(D) n = s + 23

Answer:

(A) s = n + 23,

Explanation:

If s is the amount of food a bottlenose dolphin cats in a

day and n is the number of days, Number pairs that relate

input n and output s we see

(1,23),(2,46), (3,69), the following describes the

rule for the pattern shown in the graph the relationship between the

input number of days n and output s is the amount of food a

bottlenose dolphin cats in a day is additive of 23 more with input n

is output s by using additive pattern rule is s = n + 23

which exactly matches with (A).

**Texas Test Prep**

Question 11.

Which of the following rules describes the pattern in the graph?

(A) a = 4b

(B) b = 4a

(C) b = 4 + a

(D) a = 4 + b

Answer:

(C) b = 4 + a,

Explanation:

Number pairs that relate input a and output b we see

(1,5), (2,6), (3,7), (4, 8) the following describes the

rule for the pattern shown in the graph the relationship between the

input a and output b is additive of 4 more with input a is output b by using

additive pattern rule we have b = 4 + a which exactly matches with (C).

### Texas Go Math Grade 5 Lesson 10.3 Homework and Practice Answer Key

**Is the pattern additive or multiplicative? Write the rule for the pattern.**

Question 1.

Answer:

Pattern is additive,

Rule is b = a + 4,

Explanation:

Number pairs that relate input a and output b we see

(1,5), (2,6), (3,7) the following describes the

rule for the pattern shown in the graph the relationship between the

input a and output b is additive of 4 more with input a is output b by using

additive pattern rule is b = a + 4.

Question 2.

Answer:

Pattern is Multiplicative,

Rule is d = c X 4,

Explanation:

Number pairs that relate input c and output d we see

(1,4), (2,8), (3,12) the following describes the

rule for the pattern shown in the graph the relationship between the

input c and output d is multiplicative of 4 more with input c is output d

by using multiplicative pattern rule is d = c X 4.

Question 3.

Answer:

Pattern is Multiplicative,

Rule is f = e X 5,

Explanation:

Number pairs that relate input e and output f we see

(1,5), (2,10), (3,15) the following describes the

rule for the pattern shown in the graph the relationship between the

input e and output f is multiplicative of 5 more with input e is output f

by using multiplicative pattern rule is f = e X 5.

Question 4.

Answer:

Pattern is additive,

Rule is h = g + 5,

Explanation:

Number pairs that relate input a and output b we see

(1,6), (2,7), (3,8) the following describes the

rule for the pattern shown in the graph the relationship between the

input g and output h is additive of 5 more with input g is output h

by using additive pattern rule is h = g + 5.

**Problem Solving**

Question 5.

Patrice rents a rowboat for several hours. Use the pattern shown

in the graph to write the rule for calculating the cost of renting the rowboat.

Use c for the cost and h for the number of hours.

Answer:

The rule for calculating the cost of renting the rowboat is

c = h X $15, where c for the cost and h for the number of hours,

Explanation:

Given Patrice rents a rowboat for several hours the pattern shown

in the graph if c is for the cost and h for the number of hours is

Number pairs that relate hours h and cost c we see

(1,15), (2,30), (3,45) the following describes the

rule for the pattern shown in the graph the relationship between the

hours h and costs c is multiplicative of 15 times

by using multiplicative pattern rule is c = h X $15.

Question 6.

If Patrice rents the boat for 4 hours, what is the cost of the rental?

Answer:

The cost of the rental is $60,

Explanation:

we have the rule for calculating the cost of renting the rowboat is

c = h X $15, where c for the cost and h for the number of hours,

so if Patrice rents the boat for 4 hours, the cost of the rental is

c= 4 X $ 15 = $60.

**Lesson Check**

**Fill in the bubble completely to show your answer.**

Question 7.

The graph shows the relationship between the number of hours

Ivana bikes and the distance she travels. How many miles does Ivana bike in 4 hours?

(A) 28 miles

(B) 12 miles

(C) 32 miles

(D) 30 miles

Answer:

(C) 32 miles,

Explanation:

Given the graph shows the relationship between the number of hours

Ivana bikes and the distance she travels

Step 1: Number pairs that relate hours h and number of miles m we see

(1,8),(2,16), (3,24),

Step 2: By seeing the graph the relationship between the input and output is

multiplicative of 8 times with input hours h is output number of miles m by using

multiplicative pattern rule is m = 8 X h so number of miles does

Ivana bike in 4 hours is 8 X 4 = 32 miles which matches with (C).

Question 8.

Rashid uses cubes to build towers. The graph shows the relationship between

the number of towers, t, and the number of cubes, c, he uses.

Which equation describes this relationship?

(A) c = 12 + t

(B) c = 12t

(C) t = 12 + c

(D) t = 12c

Answer:

(B) c = 12t,

Explanation:

Given Rashid uses cubes to build towers.

The graph shows the relationship between

the number of towers t and the number of cubes c,

Step 1: Number pairs that relate the number of towers t and the number of cubes c,

we see (1,12),(2,24), (3,36),

Step 2: By seeing the graph the relationship between the input and output is

multiplicative of 12 times with input the number of towers t is

output by using the number of cubes c multiplicative pattern rule is

c = 12 X t therefore equation describes this relationship is (B).

Question 9.

**Multi-Step** For every $1 Paula donates to her favorite charity,

her mom donates $3. Which of the following identifies the pattern and

the amount her mom donates if Paula donates $6?

(A) $18, multiplicative

(B) $24, multiplicative

(C) $24, additive

(D) $12, additive

Answer:

(A) $18, multiplicative,

Explanation:

Given for every $1 Paula donates to her favorite charity,

her mom donates $3, The graph shows the relationship between

Paula donation as p and mom donation as m

Step 1: Number pairs that relate the Paula donation as p and mom donation m

we see (1,3),(2,6), (3,9),

Step 2: By seeing the graph the relationship between the input and output is

multiplicative of 3 times with input Paula donation p is

output mom donation as m by using multiplicative pattern rule is

m = 3 X p therefore the amount her mom donates if Paula donates $6

is 3 X $6 = $18 matches with (A) $18, multiplicative.

Question 10.

**Multi-Step** The graph shows how much time Christina spends making

flower arrangements to sell. How many baskets can she make in two hours?

(A) 15

(B) 4

(C) 30

(D) 8

Answer:

(D) 8

Explanation:

Given the graph shows how much time Christina spends making

flower arrangements to sell. Number of baskets can she make in two hours

as we know 2 hours means 2 X 60 minutes = 120 minutes,

Step 1: Number pairs that relate the Christina as b means baskets and

minutes as m we see as (1,15),(2,30), (3,45),(4,60),

Step 2: By seeing the graph the relationship between the input and output is

multiplicative of 15 times with input baskets b is

output minutes as m by using multiplicative pattern rule is

m = b X 15, so for 120 minutes means 120/15 = 8 baskets,

which matches with (D).