All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 6 Lesson 7 Problem-Solving Investigation: Look for a Pattern will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 6 Lesson 7 Problem-Solving Investigation: Look for a Pattern
The table shows the amount Hank pays for his clothes and the amount of his discount. How much will he pay, and how much will the discount be for a shirt that costs $34.70?
1. Understand
What facts do you know?
• Hank will receive a ___________ on his ____________.
What do you need to find?
I need to find the amount Hank will pay for the ____________.
2. Plan
Look for a pattern. Extend the pattern to find the final.
3. Solve
Multiply the cost of the item by ______________ to find the discount
Subtract the discount from the ______________ to find the final cost
$34.70 × _____________ = _____________ The discount is _____________.
$34.70 – _____________ = _____________ Hank will pay _____________.
4. Check
Does your answer make sense? Explain.
Answer:
Hank will pay $31.23 and $3.47 will the discount for a shirt that costs $34.70.
Explanation:
Hank will receive a discount on his cost
the amount Hank will pay for the shirt
Plan
Multiply the cost of the item by 0.1 to find the discount
Subtract the discount from the cost to find the final cost
$34.70 × 0.1 = $3.47 The discount is $3.47.
$34.70 – $3.47 = $31.23 Hank will pay $31.23.
Check
Does your answer make sense? Explain.
$31.23 much will he pay, and $3.47 will the discount be for a shirt that costs $34.70
$34.70 × 0.1 = $3.47
The discount is $3.47.
$34.70 – $3.47 = $31.23
Hank will pay $31.23.
Practice the Strategy
Adrienne did 13 sit-ups the first day, 20 sit-ups the second day, and 27 sit-ups the third day. if the pattern continues, how many sit-ups will she do on the sixth day?
1. Understand
What facts do you know?
What do you need to find?
2. Plan
3. Solve
4. Check
Is my answer reasonable?
Answer:
48
Explanation:
Plan
Look for a pattern. Extend the pattern
Day 1) 13
Day 2) 13 + 7 = 20
Day 3) 20 + 7 = 27
Day 4) 27 + 7 = 34
Day 5) 34 + 7 = 41
Day 6) 41 + 7 = 48
solve:
13 + 7 x 5 days
13 + 35 = 48
Check
13 + 7 x 5 = 48
Yes, answer is reasonable.
Apply the Strategy
Solve each problem by looking for a pattern.
Question 1.
Every year, Victoria receives $30 for her birthday, plus $2 for each year of her age. Lacey receives $20 for her birthday and $4 for each year of her age. In 2013, Victoria is 10, and Lacey is 6. In what year will they both receive the same amount of money?
Answer:
2016
Explanation:
Every year, Victoria receives $30 for her birthday,
plus $2 for each year of her age.
$30 + 13 x $2 ( each year of her age)= $30 + $26 =$56 at the age 13 years in 2016
Lacey receives $20 for her birthday and $4 for each year of her age.
$20 + 9 x $4 ( each year of her age)= $20 + $36 =$56 at the age 9 years in 2016
In 2016 year both receive the same amount of money as shown in the above table.
Question 2.
Trent lifts weights 7 days a week. He spends 18 minutes lifting weights on Monday, 29 minutes on Tuesday, 40 minutes on Wednesday, and 51 minutes on Thursday. If this pattern continues, how many minutes will Trent lift weights on Saturday?
Answer:
73 minutes,
Explanation:
Trent lifts weights 7 days a week.
He spends 18 minutes lifting weights on Monday,
29 minutes on Tuesday,
40 minutes on Wednesday,
51 minutes on Thursday.
Number of minutes will Trent lift weights on Saturday,
18 + 11 x 5(day) = 18 + 55 = 73 min
Question 3.
Find the missing numbers in the table. Then describe the pattern.
Answer:
Explanation:
input output
5 x 1 9
5 x 2 9 + 10 = 19
5 x 3 9 + 20 = 29
5 x 4 9 + 30 = 39
5 x 5 9 + 40 = 49
Question 4.
Mathematical PRACTICE Look for a Pattern Describe the pattern below. Then find the next three numbers.
0.03, 0.3, 3, 30, __________, ___________, ____________
Answer:
0.03, 0.3, 3, 30, 300, 3000, 30000
Explanation:
Each pattern above can be found by multiplying 10 to the previous number in the sequence.
0.03 x 10 = 0.3
0.3 x 10 = 3
3 x 10 = 30
30 x 10 = 300
300 x 10 = 3000
3000 x 10 = 30000
Question 5.
Describe the pattern below. Then find the next two numbers. .
784.5, 78.45, 7.845, ________, ____________
Answer:
0.7845
0.7845, 0.07845, 0.007845
Explanation:
Each pattern above can be found by multiplying 0.1 to the previous number in the sequence.
78.45 x 0.1 = 78.45
78.45 x 0.1 = 7.845
7.845 x 0.1 = 0.7845
0.7845 x 0.1 = 0.07845
0.07845 x 0.1 = 0.007845
Review the Strategies
Use any strategy to solve each problem.
- Make a table.
- Choose an operation.
- Act it out.
- Draw a picture.
Question 6.
Mathematical PRACTICE if Plan Your Solution Samuel will arrive at the airport on the first plane after 10 A.M. Airplanes arrive every 50 minutes beginning at 6 A.M. When will Samuel’s plane arrive?
Answer:
10.10 A. M.
Explanation:
Samuel will arrive at the airport on the first plane after 10 A.M.
Airplanes arrive every 50 minutes beginning at 6 A.M.
Each pattern above can be found by adding 50 minutes to the previous time.
6:00 A.M. + 50 min = 6:50 A.M.
6:50 A.M. + 50 min = 7:40 A.M.
7:40 A.M. + 50 min = 8:30 A.M.
8:30 A.M. + 50 min = 9:20 A.M.
9:20 A.M. + 50 min= 10:10 A.M.
Question 7.
On Serena’s tenth birthday, her mom was 3 times Serena’s age. How old will Serena and her mom be when her mom’s age times 0.5 will equal Serena’s age?
Answer:
Serena 20 years,
Mom 40 years.
Explanation:
On Serena’s tenth birthday, her mom was 3 times Serena’s age.
Mom age 10 x 3 = 30 years.
Serena and her mom be when her mom’s age times 0.5 will equal Serena’s age.
Serena’s age = 10 x 0.5 = 20 years.
Mom’s age = 30 + 10 = 40 Years.
Question 8.
Mindy read 8 pages of her book the first day, 15 pages the second day, and 22 pages the third day. If the pattern continues, how many pages of her book will she read on the sixth day?
Answer:
43 pages.
Explanation:
Mindy read 8 pages of her book the first day,
15 pages the second day,
22 pages the third day.
The pattern continues by adding 7 pages each day to the previous day.
Number of pages of her book she read on the sixth day,
fourth day she reads 22 + 7 = 29 pages.
fifth day she reads 29 + 7 = 36 pages.
sixth day she reads 36 + 7 = 43 pages.
Question 9.
A 1-mile hiking path has signs placed every 240 feet. There are signs placed at the beginning and end of the mile. How many signs are there? (Hint: 1 mile = 5,280 feet)
Answer:
22 signs.
Explanation:
A 1-mile hiking path has signs placed every 240 feet.
1 mile = 5,280 feet.
There are signs placed at the beginning and end of the mile.
Number of signs placed in 5280 ÷ 240 = 22 signs.
Question 10.
Jada lives in a city that has an area of 344.6 square miles. Her friend lives in a town that is one-tenth, or 0.1, that size. What is the area of her friend’s town?
Answer:
34.46 square miles.
Explanation:
Jada lives in a city that has an area of 344.6 square miles.
Her friend lives in a town that is one-tenth, or 0.1, that size.
The area of her friend’s town is 344.6 x 0.1 = 34.46 square miles.
Question 11.
Dennis has 9.5 weeks to prepare for a bike tour. If he rides 8.2 miles each week, how many miles will he ride before the bike tour?
Answer:
77.9 miles.
Explanation:
Dennis has 9.5 weeks to prepare for a bike tour.
If he rides 8.2 miles each week,
Total many miles will he ride before the bike tour,
9.5 x 8.2 = 77.9 miles.
McGraw Hill My Math Grade 5 Chapter 6 Lesson 7 My Homework Answer Key
Problem Solving
Solve each problem by looking for a pattern.
Question 1.
Harold has 4 classes each school morning. Each class is 1 hour long, and there are 10 minutes between classes. The first class starts at 8:00 A.M. What time does the fourth class end?
Answer:
Fourth class ends at 12:40 P.M.
Explanation:
Harold has 4 classes each school morning.
Each class is 1 hour long, and there are 10 minutes between classes.
The first class starts at 8:00 A.M.
By adding 1:10 minutes to the starting class we find the time of four classes.
Time duration of first class is, 8:00 A.M. + 1:10 A.M. = 9:10 A.M.
Time duration of second class is, 9:10 A.M. + 1:10 A.M. = 10:20 A.M.
Time duration of third class is, 10:20 A.M. + 1:10 A.M. = 11:30 A.M.
Time duration of fourth class is, 11:30 A.M. + 1:10 A.M. = 12:40 P.M.
Question 2.
Mr. Moore read 25 pages of a book on Monday. He read 32 pages on Tuesday, 39 pages on Wednesday, and 46 pages on Thursday. If this pattern continues, how many pages will Mr. Moore read on Sunday?
Answer:
67 pages.
Explanation:
Mr. Moore read 25 pages of a book on Monday.
He read 32 pages on Tuesday,
39 pages on Wednesday,
46 pages on Thursday.
The pattern continues by adding 7 pages every day to the previous pages.
No. of pages read on Friday 46 + 7 = 53 pages.
No. of read on Saturday 53 + 7 = 60 pages.
No. of pages read on Sunday 60 + 7 = 67 pages.
Question 3.
Mathematical PRACTICE Look for a Pattern Describe the pattern below. Then find the next two numbers.
547, 54.7, 5.47, 0.547, ___________, _________
Answer:
0.0547
0.0547, 0.00547, 0.000547
Explanation:
Each pattern above would be found by dividing 10 to the previous term .
0.547 ÷ 10 = 0.0547
0.0547 ÷ 10 = 0.00547
0.00547 ÷10 = 0.000547
Question 4.
Draw the next two figures in the pattern.
Answer:
Explanation:
Each pattern would be followed by adding 2 lines to the previous one as shown above.
Question 5.
Marissa can buy 3 oranges for $1.35, 4 oranges for $1.80, or 5 oranges for $2.25. Marissa can buy 10 oranges for a price that fits this pattern or a bag of 10 oranges for $4.25. Which way costs less for 10 oranges? Explain.
Answer:
Buying a bag of 10 oranges is less than the the following the pattern.
Explanation:
Marissa can buy 3 oranges for $1.35,
4 oranges for $1.80,
5 oranges for $2.25
Marissa can buy 10 oranges for a price that fits this pattern,
A bag of 10 oranges for $4.25.
The above pattern follows adding $0.45 to the previous term.
4 oranges $1.35 + $0.45 = $1.80
5 oranges $1.80 + $0.45 = $2.25
6 oranges $2.25 + $0.45 = $2.70
7 oranges $2.70 + $0.45 = $3.15
8 oranges $3.15 + $0.45 = $3.60
9 oranges $3.60 + $0.45 = $4.05
10 oranges $4.05 + $0.45 = $4.50
But the cost of 10 oranges $4.25.
So, buying 10 oranges at a time costs less then following the pattern.
$4.50. – $4.25. = $0.25.