All the solutions provided in McGraw Hill Math Grade 4 Answer Key PDF Chapter 7 Lesson 2 Numeric Patterns will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 7 Lesson 2 Numeric Patterns
Math in My World
Example 1
Carla sells 3 picture frames for $15 and 4 picture frames for $20. The pattern for the price of the frames is the same. How much money will Carla make if she sells 6 frames?
Identify and describe the pattern by dividing the total cost by the number of frames.
Carla sells 3 picture frames for $15, and 4 picture frames for $20.
$15 ÷ 3 = $5
$20 ÷ 4 = $5
So, one picture frame costs $5. The rule is to multiply the number of frames by $5.
Use the rule to extend the pattern.
So, Carla will make 6 × $5, or ____ , if she sells 6 picture frames.
Answer:
Carla will make 6 × $5, or $30, if she sells 6 picture frames.
Explanation:
Cost of 3 picture frames Carla sells = $15.
Number of picture frames = 3.
Cost of one picture frame = Cost of 3 picture frames Carla sells ÷ Number of picture frames
= $15 ÷ 3
= $5.
Cost of 4 picture frames = $20.
Number of picture frames = 4.
Cost of one picture frame = Cost of 4 picture frames Carla sells ÷ Number of picture frames
= $20 ÷ 4
= $5.
Number of each picture frame = $5.
Number of picture frames = 6.
Cost of Six picture frame = $5 × 6
= $30.
Example 2
The chapters in Daniel’s book follow a pattern. The even chapters have 12 pages. The odd chapters have 16 pages. The first page number of Chapter 1 is 1. Extend the pattern to find the page number of the last page in Chapter 6.
So, the last page number of Daniel’s book is ____
Describe another pattern you see in this chart.
Answer:
So, the last page number of Daniel’s book is 84.
Explanation:
Number of pages of even chapters = 12.
Number of pages of odd chapters = 16.
First page number of Chapter 1 = 1.
Number of pages of Chapter 1 = Number of pages of odd chapters = 16.
Number of pages of Chapter 2 = Number of pages of Chapter 1 + Number of pages of even chapters
= 16 + 12
= 28.
Number of pages of Chapter 3 = Number of pages of Chapter 2 +Number of pages of odd chapters
= 28 + 16
= 44.
Number of pages of Chapter 4 = Number of pages of Chapter 3 + Number of pages of even chapters
= 44 + 12
= 56.
Number of pages of Chapter 5 = Number of pages of Chapter 4 + Number of pages of odd chapters
= 56 + 16
= 72.
Number of pages of Chapter 6 = Number of pages of Chapter 5 + Number of pages of even chapters
= 72 + 12
= 84.
Talk Math
Describe a real world example of a growing numeric pattern.
Answer:
The row of cubes is an example of a growing numeric pattern in the real life.
Explanation:
The row of cubes is an example of a growing numeric pattern in the real life. In growing patterns, the chunks are called terms. There has to be a rule that tells you how each term is obtained.
Guided Practice
Identify, describe, and extend each pattern.
Question 1.
9, 12, 15, 18, 21, ____
The pattern is add ____.
Answer:
9, 12, 15, 18, 21, 24.
The pattern is add 3.
Explanation:
9, 12, 15, 18, 21, ____
9 + 3 = 12.
12 + 3 = 15.
15 + 3 = 18.
18 + 3 = 21.
21 + 3 = 24.
The pattern is add 3.
Question 2.
5, 6, 4, 5, 3, ______
The pattern is add ____, then subtract ____
Answer:
5, 6, 4, 5, 3, 4.
The pattern is add 1, then subtract 1.
Explanation:
5, 6, 4, 5, 3, ??
1 – 5
2 – 5+ 1 = 6.
3 – 5 – 1 = 4.
4 – 6 – 1 = 5.
5 – 4 – 1 = 3.
6 – ?? = 5 – 1 = 4.
Pattern is add 1, subtract 1.
Question 3.
Antonio runs 30 minutes each day. Extend the pattern to find the number of minutes he will have run by Day 5.
Answer:
Explanation:
Number of minutes Antonio runs each day (R)= 30.
Number of minutes Antonio runs (R)× Number of days (D)= Total number of minutes he ran (T)
Equation: R × D = T
When D = 2;
30 × 2 = 60 minutes.
When D = 3;
30 × 3 = 90 minutes.
When D = 4;
30 × 4 = 120 minutes.
When D = 5;
30 × 5 = 150 minutes.