01a-NEM-6-ON-TR-CH01a 7/21/05 10:53 AM Page 36
CHAPTER 1
STUDENT BOOK PAGES 18 –19
Mid-Chapter Review
Preparation and Planning
Materials
•calculator (1/student or pair), grid paper
•Mid-Chapter Review—Frequently Asked Questions
(Master) p. 71
Using the Frequently Asked
Questions (Whole Class) ➧ 10 min
Have students keep their Student Books closed. Show the
Frequently Asked Questions on an overhead or write them
on the board, or use Mid-Chapter Review—Frequently
Asked Questions p. 71. Discuss what the class thinks is
the best answer to each question. Then have students
compare the class answers with the answers on Student
Book page 18. Students can refer to these answers as they
work through the review questions.
Using the Mid-Chapter Review
Use this page to assess students’ understanding of the
concepts developed in the chapter so far. Refer to the
assessment chart on pages 38 and 39 for the details of
each question.
1. Students who write the pattern rule as 15 + 15 × (term
number − 1) should be encouraged to see that this can
also be written as 15 × term number, or 15 × d.
2. Some students may think that “after five weeks” means
the sixth week. Accept this answer if students can explain
their thinking. If we consider $200 as the first week,
Tristen will have $240 in the fifth week.
Related Questions to Ask
Ask
Possible Responses
About Question 1:
• Explain how you would represent • I would use days (1, 2, 3, 4, …)
on the x-axis and number of
the number of sunrises in a graph.
sunrises (15, 30, 45, 60, …) on
the y-axis. I would place each
coordinate pair (1,15), (2, 30),
(3, 45), and so on by going to
the right and then going up.
• No. Each point represents a time
• Should the points on this graph
when the astronaut saw a sunset.
be joined?
They did not see a sunset in
between these times, so the
points cannot be joined.
About Question 3:
• What pattern rule would you
write if you were calculating
a) the number of Jupiter days?
b) the number of Neptune days?
36
Answers
1. a)
Number of Earth days
Number of sunrises seen
on the space station
1
15
2
30
3
45
4
60
5
75
b) Since the first term and the common difference are
the same, I can multiply the term number by 15 to
get the number of sunrises.
(number of sunrises for 7 days) 7 × 15 = 105. An
astronaut would see 105 sunrises in 7 Earth days.
c) The pattern rule is number of sunrises = term
number × 15. For 188 days, Shannon could have
seen 188 × 15 = 2820 sunrises.
• To calculate the number of
Jupiter days I would use h ÷ 10.
• To calculate the number of
Neptune days I would use h ÷ 16.
Chapter 1: Patterns in Mathematics
Copyright © 2006 by Thomson Nelson
01a-NEM-6-ON-TR-CH01a 7/21/05 10:53 AM Page 37
2. a)
Number weeks
Savings ($)
1
200
2
210
3
220
4
230
5
240
b) After the nth week, savings = 200 + (n − 1) × 10.
c) (52nd week) 200 + fifty-one 10s = 200 + 510
or $710. There will be $710 in Tristen’s account.
3. a) For h = 48, 48 ÷ 24 = 2 Earth days.
b) For h = 96, 96 ÷ 24 = 4 Earth days.
c) For h = 100, 100 ÷ 24 = 4.2 Earth days.
d) For h = 600, 600 ÷ 24 = 25 Earth days.
4. For example, I’ll use a table to show the pattern.
Follow-Up and Preparation for Next Class
Have students record their answers to the Frequently
Asked Questions in their notes. For convenience, provide
copies of Mid-Chapter Review—Frequently Asked
Questions on page 71. Encourage students to summarize
their understanding of number patterns.
Alternatively, students can work in pairs or small
groups to produce a chart that represents a synthesis
of their collective understanding.
Copyright © 2006 by Thomson Nelson
Number of pages used
1
6
2
12
3
18
4
24
I’ll use the variable d to represent the number of days.
The pattern rule is number of pages used = d × 6.
Half of 64 is 32. For Kristen to have less than half a
notebook left, she must use at least 33 pages. So I need
to find what value of d will make d ÷ 6 at least 33.
From my graph, on the 6th day, Kristen will have used
36 pages. So she will have less than half a notebook left
on that day.
Number of Pages Compared
to Number of Days
40
35
30
25
20
15
10
5
0
0 1 2 3 4 5 6
Number of days, d
Number of pages used
All questions can be used for assessment. (See chart on pp. 38–39.)
Number of days
Mid-Chapter Review
37
01a-NEM-6-ON-TR-CH01a 7/21/05 10:53 AM Page 38
Assessment of Learning—What to Look for in Student Work…
Assessment Strategy: written answer
Problem Solving/Thinking
Key Assessment Question 1
• As a space station orbits Earth, astronauts see 15 sunrises in 24 h.
a) Complete this table for up to five Earth days.
b) How many sunrises would an astronaut see in seven Earth days?
c) Shannon Lucid spent 188 Earth days on the space station. How many sunrises could she have seen? Use a pattern rule. Show your work.
1
2
3
4
Carry Out the Plan
• uses a strategy and attempts to
solve the problem but does not
arrive at an answer
• carries out the plan to some extent,
using a strategy, and develops a
partial and/or incorrect solution
• carries out the plan effectively by
using an appropriate strategy
(e.g., completing the table and using
a pattern rule) to solve the problem
• shows flexibility and insight when
carrying out the plan by trying and
adapting, when necessary, one or
more strategies (e.g., completing
the table and using a pattern rule)
to solve the problem
• includes major errors and/or
omissions when using a procedure
(e.g., calculations)
• includes several errors and/or
omissions when using a procedure
(e.g., calculations)
• includes few errors and/or
omissions when using a procedure
(e.g., calculations)
• includes almost no errors and/or
omissions when using a procedure
(e.g., calculations)
• shows partial work with some
clarity
• shows complete work that is clear
• shows thorough work that is clear
and insightful
Communicate
• shows limited work that lacks
clarity
Assessment Strategy: written answer
Problem Solving/Thinking
Key Assessment Question 2
• Tristen has $200 in his savings account. Starting next week, he plans to add $10 each week.
a) Make a table to show Tristen’s balance after five weeks.
b) Write a pattern rule that tells how to calculate his balance after any number of weeks.
c) How much will be in Tristen’s account after 52 weeks?
1
2
3
4
Make a Plan
• shows little or no evidence of
a plan
• shows some evidence of a plan
• shows evidence of an
appropriate plan
• shows evidence of a thorough plan
• uses a strategy and attempts to
solve the problem but does not
arrive at an answer
• carries out the plan to some extent,
using a strategy, and develops a
partial and/or incorrect solution
• carries out the plan effectively
by using an appropriate strategy
(e.g., making a table and using
a pattern rule) to determine the
account balance
• shows flexibility and insight when
carrying out the plan by trying and
adapting, when necessary, one or
more strategies (e.g., making a
table and using a pattern rule) to
determine the account balance
• includes major errors and/or
omissions when using a procedure
(e.g., calculations)
• includes several errors and/or
omissions when using a procedure
(e.g., calculations)
• includes few errors and/or
omissions when using a procedure
(e.g., calculations)
• includes almost no errors and/or
omissions when using a procedure
(e.g., calculations)
Carry Out the Plan
38
Chapter 1: Patterns in Mathematics
Copyright © 2006 by Thomson Nelson
01a-NEM-6-ON-TR-CH01a 7/21/05 10:53 AM Page 39
Assessment Strategy: short answer
Application of Learning
Key Assessment Question 3
• This sentence describes how many days an astronaut is in space. Earth days = h ÷ 24. The symbol h represents the variable ‘number of hours in space.’
Calculate the number of Earth days an astronaut is in space for each value of h.
a) 48
b) 96
c) 100
d) 600
(Score correct responses out of 4.)
Assessment Strategy: written answer
Problem Solving/Thinking
Key Assessment Question 4
• Kristen has a notebook with 64 pages. Each day she uses six pages of the book. On what day will she have less than half the notebook left? Use a graph.
1
2
3
4
Make a Plan
• shows little or no evidence of
a plan
• shows some evidence of a plan
• shows evidence of an
appropriate plan
• shows evidence of a thorough plan
• uses a strategy and attempts to
solve the problem but does not
arrive at an answer
• carries out the plan to some extent,
using a strategy, and develops a
partial and/or incorrect solution
• carries out the plan effectively by
using an appropriate strategy
(e.g., making a graph and using a
pattern rule) to determine the day
Kristen will have less than half
a notebook left
• shows flexibility and insight when
carrying out the plan by trying and
adapting, when necessary, one or
more strategies (e.g., making a
graph and using a pattern rule) to
determine the day Kristen will
have less than half a notebook left
• includes major errors and/or
omissions when using a procedure
(e.g., drawing a graph)
• includes several errors and/or
omissions when using a procedure
(e.g., drawing a graph)
• includes few errors and/or
omissions when using a procedure
(e.g., drawing a graph)
• includes almost no errors and/or
omissions when using a procedure
(e.g., drawing a graph)
Carry Out the Plan
Copyright © 2006 by Thomson Nelson
Mid-Chapter Review
39