CHAPTER 8
STUDENT BOOK PAGE 248–249
Mid-Chapter Review
Preparation and Planning
Materials
•ruler, 1 cm grid paper
•Mid-Chapter Review—Frequently Asked Questions
(Master) p. 57
Using the Frequently Asked
Questions (Whole Class) ➧ about 10 min
Have students keep their Student Books closed. Write the
Frequently Asked Questions on the board, or use MidChapter Review—Frequently Asked Questions p. 57.
(Distribute the master or show it on an overhead.) Use the
discussion to draw out 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 248.
Students can refer to the answers to the Frequently Asked
Questions 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 32–33 for the details of
each question.
2., 4., & 6. Encourage students to use grid paper and a ruler
to sketch or draw the shapes to their correct proportions.
Related Questions to Ask
Ask
1. a) 50 000 cm2
b) 80 000 cm2
2. a) For example:
c) 130 000 cm2
d) 44 000 cm2
1.2 m
1m
Possible Responses
About Question 6:
• What might be the base and
height of a triangle with an area
of 16 cm2? Explain.
30
Answers
Chapter 8: Area
• The height might be 8 cm and
the base might be 4 cm because
8 × 4 = 32 and 32 ÷ 2 =16 cm2.
• The base might be 16 cm and the
height might be 2 cm because 16
× 2 = 32 and 32 ÷ 2 = 16 cm2.
b) 12 000
Copyright © 2006 by Thomson Nelson
5. The area of a triangle is equal to its base times its height
divided by 2
a) (5 cm × 1 cm) ÷ 2 = 5 cm2 ÷ 2 = 2.5 cm2
b) (2 cm × 2 cm) ÷ 2 = 4 cm2 ÷ 2 = 2 cm2
c) For example, the base measures 4 cm and the height
1.8 cm, so (4 cm × 1.8 cm) ÷ 2 = 7.20 cm2 ÷ 2
= 3.6 cm2.
6. For example:
4 cm
8 cm
8 cm
4 cm
Follow-Up and Preparation for Next Class
All questions can be used for assessment. (See chart on pp. 32–33.)
3. The area of a parallelogram is equal to its base times
its height.
a) 2 cm × 3 cm = 6 cm2
b) 20 cm × 50 cm = 1000 cm2
c) First, I have to convert the dimensions to the same
units: 1 m = 100 cm. Then I multiply to find the
area: 100 cm × 30 cm = 3000 cm2.
4. For example:
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 248. Encourage students to summarize their
understanding of unit relationships and area of rectangles,
parallelograms and triangles in diagram form. Collect
students’ work and post it for comment next class.
Alternatively, students can work in pairs or small groups
to produce a chart that represents a synthesis of their
collective work.
2 cm
8 cm
4 cm
4 cm
Copyright © 2006 by Thomson Nelson
Mid-Chapter Review
31
Assessment of Learning—What to Look for in Student Work…
Assessment Strategy: Short Answer
Application of Learning
Question 1
• Express each of the following in square centimeters. a) 5 m2
(Score correct responses out of 4.)
b) 8 m2
c) 13 m2
d) 4.4 m2
Assessment Strategy: Written Answer
Problem Solving/Thinking
Question 2
• a) Carlos wants to make a skim board with an area of 1.2 m2. He has a rectangle of plywood that has sides of 1.0 m and 1.5 m. Sketch the board.
b) He wants to cover the surface of the board with 1 cm2 decals. How many decals will he need?
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 problem but does not arrive
at an answer
• carries out the plan to some extent,
using a strategy (e.g., using grid
paper or base ten blocks) and develops
a partial and/or incorrect solution
• carries out the plan effectively by
using an appropriate strategy
(e.g., using grid paper or base ten
blocks) and solving the problem
• shows flexibility and insight when
carrying out the plan by trying and
adapting, when necessary, one or
more strategies (e.g., using grid
paper or base ten blocks) to solve
the problem
• use of procedures includes major
errors and/or omissions
• use of procedures (e.g., converting
metric units of measure) includes
almost no errors and/or omissions
• use of procedures (e.g., converting
metric units of measure) is mostly
correct, but there may be a few
minor errors and/or omissions
• use of procedures (e.g., converting
metric units of measure) includes
almost no errors or omissions
Carry Out the Plan
Assessment Strategy: Written Answer
Application of Learning
Question 3
• Calculate the area of each parallelogram. Show your work.
1
• demonstrates limited ability to
apply mathematical knowledge and
skills in familiar contexts (e.g., has
difficulty using a rule (i.e., base ×
height) to calculate the area of each
parallelogram)
32
Chapter 8: Area
2
• demonstrates some ability to apply
mathematical knowledge and skills
in familiar contexts (e.g.,
demonstrates some ability to use a
rule [i.e., base x height] to calculate
the area of each parallelogram)
3
• demonstrates considerable ability
to apply mathematical knowledge
and skills in familiar contexts (e.g.,
uses a rule [i.e., base x height] to
calculate the area of each
parallelogram)
4
• demonstrates sophisticated ability
to apply mathematical knowledge
and skills in familiar contexts (e.g.,
demonstrates sophisticated ability
to use a rule [i.e., base x height] to
calculate the area of each
parallelogram)
Copyright © 2006 by Thomson Nelson
Assessment Strategy: Written Answer
Problem Solving/Thinking
Question 4
• Draw two non-congruent parallelograms on grid paper each with an area of 16 cm2. Label the base and height on each.
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 problem but does not arrive
at an answer
• carries out the plan to some
extent, using a strategy (e.g.,
using the area rule for
parallelograms) and develops a
partial and/or incorrect solution
• carries out the plan effectively by
using an appropriate strategy
(e.g., using the area rule for
parallelograms) and solving
the problem
• shows flexibility and insight when
carrying out the plan by trying and
adapting, when necessary, one or
more strategies (e.g., using the
area rule for parallelograms) to
solve the problem
• use of procedures (e.g., calculating
areas of parallelograms) includes
major errors and/or omissions
• use of procedures (e.g., calculating
areas of parallelograms) includes
almost no errors and/or omissions
• use of procedures (e.g., calculating
areas of parallelograms) is mostly
correct, but there may be a few
minor errors and/or omissions
• use of procedures (e.g., calculating
areas of parallelograms) includes
almost no errors or omissions
Carry Out the Plan
Assessment Strategy: Written Answer
Application of Learning
Question 5
• Calculate the area of each triangle. Use a ruler to help you. Show your work.
1
• demonstrates limited ability to
apply mathematical knowledge
and skills in familiar contexts
(e.g., has difficulty using a rule (i.e.,
1
× base × height) to calculate the
2
area of each triangle)
2
• demonstrates some ability to apply
mathematical knowledge and skills in
familiar contexts (e.g., demonstrates
some ability to use a rule (i.e., 12 ×
base × height) to calculate the area
of each triangle)
3
• demonstrates considerable ability
to apply mathematical knowledge
and skills in familiar contexts (e.g.,
uses a rule (i.e., 12 × base × height)
to calculate the area of each triangle)
4
• demonstrates sophisticated ability
to apply mathematical knowledge
and skills in familiar contexts (e.g.,
demonstrates sophisticated ability to
use a rule (i.e., 12 × base × height) to
calculate the area of each triangle)
Assessment Strategy: Written Answer
Application of Learning
Question 6
• Draw two non-congruent triangles on grid paper each with an area of 16 cm2. Label the base and height on each.
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 problem but does not arrive
at an answer
• carries out the plan to some
extent, using a strategy (e.g.,
using the area rule for triangles)
and develops a partial and/or
incorrect solution
• carries out the plan effectively by
using an appropriate strategy
(e.g., using the area rule for
triangles) and solving the problem
• shows flexibility and insight when
carrying out the plan by trying and
adapting, when necessary, one or
more strategies (e.g., using the
area rule for triangles) to solve
the problem
• use of procedures (e.g., calculating
areas of triangles) includes major
errors and/or omissions
• use of procedures (e.g., calculating
areas of triangles) includes almost
no errors and/or omissions
• use of procedures (e.g., calculating
areas of triangles) is mostly correct,
but there may be a few minor
errors and/or omissions
• use of procedures (e.g., calculating
areas of triangles) includes almost
no errors or omissions
Carry Out the Plan
Copyright © 2006 by Thomson Nelson
Mid-Chapter Review
33