02b-NEM5-TG-ON-CH02 7/19/04 4:25 PM Page 55
CHAPTER 2
10
STUDENT BOOK PAGES 48–49
Comparing and
Ordering Decimals
Guided Activity
Goal Compare and order numbers to decimal hundredths.
Prerequisite Skills/Concepts
Expectations
• Compare and order decimal tenths.
5m2
5m8
5m10
5m14
5m18
5m26
compare, order, and represent [whole numbers], decimals, [and fractions]
using concrete materials and drawings
solve problems involving decimals [and fractions], and describe and explain
the variety of strategies used
recognize and read numbers from 0.01 [to 100 000]
compare, order, and represent the place value of [whole numbers and] decimals
from 0.01 [to 100 000] using concrete materials, drawings, and symbols
explain processes and solutions with [whole numbers and] decimals using
mathematical language
read and write decimal numbers to hundredths
Assessment for Feedback
What You Will See Students Doing…
Students will
When Students Understand
If Students Misunderstand
• compare, order, and represent the place value
of decimals using concrete materials, drawings,
and symbols
• Students will represent and compare decimal
hundredths using base ten blocks, indicating
which is greater with the correct symbol.
• Students may have difficulty ordering a large set
of numbers. Have them write all the numbers as
decimal hundredths, then use a coloured pencil to
circle the non-zero digits
• explain processes and solutions with decimals
using mathematical language
• Students will use place value language to explain
their strategies for comparing decimals numbers.
• Model the process for comparing three or more
decimal numbers and have students describe
what you are doing. Prompt them to use place
value language.
Preparation and Planning
Pacing
5–10 min Introduction
15–20 min Teaching and Learning
20–30 min Consolidation
Materials
•base ten blocks (hundreds,
tens, ones)
Masters
•Decimal Place Value Chart,
Masters Booklet p. 43
•Manipulatives Substitute: Base Ten
Blocks, Masters Booklet pp. 38–40
Workbook
p. 17
Key
Assessment
of Learning
Question
Question 5, Understanding
of Concepts
Copyright © 2005 by Thomson Nelson
Meeting Individual Needs
Extra Challenge
• Challenge students to use the Internet or other resources to research the
average annual precipitation statistics for at least five major cities in Canada.
They can present and compare the data in a chart, expressing the statistics
in either millimetres or centimetres.
• Challenge students to use the Internet or other resources to research the
world records for athletic races such as swimming, skiing, or track and
field. Students can make posters showing the winners and their times,
presented in decimal hundredths.
Extra Support
• Some students may need additional practice comparing decimal
hundredths. Show students a decimal hundredth (e.g., 3.58) and have
them write a number that is greater and a number that is less than the
decimal number. Ask students to explain how they choose each number.
Lesson 10: Comparing and Ordering Decimals
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1.
Introduction (Whole Class)
➧ 5–10 min
Ask two student volunteers to each take a giant step, but
have them stand at opposite sides of the classroom. Mark
the start and end spots for each step. Ask students how they
can determine which step is longer. Invite two other students
to measure the distances in centimetres. Encourage them to
use tenths of centimetres to describe the distances as precisely
as possible.
Sample Discourse
“Whose step is longer — Matteo’s or Kim’s?”
• They look as if they are about the same length.
“After measuring, we know Matteo’s giant step is 101 cm
and Kim’s is 101 cm. Whose step is longer?”
• They are the same.
“If we measure to the decimal tenth, we know Matteo’s
giant step is 101.2 cm and Kim’s is 101.8 cm. Whose step
is longer now?”
• Kim’s. That’s because 8 tenths is greater than 2 tenths.
Tell students that, in this lesson, they are going to use
base ten blocks and other strategies to compare decimal
hundredths.
2.
Teaching and Learning
(Whole Class/Pairs) ➧ 15–20 min
Ask students to turn to Student Book page 48. Introduce
the data for women’s long jump and, as a class, read the
central questioning. Read Drake’s Comparison, modelling
the numbers shown using base ten blocks, and discuss how
to compare the decimal numbers.
Have students complete prompts A to D in pairs, using
the base ten blocks and decimal place value charts.
Sample Discourse
“How is Drake’s place value chart different from the ones
you have used?”
• It has a decimal point on one of the lines.
• It shows decimals and not just whole numbers.
• There are two columns to the right of the ones column. In
the charts we have used before, the ones’ place was always
the last column on the right.
• The flats are used to represent ones, the rods are used for
tenths, and the smallest cubes are used for hundredths.
Reflecting
Use these questions to ensure that students understand
how to compare decimal hundredths, and have moved
from modelling to comparing decimal numbers. Discuss
the questions, encouraging varied examples.
56
Chapter 2: Numeration
Sample Discourse
1. • When the whole numbers are different, you just have
to compare those numbers, not the decimal tenths
or hundredths.
• It’s like when you are comparing tens and ones. You only
have to look at the tens, and if one digit is greater than
the other, you don’t have to compare the ones.
• 2 is greater than 1, so 2.■ ■ is always greater than
1. ■ ■. You don’t have to compare the tenths or
hundredths digits.
2. • I thought of the numbers as 6 and 78 hundredths and
6 and 92 hundredths. The whole numbers are the same.
There are more hundredths in the final jump so the final
is the longer jump.
• You compare the digits in the tenths place and the
hundredths place. It’s like comparing the whole numbers,
except you’re comparing the digits farther to the right.
• I would compare the ones digits—they are the same. Then
I would compare the tenths digits—9 is greater than 8,
so then I know that 6.99 is greater than 6.84.
Copyright © 2005 by Thomson Nelson
02b-NEM5-TG-ON-CH02 7/19/04 4:25 PM Page 57
3.
Consolidation ➧ 20–30 min
Checking (Pairs)
For intervention strategies, refer to Meeting Individual
Needs or the Assessment for Feedback chart.
3. b) Provide base ten blocks and decimal place value
charts for students who want to use them.
Practising (Individual)
4. Refer students to Student Book page 34 if they need
to review how to use the inequality signs.
5. Some students may find it helpful to list the numbers
in a column before ordering them. Encourage students
to use base ten blocks and decimal place value charts.
6. Students may find it easier to make comparisons if
they organize their answers in a chart, creating a new
column for each new number substitution.
Related Question to Ask
Ask
Possible Responses
About Question 5:
• Which group of numbers was
the easiest to order and which
was the most difficult? Why?
Key Assessment of Learning question. (See chart on next page.)
Answers
A. For example, a flat is made up of 10 rods, so a rod is one
tenth of a flat. A rod is made up of 10 cubes, so a cube is
one tenth of a rod, or one hundredth of a flat.
B. Drechsler’s final jump was better; for example, the model
shows this because there are only 8 tenths in the qualifying
jump but there are 9 tenths rods in the final. 9 is greater
than 8, so the final jump is better.
C. 6.84, 6.92, 6.99
D. Jones: 6.78 < 6.92, final is better; Rubleva: 6.65 < 6.79,
final is better; Tiedtke: 6.65 < 6.74, final is better; Vaszi:
6.70 > 6.59, qualifying is better
1.–2. See sample responses under Reflecting.
3. a) 1948, 1960, 1972, 1984, 2000
b) 5.69, 6.37, 6.78, 6.96, 6.99, 7.12, 7.14, 7.40
4. a) 6.92 < 6.99 b) 29.04 > 28.04 c) 10.70 > 10.07
5. a) 0.14, 0.97, 3.56, 3.65, 8.12
b) 0.01, 0.05, 0.15, 0.51
c) 0.21, 1.22, 2.12, 12.01
d) 3, 3.03, 3.1, 3.5, 3.75
6. a) For example, 0.45, 3.44, 3.45, 3.54, 5.34, 5.43; 5.43
is greatest
Copyright © 2005 by Thomson Nelson
• I thought c) was the easiest
because I could just compare
whole numbers. They were all
different, so I didn’t have to
compare the tenths and hundredths.
• b) was the hardest because
the whole numbers were all the
same, so I had to compare the
tenths and hundredths. Then, all
the tenths and hundredths were
the same digits, but in different
places.
• I found d) hard because some
numbers were tenths and some
were hundredths.
Closing (Whole Class)
Have students summarize their learning by asking, “What
is a number that is greater than 4.58 and less than 4.85?
How do you know?”
• I choose 4.6. It is the same as 4.60. It has the same whole
number, but 60 hundredths is more than 58 hundredths
and less than 85 hundredths.
b) 3.44
c) For example, for part a), I chose to use 5 as my missing
digit, so the greatest number was 5.43. If the missing
digit is less than 4, then 3.44 is always the greatest. If
the missing digit is greater than 4, then the number
■.43 is always the greatest. If you compare the tens
digits before choosing a digit, you can predict that.
Lesson 10: Comparing and Ordering Decimals
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Assessment of Learning—What to Look for in Student Work…
Assessment Strategy: short answer
Understanding of Concepts
Key Assessment Question 5
• Order each set of numbers from least to greatest.
a) 0.14, 3.56, 8.12, 0.97, 3.65
b) 0.51, 0.15, 0.05, 0.01
c) 2.12, 1.22, 0.21, 12.01
d) 3, 3.03, 3.1, 3.75, 3.5
(Score 2 points for each correct order of numbers, 1 point for partially correct order of numbers, for a total of 8.)
Extra Practice and Extension
At Home
• You might assign any of the questions related to this lesson,
which are cross-referenced in the chart below.
• Students can look through store flyers and catalogues to
find 10 items they would like to purchase. Have them list
the names of the items and their prices in order from least
to greatest.
Math Game
Student Book p. 45
Skills Bank
Student Book p. 54, Questions 18 & 19
Problem Bank
Student Book p. 55, Question 8
Chapter Review
Student Book p. 57, Question 16
Workbook
p. 17, all questions
Nelson Web Site
Visit www.mathK8.nelson.com and follow the
links to Nelson Mathematics 5, Chapter 2.
Decimal Place Value Chart,
Masters Booklet p. 43
Math Background
It is common for students to be taught to compare decimals
by simply focusing on each place value in turn, beginning
from the left and moving to the right. Although this can
be an effective strategy, it must be accompanied with a
conceptual understanding of the number. Using base ten
blocks and linear measurement ensures students develop
a quantitative sense of decimal hundredths.
Common Misconceptions: Some students develop the
misconception that the more digits the number has, the
greater its value. Hence, they will say that 0.8 is less that
0.67. This rule will actually work at times, so it is important
to have students explain their thinking and then test their
assumptions using many different decimals.
58
Chapter 2: Numeration
Manipulatives
Substitute: Base
Ten Block, Masters
Booklet pp. 38–40
Copyright © 2005 by Thomson Nelson