02b-NEM6-ON-TR-CH02b 7/18/05 2:49 PM Page 48
CHAPTER 2
8
Comparing and
Ordering Decimals
STUDENT BOOK PAGES 56–57
Guided Activity
Goal Compare and order decimals to thousandths.
Prerequisite Skills/Concepts
Expectations
• Compare and order decimal
hundredths.
• Model decimal thousandths using
a variety of tools.
• represent, compare, and order whole numbers and decimal numbers from
0.001 to 1 000 000, using a variety of tools
• demonstrate an understanding of place value in whole numbers and decimal
numbers from 0.001 to 1 000 000, using a variety of tools and strategies
Assessment for Feedback
What You Will See Students Doing…
Students will
When Students Understand
If Students Misunderstand
• recognize, order, and compare decimal numbers
to thousandths
• Students will compare and order three or more
decimal thousandths using place value charts,
number lines, or thousandths grids and an
efficient numerical procedure.
• Ask students who have difficulty to write each
decimal thousandth below the other, aligning
the decimals. Have them cover all but the largest
place value with a sheet of paper, compare digits,
uncover the next place to the right, compare
digits, and so on.
• explain the place value of numbers from 0.001
• Students will use place value language to explain
strategies for comparing and ordering a set of
decimals numbers to thousandths.
• Students who need language prompts may find it
helpful to refer to the place value chart as they
are explaining their strategies.
Preparation and Planning
Pacing
5–10 min Introduction
15–20 min Teaching and Learning
20–30 min Consolidation
Materials
•decimal place value charts
(thousands) (several/pair)
•number lines (several/pair)
•1000ths grid (several/pair)
•Optional: stop watch
Masters
•Decimal Place Value Chart
(thousands), Masters Booklet p. 44
•Number Lines, Masters Booklet
p. 37
•Thousandths Grid,
Masters Booklet p. 57
•Optional: Chapter 2 Mental
Math p. 65
Workbook
p. 18
Key
Assessment
of Learning
Question
Question 8, Application of Learning
Meeting Individual Needs
Extra Challenge
• Have students design a game where the results are measured in decimal
thousandths. A round of competition might result in something measured
to the nearest thousandths of a metre, for instance. Ask the designers to
get several students to play their game and to then order their results.
Extra Support
• Have students use place value charts to record several decimal thousandths
with the decimal points aligned.
Mathematical Representing, Problem Solving
Processes
48
Chapter 2: Numeration
Copyright © 2006 by Thomson Nelson
02b-NEM6-ON-TR-CH02b 7/18/05 2:49 PM Page 49
1.
Introduction (Whole Class)
➧ 5–10 min
Ask students to name sports events in which the winner
is determined by elapsed time and discuss the tools that
are used to measure it. If possible, show students a stopwatch
or a watch with a timer function and have them look at its
display. Ask what degree of accuracy (for example, to the
nearest minute, second, tenth of a second, hundredth of
a second, etc.) could be measured using it. Using race
results from your school or the following list, ask students
to read and explain each time and say who was the winner:
Bantam Girls 100 m: Runner A, 13.9 s; Runner B, 14.2 s;
Runner C, 13.8 s.
Sample Discourse
“Which runner won the race? How do you know?”
• Runner C took the least time and so won the race. I know
that 13.8 is 13 and 8 tenths and that 13.9 is 13 and 9 tenths.
13.8 is one-tenth less time.
• You know that runner B came last because the number
of whole seconds, 14, is greater than 13.
“Would races in the Olympics or other world events be
measured to the nearest tenth of a second? Why or why not?
• I think they would use hundredths of a second because there
are many racers. With tenths there would be lots of ties.
• I think they measure to hundredths or thousandths because
they use computer timers and they are a lot more accurate.
Tell students that, in this lesson, they will be comparing
and ordering race times and other decimal numbers
to thousandths.
2.
Teaching and Learning (Whole Class/Pairs) ➧ 15–20 min
Ask students to turn to Student Book page 56. As a class,
read the information about races and the information in
the table, directing students’ attention to the way in which
minutes and seconds are expressed as elapsed time, with a
colon separating the minutes on the left from the seconds
on the right. Ask them to say why a zero has been placed
in the thousandths place in the Thorpe/Ives time. They
should respond that it is needed to indicate the degree of
the measurement’s accuracy. If it was not present, in other
words, the reader might think that the measurement had
only been taken to the nearest hundredth of a second.
Have the class read the central question.
Form students into pairs and distribute several place
value charts, number lines, and thousandths grids to each.
With their partners, have them read and discuss Tara’s
solution, and then answer prompts A and B. As you
observe the pairs working, interact by asking students
to explain their ordering strategy.
Copyright © 2006 by Thomson Nelson
Reflecting
Here students are asked to generalize their strategy
for comparing decimal thousandths. They should realize
that their previously learned skills of modelling decimal
thousandths on thousandths grids and number lines can
be as effective for ordering as place value charts.
Lesson 8: Comparing and Ordering Decimals
49
02b-NEM6-ON-TR-CH02b 7/18/05 2:49 PM Page 50
Answers
A. 1:26.082, 1:26.216, 1:26.220, 1:26.501, 1:27.586
B. Leitner/Resch
1. For example: It’s a very fast sport and the differences
between being first, second, or even last are based on
very tiny amounts of time.
2. For example: I first compared digits in the same place
value from left to right. To double-check my results,
I also compared the times on a number line.
3. For example: I agree. The numbers can be placed on a
number line and compared by their positions on it. Or,
since the ones digits are all the same, the decimals can
be compared by colouring them in on 1000ths grids.
The grid that has the most surface coloured is the
larger decimal.
4. a) 2:54.162 < 2:54.254
b) 2:52.464, 2:52.785, 2:52.865, 2:54.162, 2:54.254;
for example, I placed the numbers on a number line.
c) Otto
5. 3:12.987, 3:14.5, 3:21.175, 4:1.122
6. 0.613 kg
7. 2.198 km, since 1315 m is only 1.315 km and
1.315 < 2.198
8. a) 0.035, 0.305, 1.024, 1.204
b) For example, I could change them to 2.035, 1.305,
1.124, and 0.204
9. For example, because 2 ones is always larger than 1 one,
so even 1.999 is smaller than 2.000.
10. 19 beginning with 3.61 and ending with 3.79
11. any of 1.398 kg, 1.399 kg, or 1.400 kg
3.
Consolidation ➧
Key Assessment of Learning Question (See chart on next page.)
20–30 min
Checking (Whole Class)
Closing (Individual)
For intervention strategies, refer to Meeting Individual
Needs or the Assessment for Feedback chart.
4. Ask students why it would be a good strategy to
divide the times into two groups before comparing.
Ask several students to explain the strategy they used
to order the times.
Have students complete the following prompt in their
journal: “The steps I follow when ordering decimal
thousandths are…”
• I begin with the largest place value on the left and compare
the digits. If the digits are the same I move to the next place
value to the right until I see that one digit is larger than
the other.
Practising (Individual)
Have number lines and thousandths grids available for those
students who want to use them.
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Chapter 2: Numeration
Copyright © 2006 by Thomson Nelson
02b-NEM6-ON-TR-CH02b 7/18/05 2:49 PM Page 51
Assessment of Learning—What to Look for in Student Work…
Assessment Strategy: written answer
Application of Learning
Key Assessment Question 8
a) Order these decimal numbers from least to greatest. 1.024
0.305
1.204
b) Change one digit in each number so that the order of the numbers reverses.
1
0.035
2
• demonstrates limited ability to
transfer mathematical knowledge
and skills to new contexts (e.g.,
has difficulty using place value
relationships to solve unfamiliar
or non-routine problems)
• demonstrates some ability to
transfer mathematical knowledge
and skills to new contexts (e.g.,
demonstrates some ability to use
place value relationships to solve
unfamiliar or non-routine problems)
3
4
• demonstrates considerable
ability to transfer mathematical
knowledge and skills to new
contexts (e.g., demonstrates
considerable ability to use place
value relationships to solve unfamiliar
or non-routine problems)
• demonstrates sophisticated
ability to transfer mathematical
knowledge and skills to new
contexts (e.g., demonstrates
sophisticated ability to use place
value relationships to solve unfamiliar
or non-routine problems)
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 gather real data that is reported in decimal
thousandths, order the numbers, and explain their strategy.
Examples of real data could be the amount of gas used to
heat their homes each month, the standings of their favourite
baseball team, yield changes on bonds, and so on.
Skills Bank
Student Book p. 61, Questions 17, 18, & 19
Problem Bank
Student Book p. 62, Question 10
Chapter Review
Student Book p. 65, Question 13
Workbook
p. 18, all questions
Nelson Web Site
Visit www.mathK8.nelson.com and follow
the links to Nelson Mathematics 6, Chapter 2.
Math Background
This lesson continues to develop concepts of decimal
numbers. Students are not just expected to order decimal
thousandths by looking at place values one at a time, but
are given the opportunity to look at the complete number
and consider where it is in relation to another number,
either using a place value chart or a number line.
Decimal Place Value
Chart (thousands)
Masters Booklet p. 44
Copyright © 2006 by Thomson Nelson
Number Lines, Masters
Booklet p. 37
Thousandths Grid,
Masters Booklet p. 57
Optional: Chapter 2
Mental Math p. 65
Lesson 8: Comparing and Ordering Decimals
51