CHAPTER 9
5
STUDENT BOOK PAGES 276–277
Multiplying Multiples
of Ten by Tenths
Direct Instruction
Goal Multiply to calculate the decimal portion of a multiple of 10.
Prerequisite Skills/Concepts
Expectations
• Divide whole number multiples
of 10 by 10.
• multiply decimal numbers to tenths by whole numbers, using concrete materials
[, estimation,] algorithms [, and calculators]
• solve problems involving the multiplication of whole numbers and decimal
numbers, using a variety of strategies
Assessment for Feedback
What You Will See Students Doing…
Students will
When Students Understand
If Students Misunderstand
• multiply decimal numbers to tenths by whole
numbers, using a variety of computational strategies
• Students will correctly multiply 2- and 3-digit
multiples of 10 by tenths using a place value
chart, mental math, and pencil and paper.
• Students will have the correct digits in the product
but place the decimal incorrectly. Continue to have
students represent the whole number on the place
value chart and describe the movement to the right
or left. Have them explain if the product should be
larger or smaller than the original whole number.
Preparation and Planning
Pacing
5–10 min Introduction
15–20 min Teaching and Learning
20–30 min Consolidation
Masters
•Place Value Chart, Masters
Booklet p. 41
•Optional: Chapter 9 Mental Math
p. 60
•Optional: Scaffolding pp. 68–69
Workbook
p. 83
Key
Assessment
of Learning
Question
Question 5, Knowledge
and Understanding
Mathematical Computational Strategies,
Processes
Representing, Reflecting,
Problem Solving
Copyright © 2006 by Thomson Nelson
Meeting Individual Needs
Extra Challenge
• Challenge students to solve problems that contain 3-digit numbers that
are not multiples of ten; for example:
There are 675 students at Algonquin school. A survey found that fourtenths of the students bring their lunch to school every day, two-tenths
always buy food in the cafeteria, and the rest do both. How many students
both bring food and buy food?
Extra Support
• Have students use patterns to reinforce their understanding of multiplication
by tenths. For example:
0.1 × 320
0.2 × 320
0.3 × 320
0.4 × 320, and so on to 1 × 320.
• Students can write expressions, using whole numbers only, that are
equivalent to the following:
a) 0.6 × 360
b) 0.8 × 380
c) 0.2 × 670
Lesson 5: Multiplying Multiples of Ten by Tenths
33
1.
Introduction (Whole Class)
➧ 5–10 min
Display a table such as the one below.
How Students Get to School
1
2
1
8
1
8
1
4
Bus
Walk
Bicycle
Car
Have students describe the data in a number of different ways.
Sample Discourse
“Half of the students come to school by bus. How can this
be expressed as a decimal?”
• This is 0.5 of the population of the school.
“If the population of the school is 100, how many students
come by bus? How many come by bus if the population is
200? 1000? Explain how you would calculate these numbers.”
• If the population is 100, then 50 students come by bus,
1
2
because of 100 is 50.
5
10
50
100
• I know that is the same as , so 50 students would
ride by bus. If the population were 200, just double that
amount (100), and if the population were 1000, then
multiply the number by 10 (500) because 1000 is 100 × 10,
so the number of students taking the bus would be 10 times.
“How many students come by car, and how many ride
their bikes, if the school population is 1000? Explain
your calculation.”
1
1
• of 1000 is 250; of 1000 is half that, so 125.
4
2.
8
Teaching and Learning (Pairs/Whole Class) ➧ 15–20 min
Ask students to turn to Student Book page 276 to read the
information from the inset map to determine the population
of Maple School and read the information about youth
fitness. Have students cover Jorge’s Method with a piece
of paper, and then work with a partner to discuss how they
would answer the central question. Have pairs share their
results and the strategies they used to find them. Record
several of the strategies on the chalkboard or overhead.
As a class, read Jorge’s Method. Ask students to compare his
thinking to the strategies they used. How are they different,
and how are they the same? How did Jorge use skills learned
34
Chapter 9: Multiplying Decimals
in previous lessons to calculate? What new step did he
use to find 0.3 of the students?
Call students’ attention to the place value chart to
ensure they understand that the product gets 10 times
smaller each time a factor gets 10 times smaller.
Reflecting
Here students explain the connections between multiplying
by 0.01 and multiplying by any decimal tenth.
Copyright © 2006 by Thomson Nelson
3.
Consolidation ➧ 20–30 min
Checking (Whole Class)
For intervention strategies, refer to Meeting Individual
Needs or the Assessment for Feedback chart.
4. Take some time to discuss the relationship between
4 a) and 4 b). Have students make up other
expressions (e.g., 670 × 0.1) and write them as
division expressions.
Practising (Individual)
5. Have students explain how they calculated.
8. Students should complete each solution using the
different strategies. If extra support is required, guide
those students and provide copies of Scaffolding
pp. 68–69.
Related Questions to Ask
Ask
Possible Responses
About Question 6a:
• Diane solved this problem by
multiplying 45 × 6. Is this a
reasonable strategy? Why?
Key Assessment of Learning Question (See chart on next page.)
Answers
1. For example, yes, because each time the first factor
gets ten times smaller (divided by 10), the product gets
10 times smaller. The digits in the product move to the
right one place each time.
2. For example, 0.1 × something is one tenth of a group
of that thing; that’s the same as dividing by 10.
3. For example, yes, because 0.6 is 6 tenths, and 6 tenths
is 6 times as much as 1 tenth. It’s easy to take 1 tenth
by just moving digits, and then you can multiply by 6.
4. a) 30 students; for example, to multiply 0.1 × 300,
I move the digits of 1 × 300 one place to the right:
0.1 × 300 = 30.
b) 30 students; for example, 0.1 × 300 is the same
as 110 of 300, which is the same as dividing
300 by 10: 300 ÷ 10 = 30.
5. a) 48
b) 132
c) 246
d) 126
6. a) 270 students
b) For example, 0.6 is close to 0.5, which is half, and
half of 450 is 225, which is fairly close to 270.
7. a) 1400 mL
b) 140 mL
(Lesson 5 Answers continued on p. 80)
Copyright © 2006 by Thomson Nelson
About Questions 8:
• Which method do you think is
most efficient when multiplying
by 0.5? Explain.
• Yes. She multiplied 450 × 0.01
mentally to get 45, and then she
just needed to multiply by 6.
• Yes, 0.6 = 6 × 0.01, so she could
multiply mentally by 0.01 first,
and then use her pencil to
multiply by 6.
• I think taking half of the number
is the most efficient method.
Finding half is the same as
dividing by 2 and it is easy
to divide by 2 mentally.
• Dividing by 2 has fewer steps,
so that would be the most
efficient way.
• It depends on the number that is
being multiplied. If I multiplied
60 × 0.5, it would be easy to
find half of 60. But if it were
9370 × 0.05, either way would
be okay. It would be just as easy
to multiply 937 × 5 as it would
be to find half of 9370.
Closing (Individual)
Have students summarize their learning by completing the
following prompt in their journal: “Two ways that I could
multiply 740 × 0.4 are …”
Multiply 740 × 0.01 = 74, and then multiply 74 × 6 = 444.
Multiply 740 × 6 = 4440, and then move the digits to the
right one place to get 444.
Lesson 5: Multiplying Multiples of Ten by Tenths
35
Assessment of Learning—What to Look for in Student Work…
Assessment Strategy: short answer
Knowledge and Understanding
Key Assessment Question 5
• Calculate.
a) 0.1 × 480
b) 0.6 × 220
(Score responses out of 4.)
c) 0.2 × 1230
d) 0.9 × 140
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 calculate one-tenth and six-tenths of the
volume of 5 containers (soda, juice, tomato sauce, soups,
and so on). Remind students to record the volume of each
container in mL, rounded to the nearest multiple of ten.
Skills Bank
Student Book p. 285, Questions 13, 14, 15, & 16
Problem Bank
Student Book p. 286, Question 7
Chapter Review
Student Book p. 289, Questions 12, 13, & 14
Workbook
p. 83, all questions
Nelson Web Site
Visit www.mathK8.nelson.com and follow
the links to Nelson Mathematics 6, Chapter 9.
Place Value Chart,
Masters Booklet p. 41
Math Background
When students previously multiplied tenths by whole
numbers, they understood the multiplication process as
repeated addition (e.g., 0.2 × 3 = 0.2 + 0.2 + 0.2 = 0.6).
The product is 3 times the original number. This lesson
extends operational understanding to include the idea that
multiplying by decimal tenths results in a product that is
smaller than the original number. Although 6 × 0.2 (6 groups
of 0.2) results in the same product as 0.2 × 6 (two-tenths
of 6), the model for each will be different. Students come
to understand that finding 0.1 of a whole number will
help them to find 0.2 or 0.3, and so on, of the same whole
number. Although the lesson provides opportunity for
students to multiply tenths by multiples of ten, some
students can extend this skill to multiply any 3-digit
number by tenths.
36
Chapter 9: Multiplying Decimals
Optional: Scaffolding
(Master) pp. 68–69
Optional: Chapter 9
Mental Math (Master)
p. 60
Copyright © 2006 by Thomson Nelson