More Multiplication
Facts Practice
Objectives To give a 50-facts test and record the results;
and
to provide practice with multiplication facts.
a
www.everydaymathonline.com
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Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
Math Boxes 3 4
• Rename a fraction as an equivalent fraction
and as a percent. Math Journal 1, p. 60
Students practice and maintain skills
through Math Box problems.
[Number and Numeration Goal 5]
• Solve multiplication facts. [Operations and Computation Goal 3]
• Use data to create a line graph. [Data and Chance Goal 1]
Study Link 3 4
Math Masters, p. 82
Students practice and maintain skills
through Study Link activities.
• Find the median and mean of a data set. [Data and Chance Goal 2]
Key Activities
Students take their first 50-facts test
of record. They graph individual and
optional class scores.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Finding the Mean
Math Masters, p. 83
centimeter cubes
Students “even out” stacks of cubes to find
the mean of a data set.
ENRICHMENT
Comparing the Mean and Median
Math Masters, p. 84
calculator
Students apply the concepts of mean and
median to analyze baseball players’ salaries.
Ongoing Assessment:
Recognizing Student Achievement
Use Mental Math and Reflexes. [Operations and Computation Goal 3]
Materials
Study Link 33
Math Masters, pp. 81, 411, 414, and 415;
pp. 416 and 417 (optional)
transparency of Math Masters, p. 414
(optional) slate chart paper calculator pen or colored pencil
Advance Preparation
If you choose to do the optional Part 1 activity of graphing class results, use Math Masters, pages 416 and
417 as a model to draw a classroom graph on a large sheet of chart paper. Alternately, tape copies of these
masters together to make a smaller version of the graph. Copy Math Masters, page 414 for each student.
Copy and cut apart Math Masters, page 81 so each student has one answer sheet for the Math Message.
Teacher’s Reference Manual, Grades 4–6 p. 271
Lesson 3 4
175
Mathematical Practices
SMP1, SMP2, SMP4, SMP6, SMP8
Content Standards
Getting Started
4.OA.1
Mental Math and Reflexes
Math Message
Pose multiplication facts and extended facts.
Suggestions:
4 ∗ 4 = 16
6 ∗ 5 = 30
7 ∗ 3 = 21
8 ∗ 3 = 24
Take an answer sheet (Math Masters,
page 81) and complete it.
30 ∗ 9 = 270
60 ∗ 7 = 420
90 ∗ 90 = 8,100
60 ∗ 50 = 3,000
6 ∗ 7 = 42
5 ∗ 7 = 35
9 ∗ 8 = 72
8 ∗ 6 = 48
Study Link 3 3 Follow-Up
Students describe how they completed the
multiplicative comparison statements in
Problems 7–12.
Ongoing Assessment:
Recognizing Student Achievement
Mental Math
and
Reflexes
Use Mental Math and Reflexes to assess students’ automaticity with
multiplication facts. Students are making adequate progress if they demonstrate
automaticity with the
and
problems. Some students may
demonstrate automaticity with the extended facts in the
problems.
[Operations and Computation Goal 3]
1 Teaching the Lesson
Math Message Follow-Up
(Math Masters, p. 81)
Date
LESSON
34
Time
Math Message
Ask students to calculate another typical score, the mean.
1. Find the total of all the scores.
Name
Name
Date
Date
Ms. Chen’s students took their first
50-facts test. These are their scores
for the first minute of the test.
Ms. Chen’s students took their first
50-facts test. These are their scores
for the first minute of the test.
26%, 8%, 36%, 18%, 18%, 20%, 40%,
10%, 22%
26%, 8%, 36%, 18%, 18%, 20%, 40%,
10%, 22%
20 %
22 %
1.
What is the median score?
1.
What is the median score?
2.
What is the mean score?
2.
What is the mean score?
2. Count the number of scores that make up the sum.
%
%
Name
Name
Date
Date
Ms. Chen’s students took their first
50-facts test. These are their scores
for the first minute of the test.
Ms. Chen’s students took their first
50-facts test. These are their scores
for the first minute of the test.
26%, 8%, 36%, 18%, 18%, 20%, 40%,
10%, 22%
26%, 8%, 36%, 18%, 18%, 20%, 40%,
10%, 22%
1.
What is the median score?
1.
What is the median score?
2.
What is the mean score?
2.
What is the mean score?
3. Divide the sum of the scores by the number of scores. 22
The result is the mean test score. Ask: Are the median and mean
test scores fairly close to each other? yes As indicators of typical
values, the median and mean of a data set are often close but may
be skewed differently by extreme values.
To support English language learners, discuss the everyday and
mathematical meanings of the words mean and average.
py g
g
p
%
%
%
%
Math Masters, p. 81
EM3MM_G4_U03_072-105.indd 81
176
ELL
Ask students to help you find the “typical” or median test score.
Have them order the test scores from least to greatest and find the
middle number. 20
Teaching Master
Name
WHOLE-CLASS
DISCUSSION
1/11/11 12:50 PM
Unit 3 Multiplication and Division; Number Sentences and Algebra
Administering a
WHOLE-CLASS
ACTIVITY
Teaching Aid Master
Name
50-Facts Test
Date
50-Facts Test 2
(Math Masters, p. 411)
36
0
16
18
56
14
36
15
8
24
63
42
15
6º6=
Briefly review the procedure for taking the test as described on
page 171. After reviewing the procedure, pass out 50-Facts Test 2
and begin.
5º0=
4º4=
6º3=
8º7=
2º7=
NOTE The 50-facts test should not be used for grading purposes. These tests
are one type of screening tool. They will help identify any students who have not
yet memorized the multiplication facts. You can revisit these tests in the optional
Part 3 Extra Practice activities in Lessons 3-10, 4-10, 5-10, 6-10, 7-8, 8-2, 9-6,
11-3, and 12-6. The 50-Facts Test routine can be used to show students’
progress over time.
Recording and Graphing
Time
WHOLE-CLASS
ACTIVITY
Individual Test Results
4º9=
5º3=
8º1=
3º8=
7º9=
6º7=
3º5=
4º7=
4º2=
5º8=
5º9=
2º5=
8º8=
4º8=
6º8=
7º3=
9º6=
7º4=
4º3=
9º3=
1-Minute Score:
50
3-Minute Score:
50
=
=
28
8
40
45
10
64
32
48
21
54
28
12
27
100
100
8º3=
6º5=
5º5=
9º8=
8º2=
7º8=
8º6=
9º7=
3º3=
7º5=
9º4=
4º5=
24
30
25
72
16
56
48
63
9
35
36
20
7º7=
6º9=
4º6=
3º6=
9º5=
9º9=
8º5=
7º6=
5º4=
3º7=
9º2=
8º9=
49
54
24
18
45
81
40
42
20
21
18
72
=
=
(Math Masters, pp. 414 and 415)
Have students correct their tests and record the one-minute and
three-minute scores on their test sheets.
Math Masters, p. 411
EM3MM_G4_U03_072-105.indd 411
11/10/10 1:57 PM
Review the graph on Math Masters, page 414, using a
transparency if available.
Discuss the title and how the axes are labeled.
Show students how to enter the date and how to graph their
scores with dots, using pencil for the one-minute scores and
pen or colored pencil for the three-minute scores.
If students take another 50-facts test, they will mark the results
on the graph and draw line segments to connect the points on
their grids, using pencil for the one-minute scores and pen or
colored pencil for the three-minute scores. When this master is
filled up, a copy of Math Masters, page 415 can be taped to it. This
way, students can keep track of their progress throughout the
school year if they continue taking 50-facts tests.
Recording Individual
Individual student’s test scores
(Math Masters, pages 414 and 415)
Teaching Aid Master
Name
Date
Time
My 50-Facts Test Scores
Write the date on the bottom line. Using a pencil, make a dot above each date
to record your 1-minute score. Using a pen, make a dot above each date to record
your 3-minute score. Connect the pencil dots. Then connect the pen dots.
Score
100% 50
WHOLE-CLASS
ACTIVITY
One-Minute Test Results
on the Class Graph (Optional)
(Math Masters, pp. 416 and 417)
90% 45
Sample student answer:
80% 40
70% 35
60% 30
(3-minute scores)
50% 25
From this point on, the 50-facts tests will appear only in Part 3 as
Extra Practice opportunities. You may choose to use them for your
whole class, or only for those students who need additional practice
with basic multiplication facts. If you expect that only a few
students will continue taking the tests, you may choose to skip this
optional activity of graphing the class results.
40% 20
30% 15
(1-minute scores)
20% 10
10%
5
0%
0
Date10
5 10 15
Math Masters, p. 414
Lesson 3 4
177
Teaching Aid Master
Name
Date
Time
Class 50-Facts Test Scores
Write the date on the bottom line. Make a dot above each date to record each student’s
1-minute score. On the gridline above each date, mark “M” for the class median score and
“A” for the class mean, or average, score.
Score
Ask students to write raw and percent scores for the
one-minute part on slips of paper and pass them in. Then you
call out the numbers, and students plot the scores on the class
graph. This allows you to point out any errors in converting
raw scores to percent scores.
100% 50
90% 45
80% 40
70% 35
Sample class answers for
1- minute scores:
60% 30
Have students turn in their papers, and you plot the scores
yourself after class.
50% 25
40% 20
After plotting the class scores, have students find the median and
calculate the mean for the day’s scores. Mark “M” for median and
“A” for mean, or average, on the appropriate vertical scale. Later
you can compare these landmarks with those of previous tests.
To monitor the progress of the entire class, use different colors to
connect the median and mean scores for each test administration.
M
A
M
A
30% 15
20% 10
10%
5
0%
0
Date10
Use a large copy of Math Masters, pages 416 and 417 to record
the one-minute scores, preserving the anonymity of students. Here
are some ways to collect and graph the class results:
5 10 15
Math Masters, p. 416
2 Ongoing Learning & Practice
Class’s test scores (optional)
(Math Masters, pages 416 and 417)
Math Boxes 3 4
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 60)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 3-2. The skill in Problem 5
previews Unit 4 content.
Writing/Reasoning Have students write a response to the
following: Explain how you solved Problem 3c. Sample answer:
The part of the circle graph that represents apples is bigger than
the part that represents peaches.
Student Page
Date
Time
LESSON
Math Boxes
3 4
䉬
1.
Complete.
a.
Sample answers:
2.
Name four multiples of 5.
Rule:
5 , 10 , 15 , 20
b.
Complete the “What’s My Rule?” table
and state the rule.
in
out
⫺156
Name four multiples of 9.
502
346
1,238
1,082
1,083
9 , 18 , 27 , 36
9
3.
a.
b.
c.
d.
4.
162–166
Mr. Rosario’s fourth graders collected data about their favorite fruits.
bananas
grapes
Which kind is preferred least?
Do more people prefer apples or peaches? apples
1
About ᎏᎏ of the students prefer apples .
4
Favorite Fruits
Which kind of fruit do most students prefer?
Name as many line segments as you can
in the figure below.
E
F
G
5.
EF
៮៮៮, EG
៮៮៮, EH
៮៮៮, FG
៮៮៮, FH
៮៮៮, GH
៮៮៮
90
0.007
0.5
Home Connection Students find missing factors in
multiplication facts. They also write their own
mystery-number problem involving multiplication facts
and solve multiplicative comparison problems.
bananas
apples
0.63
0.007
0.5
0.63
0.7
32 33
Math Journal 1, p. 60
178
INDEPENDENT
ACTIVITY
(Math Masters, p. 82)
Put these numbers in order from smallest
to largest.
0.7
H
peaches
grapes
927
715
1,444
871
1,600
Study Link 3 4
Unit 3 Multiplication and Division; Number Sentences and Algebra
Study Link Master
Name
3 Differentiation Options
Finding the Mean
34
5–15 Min
(Math Masters, p. 83)
To explore finding the mean using a concrete model, have students
use centimeter cubes to build a bar graph of a data set and “even
out” the centimeter cubes to find the mean of the data set.
1.
I am thinking of a mystery number. If I multiply
it by 4, the answer is 24. What is the number?
6
2.
I am thinking of another number. If I multiply it
by 3, the answer is 24. What is the number?
8
3.
I am thinking of a mystery number. 24 is 4 times
as many as this number. What is the number?
6
4.
I am thinking of a mystery number. This number
is 7 times as many as 3. What is the number?
21
5.
Write your own mystery number problem.
INDEPENDENT
ACTIVITY
Comparing the Mean
20
4º5=
6.
7.
18
8.
7º7=
9
9.
10.
35 =
11.
28 =
5
=6º3
49
7
º 2 = 18
7
7
º 4 = 20
6
18 =
2
18 =
5
4
º5
º4
º3
º 7 = 49
º9
º 7 = 35
º 7 = 28
Sample answers:
Practice
12.
13.
14.
Have students describe the process they used to find the mean.
16
Answers vary.
Fill in the missing numbers.
In this activity, there are 21 books in all (5 + 2 + 6 + 4 + 0 + 1 +
3 = 21). Students even out the centimeter cubes by sharing them
equally among the 7 students’ backpacks. After moving the cubes,
they end up with 21 / 7, or 3 books in each student’s backpack.
The number model for finding the mean of the data set is
21 / 7 = 3.
ENRICHMENT
Time
Mystery Numbers
Find the mystery numbers.
INDEPENDENT
ACTIVITY
READINESS
Date
STUDY LINK
10 , 15 , 20 , 25
List all the factors of 24. 1, 2, 3, 4, 6, 8, 12, 24
List the factors of 24 that are composite. 4, 6, 8, 12, 24
Name 4 multiples of 5.
Math Masters, p. 82
EM3MM_G4_U03_072-105.indd 82
11/10/10 1:57 PM
5–15 Min
and Median
NOTE For practice
with pictographs, see
www.everydaymathonline.com.
(Math Masters, p. 84)
To apply students’ understanding of mean and median,
have them examine and compare baseball salaries based
on these data landmarks.
Teaching Master
LESSON
34
䉬
Teaching Master
Date
Time
Name
Compare the Mean and Median
LESSON
34
䉬
Imagine that you are given a chance to play for a professional baseball team.
Before you meet the owner, you will need to think about your salary demands.
73 75
Player
Salary
Brown, Kevin
$15,714,286
Lofton, Kenny
1.
Player
Salary
Cairo, Miguel
$900,000
Matsui, Hideki
$7,000,000
Clark, Tony
$750,000
Posada, Jorge
$9,000,000
Flaherty, John
$775,000
Rodriguez, Alex
Giambi, Jason
$12,428,571
Gordon, Tom
$3,500,000
Jeter, Derek
$18,600,000
$3,100,000
Number of Books
1.
Mito
Kate
Ezra
Lina
Luz
Nick
5
2
6
4
0
1
3
Place centimeter cubes on the bar graph below to show the number of books
in each student’s backpack.
Books in Backpacks
6
Sierra, Ruben
Wilson, Enrique
5
$1,000,000
$700,000
Sample answers:
Would you want your salary to be based on the mean or the median of these
players’ salaries? Explain your answer.
When news organizations report the salaries of professional teams, they
usually use the median. Why do you think they report the median instead of
the mean?
The median because the mean salary would be better for
attracting players, but the median salary might keep players
from expecting too much money.
4
3
2
1
0
John
Mito
Kate
Ezra
Lina
Luz
Nick
Students
2.
Now move the cubes around so that all of the students have the same
number of books.
How many books are in each student’s backpack now?
3
books
When you “even out” the number of books so that each student’s backpack
has the same number of books, you are finding the mean or the average of
the data set.
If you were an owner of a team, would you rather report your players’ mean
or median salaries? Explain your answer.
Math Masters, p. 84
John
$22,000,000
Salaries of sports superstars make the mean higher, so the
median is more likely what the average player earns.
3.
Find the Mean
75
On the mean because it is greater. The mean is about
$7,300,000, but the median is $3,500,000.
2.
Time
The table shows the number of books in several students’ backpacks.
Student
Below is a list of some 2004 New York Yankees players’ salaries.
Source: USA Today Salary Database
Date
Number of Books
Name
3.
Complete the statement.
3
The mean, or average, number of books in the students’ backpacks is
.
Math Masters, p. 83
Lesson 3 4
179
Name
STUDY LINK
34
Date
Time
Mystery Numbers
Find the mystery numbers.
1.
I am thinking of a mystery number. If I multiply
it by 4, the answer is 24. What is the number?
2.
I am thinking of another number. If I multiply it
by 3, the answer is 24. What is the number?
3.
I am thinking of a mystery number. 24 is 4 times
as many as this number. What is the number?
4.
I am thinking of a mystery number. This number
is 7 times as many as 3. What is the number?
5.
Write your own mystery number problem.
16
Fill in the missing numbers.
6.
4º5=
=6º3
7.
8.
º 4 = 20
18 =
7º7=
º 7 = 49
18 =
º9
10.
35 =
º5
º 7 = 35
11.
28 =
º4
º 7 = 28
Practice
12.
Name 4 multiples of 5.
13.
List all the factors of 24.
14.
List the factors of 24 that are composite.
82
,
,
,
Copyright © Wright Group/McGraw-Hill
º 2 = 18
9.
º3