Lesson
4
Expanded Addition
Problem Solving:
Using Bar Graphs to Display Data
Lesson 4 Skills Maintenance
Lesson Planner
Name
Vocabulary Development
Date
Skills Maintenance
Basic and Extended Addition Facts
expanded addition
bar graph
title
horizontal axis
vertical axis
scale
interval
Activity 1
Solve the basic and extended facts.
Skills Maintenance
1.
90 + 40
130
2.
6+5
11
3.
60 + 50
110
4.
7+8
15
5.
70 + 80
150
6.
8+9
17
7.
900 + 400
8.
700 + 800
9.
80 + 90
11.
800 + 900
1,300
170
1,700
1,500
13
10.
9+4
12.
600 + 500
1,100
Basic and Extended Addition Facts
Building Number Concepts:
Expanded Addition
In this lesson, students take expanded
addition one step further to solve two-digit
expanded addition problems.
Objective
Students will solve addition problems using
expanded addition.
Problem Solving:
sing Bar Graphs to
U
Display Data
Students learn about bar graphs and
how they are used to present data.
Objective
Students will answer questions about
bar graphs.
Homework
Students write numbers and addition
problems in expanded form, and students
complete a chart of basic and extended
addition facts. In Distributed Practice,
students review basic and extended
addition facts.
34 Unit 1 • Lesson 4
12
Unit1•Lesson4
Skills Maintenance
Basic and Extended Addition Facts
(Interactive Text, page 12)
Activity 1
Students review basic and extended addition
facts. Students should solve the problems mentally,
if possible.
Lesson
Building Number Concepts:
Expanded Addition
How do we add using expanded form?
(Student Text, page 19)
Build Vocabulary
Use the model to demonstrate how adding
numbers in expanded form is called expanded
addition . Explain that expanded addition helps
us find sums by using place value.
Demonstrate
Engagement Strategy: Teacher Modeling
Demonstrate adding 43 + 26 with place-value
coins, and in expanded form, in one of the
following ways:
: Use the mBook Teacher
Edition for Student Text, page 19. ​
Overhead Projector: Display
Transparency 3 on an overhead
projector, and use the transparent
place-value coins. Modify as
discussed.
Board: Draw a Tens/Ones table on
the board. Modify as discussed.
•Use coins to model 43, then 26 in the Tens/
Ones Table. ​
•Show students that we use the coins to help
us find the sum of the numbers 43 and 26.
We add the tens from both numbers, then we
add the ones from both numbers. Using the
place-value coins makes this easy to see.
•Ask if anyone can find the answer using
mental math. Then collect all the tens in
the tens column and all the ones in the ones
column to show the sum is six tens
and nine ones.
•Elicit from students that the sum of six tens
and nine ones is equal to 60 + 9, or 69.
4
Expanded Addition
Problem Solving:
Using Bar Graphs to Display Data
Expanded Addition
Vocabulary
How do we add using expanded form?
expanded addition
Rememberthatwemodeladditionwithplace-valuecoins.
Look at how the numbers 43 and 26 are shown with the coins.
Tens
We can use the coins to help us find the sum of the numbers
43 and 26. We add the ones coins from both numbers, then
we add the tens from both numbers.
Ones
10
10
1
10
10
1
10
10
1
1
1
1
1
1
1
43
When we add numbers in expanded form, we use
expanded addition . There are steps to solving problems in
expanded addition.
+ 26
Example 1
Add using expanded addition.
STEP 1
Write the addition problem
in expanded form.
Now, we can add by place value
like we did with the coins.
STEP 2
Add the ones column.
Then add the tens column.
STEP 3
Write the sum in standard form.
Apply Skills
Turn to Interactive Text,
page 13.
40 3
43
+ 26 S + 20 6
40 3
+ 20 6
9
40 3
+ 20 6
60 9 = 60 + 9
60 + 9 = 69 The sum is 69.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
19
19
Unit 1 • Lesson 4
•Show how to add 43 + 26 using expanded
addition.
STEP 1
•Show 43 + 26. Explain how the number 43
expands to 40|3 and the number 26 expands to
20|6. ​
STEP 2
•Point out that the sum of the ones is 9, and
the sum of the tens is 60. Show students that
each sum is written underneath the appropriate
place-value column. The sum of 43 + 26 is
written 60 + 9. ​
STEP 3
•Show that the sum is rewritten in standard form
as 69. ​
Unit 1 • Lesson 4 35
Lesson 4
Lesson 4 Apply Skills
Apply Skills
Date
Unit 1
Name
Apply Skills
Expanded Addition
(Interactive Text, page 13)
Activity 1
Add using expanded addition. Then write the sums in standard form.
Have students turn to page 13 of the Interactive
Text and complete the activity.
Model
Activity 1
1.
Students find the sum of two-digit addition
problems. Monitor students’ work as they
complete the activity.
2.
Watch for:
3.
•Are students writing each problem in
expanded form correctly?
4.
•Are students adding ones to ones and tens
24
+ 31
20 4
+ 30 1
50 5
Answer
55
37
+ 42
+
30 7
40 2
70 9
Answer
79
61
+ 25
+
60 1
20 5
80 6
Answer
86
74
+ 13
+
70 4
10 3
80 7
Answer
87
68
+ 31
+
60 8
30 1
90 9
Answer
99
to tens?
•Are students writing the answer in standard
form to the right of the problem?
Reinforce Understanding
Remind students that they can review
lesson concepts by accessing the
online mBook Study Guide.
36 Unit 1 • Lesson 4
Unit1•Lesson4
13
Lesson 4
Problem Solving: Using Bar Graphs to Display Data
What are bar graphs, and how are they used?
Data can be displayed in many different ways. One common way to
present data is with a bar graph . In this lesson, we begin following
theCDsalesofabandcalledTheScatterPlotsbylookingatthebar
graph below.
Problem Solving:
Using Bar Graphs to Display Data
Vocabulary
bar graph
title
horizontal axis
vertical axis
scale
interval
The title of the bar graph tells
us that the graph shows the
CDsalesfortheScatterPlots
from January through April.
What are bar graphs, and how are
they used?
Number of CDs Sold
(Student Text, pages 20–21)
Demonstrate
•Direct students’ attention to page 20 in
the Student Text. Students are introduced
to the fictitious band the Scatter Plots. The
CD sales for the Scatter Plots over a fourmonth period are presented in a bar graph .
The Scatter Plots CD Sales
January–April
500
400
300
200
100
0
January
February
March
Month
April
The line across the bottom of
the graph labeled Month is
the horizontal axis .
The line along the left side of the graph
labeled Number of CDs Sold is the vertical
axis . Notice the numbers along this axis:
0, 100, 200, 300, 400, and 500. This is
the scale of the graph. The numbers in the
scale are changing by 100, so the interval
of the scale is 100.
•Point out the title of the bar graph. Explain
that a good title summarizes what the
graph shows.
•Point out the title: The Scatter Plots CD
Sales January–April. So we know that
the graph will show the number of CDs sold.
Point out that the title also tells us that
the graph will show how many CDs were
sold in a certain time period because the
title refers to January–April.
•Next have students look at the information
in the graph. Explain that the line across the
bottom of the graph is the horizontal axis .
•Make observations about this part of
the graph with the students. Show how
the label, Months, describes the things that
are listed on the horizontal axis. Point out
that the month names are written along
the horizontal axis. They show the months
that CD sales were counted. Make sure
students notice the month names are evenly
spaced across the bottom of the graph.
20
20
Unit 1 • Lesson 4
•Next talk about the vertical axis and its labels.
Tell students that this is the line along the left
side of the graph.
•Make observations about this part of the graph
with students. Point out that the label is Number
of CDs Sold and that the numbers, 100, 200,
300, 400, and 500 are shown from the bottom
to the top. Observe that the numbers along the
vertical axis are evenly spaced by 100 and the
greatest number on the scale is greater than the
tallest bar on the graph.
Unit 1 • Lesson 4 37
Lesson 4
What are bar graphs, and how are
they used? (continued)
Demonstrate
•Explain to the students that the numbers
along the vertical axis make up the scale of
the graph. Because the numbers in the scale
are changing by 100, the interval of the
scale is 100.
Lesson 4
ThebargraphshowshowmanyCDstheScatterPlotssoldoveraperiod
of four months:
Month
January
February
March
April
CDs Sold
100
200
300
400
Understanding Scale and Interval
It is important to understand the scale of the graph. Notice the scale
of the bar graph ranges from 0 to 500, and the interval is 100. We can
think of this as counting by 100 from 0 to 500.
This scale and interval were selected because they do a good job of
representing the data shown in the graph.
Pay close attention
to the scale and
the interval.
Check for Understanding
Engagement Strategy: Pair/Share
Have students look at the graph as a whole.
Ask them to turn to a partner and generalize
about what the graph shows.
Listen for:
•There are four bars in the graph. They get
taller as you move from left to right.
•The bars seem to get taller by the same
amount each time.
Then have each pair work together to answer
the following questions.
Ask:
According to the list of data, how many CDs
were sold in January? (100)
What number does the bar for January
extend to in the bar graph? (100)
Repeat these questions for February, March,
and April. Point out that the bar for each month
in the graph extends to the number listed for
each month.
38 Unit 1 • Lesson 4
Problem-Solving Activity
Turn to Interactive Text,
page 14.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 1 • Lesson 4
21
21
Lesson 4 Problem-Solving Activity
Name
Problem-Solving Activity
Problem-Solving Activity
Using Bar Graphs to Display Data
(Interactive Text, page 14)
Use the bar graph to answer the questions.
Number of CDs Sold
Have students turn to Interactive Text, page 14.
The bar graph shows CD sales for the Hipster
Records’ band 4 Floors Up. Their CD sales
over a four-month period are given.
4 Floors Up CD Sales
May—August
500
400
300
200
100
0
May
June
July
August
Month
Watch for:
1.
•Can students identify the title of the bar
What is the title of the graph?
4 Floors Up CD Sales
graph?
2.
What is the label of the horizontal axis of the graph?
Month
•Are students able to distinguish between
3.
the horizontal axis and vertical axis?
What is the label of the vertical axis of the graph?
Number of CDs sold
•Do students understand the difference
4.
What is the scale of the vertical axis?
0, 100, 200, 300, 400, 500
between scale and interval?
5.
Reinforce Understanding
Remind students that they can review
lesson concepts by accessing the
online mBook Study Guide.
Date
What is the interval of the scale?
100
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
14
Unit1•Lesson4
Unit 1 • Lesson 4 39
Lesson 4
Lesson 4
Homework
Activity 1
Write the number in expanded form.
Homework
Model 49 40 + 9
Go over the instructions on page 22 in the
Student Text for each part of the homework.
1.
35
2.
529
3.
812
4.
375
5.
16,020
6.
45,999
7.
6,015
8.
4,007
See Additional Answers below.
Activity 2
Add using expanded addition. Then write the sum in standard form.
Model
28
20 8
+ 61 S + 60 1
80 9
Activity 1
Students practice writing numbers in expanded
form.
80 + 9 Answer= 89
1.
17
+ 82
2.
45
+ 33
3.
54
+ 22
4.
61
+ 16
5.
32
+ 25
6.
40
+ 49
See Additional Answers below.
Activity 3
Copy and complete the chart of basic and extended facts.
Activity 2
Basic Fact
Students use expanded addition to solve
problems.
Extended Fact
(BasicFact×100)
200 + 400
2+8
Extended Fact
(BasicFact×10)
20 + 40
20 + 80
9+1
2+7
90 + 10
20 + 70
900 + 100
200 + 700
3+3
30 + 30
9+8
90 + 80
60 + 50
300 + 300
900 + 800
2+4
Activity 3
6+5
Students complete a chart of basic and extended
addition facts.
200 + 800
600 + 500
Activity 4 • Distributed Practice
Add.
Activity 4 • Distributed Practice
1.
2+3
4.
2,000 + 3,000
5
5,000
2.
20 + 30
5.
7+4
50
11
3.
200 + 300
6.
700 + 400
500
1,100
Students practice finding the sums of basic and
extended addition facts.
Additional Answers
Activity 1
1. 30 + 5
2. 500 + 20 + 9
3. 800 + 10 + 2
4. 300 + 70 + 5
5. 10,000 + 6,000 + 0 + 20 + 0
6. 40,000 + 5,000 + 900 + 90 + 9
7. 6,000 + 0 + 10 + 5
8. 4,000 + 0 + 0 + 7
22
22
Unit 1 • Lesson 4
Activity 2
10 7 1.
+ 80 2
90 9
Unit 1 • Lesson 4
40 5 + 30 3
70 8
3.
50 4
+ 20 2
70 6
90 + 9 = 99 70 + 8 = 78 70 + 6 = 76
60 1 5.
30 2 6.
40 0
4.
+ 10 6
+ 20 5
+ 40 9
70 7
50 7
80 9
40 2.
70 + 7 = 77
50 + 7 = 57
80 + 9 = 89