Discovering Math: Arithmetic
Teacher’s Guide
Grade Level: K–2
Curriculum Focus: Mathematics
Lesson Duration: Three class periods
Program Description
Discovering Math: Arithmetic — From the concepts of adding and subtracting to strategies for
estimation, introduce young students to the basic procedures of computation.
Lesson Plan
Student Objectives
•
Demonstrate addition and subtraction of whole numbers through counting, sums to 100.
•
Solve real-world problems involving addition and subtraction of whole numbers through
the development of word problems, sums to 100.
•
Advanced students demonstrate basic estimation strategies for addition and subtraction
of money to the nearest dollar amount.
Materials
•
Discovering Math: Arithmetic video
•
Container of objects for counting (the objects should be large enough that a student handful
does not exceed 10)
•
Number cards document
•
Dice
•
Paper to write word problems
•
Weekly sales circular from food store
•
Calculators
•
Addition and Subtraction Problem-Solving Challenges (see below)
Procedures
1. Have two students come to the front of the room. Write the number 2 on the board. Then ask
another three students to come to the front of the room. Write the number 3 on the board. Ask
the students how many students are in the front of the room in all. Elicit response from students
that five students are in the front of the room. Write 2 + 3 = 5 on the board. Explain to students
that the 2 represents the first two students; the + means to add; the 3 represents the other
Discovering Math: Arithmetic
Teacher’s Guide
2
students who came to the front of the room; the = means equals; and the 5 represents the
number of students in all. Tell students that they used addition to find the sum.
2. Set up three stations to practice addition.
•
Station 1 — Students work in pairs. Give each pair a bucket of manipulatives; see
examples above in “Materials.” The first student takes a handful of manipulatives and
counts them. Both students write the number. The second student takes a handful of
manipulatives and counts them. Both students write the number. The students add the
two numbers to find the total. They can use the manipulatives to help find the sum.
Have students write a complete number sentence each time they complete the task.
•
Station 2 — Students work in pairs. Give each pair a set of number cards and have them
place the number cards face down on the desk. Each student picks a number card. Both
students write the numbers, add them together, and write an addition number sentence.
Have students continue until all the cards have been used in addition number sentences;
use numbers that match the ability level of the students.
•
Station 3 — Students work in pairs. Give each pair a set of dice (1–6 die for beginners,
7–12 die for students with a stronger grasp of addition). Have each student roll the dice.
Both students write the numbers rolled, add them together, and write an addition
number sentence.
When students become proficient at addition, they can work in groups of three or four and add
more than two digits at a time. Students can practice adding two-digit numbers by taking
bigger handfuls of manipulatives, choosing two cards and making two-digit numbers to add,
and rolling the dice twice to form a two-digit number. For students who are not yet proficient at
regrouping, manipulatives can be used to add and subtract the numbers.
3. Have six students come to the front of the room. Write the number 6 on the board. Ask four
students to sit down. Write the number 4 on the board. Ask the students how many students
are left standing at the front of the room. Elicit response that two students are left. Write
6 – 4 = 2 on the board. Explain to students how the 6 represents the number of students
standing in the front of the room; the – means subtraction; the 4 represents the number of
students that left the group; the = means equals; and the 2 represents how many students are
left in the front of the room. Tell students that they used subtraction to find the difference.
4. Set up three stations to practice subtraction.
•
Station 1 — Students work in pairs. Give each pair a bucket of manipulatives. The first
student takes a handful of manipulatives and counts them. Both students write the
number. The second student takes a handful of manipulatives and counts them. Both
students write the number. The students determine the larger and smaller of the two
numbers and subtract the smaller number from the larger number. They can use the
manipulatives to help find the difference. Have students write a complete number
sentence each time they complete the task.
•
Station 2 — Students work in pairs. Give each pair a set of number cards and have them
place the number cards face down on the desk. Each student picks a number card. The
students determine the larger and smaller of the two numbers and subtract the smaller
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Discovering Math: Arithmetic
Teacher’s Guide
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number from the larger number. Both students write the numbers, find the difference,
and write a subtraction number sentence. Have students continue until all the cards
have been used in subtraction number sentences; use numbers that match the ability
level of the students.
•
Station 3 — Students work in pairs. Give each pair a set of dice (1–6 die for beginners,
7–12 die for students with a stronger grasp of subtraction). Have each student roll the
dice. The students determine the larger and smaller of the two numbers and subtract
the smaller number from the larger number. Both students write the numbers rolled,
find the difference, and write a subtraction number sentence.
When students become proficient at subtraction, they can practice subtracting two-digit
numbers by taking bigger handfuls of manipulatives, choosing two cards and making two-digit
numbers to subtract, and rolling the dice twice to form a two-digit number.
5. Explain to students that they can use addition to solve word problems. Display the following
word problem: Harry six stamps. He buys four more stamps from the post office. How many
stamps does Harry have in all? Ask the students the information they know (has six stamps, buys
four more stamps). Model how to highlight or underline the given information. Ask students
what they need to know to find out (how many stamps Harry has in all). Model how to highlight
or underline the question in the problem. Discuss how to solve the problem. Elicit responses
about how to solve the problem. Model using addition to solve the problem. Write a number
sentence to show the solution 6 + 4 = 10. Model how to answer the question (Harry has 10 stamps
in all).
Have students work in pairs to complete the problems on the Addition Problem-Solving
Challenge (see below). Students can use manipulatives and they should write a complete
addition number sentence for each problem.
6. Explain to students that they can use subtraction to solve word problems. Display the following
word problem: Louise has 13 books. She lends 7 books to her friend to read. How many books
does Louise have left? Ask the students the information they know (has 13 books, lends 7 books to
friend). Model how to highlight or underline the given information. Ask students what they
need to find out (how many books Louise has left). Model how to highlight or underline the
question in the problem. Discuss how to solve the problem. Elicit responses about how to solve
the problem. Model using subtraction to solve the problem. Write a number sentence to show
the solution 13 – 7 = 6. Model how to answer the question (Louise has 6 books left). Have students
work in pairs to complete the problems on the Subtraction Problem-Solving Challenge. Students
can use manipulatives and should write a complete subtraction number sentence for each
problem.
7. Have students write their own addition and subtraction word problems for classmates to solve.
They should write the questions, solve them, and make an answer key. Have them trade
problems with a partner. Students can use manipulatives.
8. This part of the lesson should only be done with students who have an advanced
understanding of numbers and addition. Have students look at a sales circular from a local food
store. Ask them how much an item costs. Now ask the students how much three of those items
would cost. Explain that students can use estimation to find the total cost of several items.
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Discovering Math: Arithmetic
Teacher’s Guide
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Model how to round a price to the nearest dollar to make it easier to add. Tell the students that
because they know one item costs about $2, then three items would cost about $6.
Have students work in groups of three. Each group should have a copy of the circular. One
student chooses an item and asks how much a specific quantity costs. A second student uses
estimation to find the total cost. The third student checks the work on a calculator. Have the
students switch roles and continue practicing estimating costs.
Assessment
Use the following three-point rubric to evaluate students’ work during this lesson.
•
3 points: Students completed Problem-Solving Challenges correctly, including all requested
information; and clearly demonstrated the ability to add, subtract, and estimate sums using
whole numbers.
•
2 points: Students partially completed Problem-Solving Challenges correctly, including
most of the requested information; and satisfactorily demonstrated the ability to add,
subtract, and estimate sums using whole numbers.
•
1 point: Students produced incomplete Problem-Solving Challenges with little or none of
the requested information; and did not clearly demonstrate the ability to add, subtract, and
estimate sums using whole numbers.
Vocabulary
addition
Definition: The process of finding a total of two or more numbers
Context: The students use addition to find that the sum of 5 and 4 equals 9.
difference
Definition: The amount by which one quantity is greater than or less than another quantity
Context: The difference between 10 and 2 is 8.
estimate
Definition: A method to figure out amounts when an exact answer is more difficult to get and
not important
Context: The students estimate that the cost of five books costing about $3 each is $15.
subtraction
Definition: The process of finding the difference between two numbers
Context: The students use subtraction to find that the difference between 7 and 3 equals 4.
sum
Definition: The total amount when two or more numbers are added together
Context: When 6 is added to 7, the sum is 13.
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Discovering Math: Arithmetic
Teacher’s Guide
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Academic Standards
Mid-continent Research for Education and Learning (McREL)
McREL’s Content Knowledge: A Compendium of Standards and Benchmarks for K–12 Education
addresses 14 content areas. To view the standards and benchmarks, visit
http://www.mcrel.org/compendium/browse.asp.
This lesson plan addresses the following benchmarks:
• Mathematics: Uses basic and advanced procedures while performing the processes of
computation.
National Council of Teachers of Mathematics (NCTM)
The National Council of Teachers of Mathematics (NCTM) has developed national standards
to provide guidelines for teaching mathematics. To view the standards online, go to
http://standards.nctm.org.
This lesson plan addresses the following standards:
• Develop a sense of whole numbers and represent and use them in flexible ways,
including relating, composing, and decomposing numbers.
Support Materials
Develop custom worksheets, educational puzzles, online quizzes, and more with the free teaching tools
offered on the Discoveryschool.com Web site. Create and print support materials, or save them to a
Custom Classroom account for future use. To learn more, visit
•
http://school.discovery.com/teachingtools/teachingtools.html
DVD Content
This program is available in an interactive DVD format. The following information and activities are
specific to the DVD version.
How to Use the DVD
The DVD starting screen has the following options:
Play Video—This plays the video from start to finish. There are no programmed stops, except by
using a remote control. With a computer, depending on the particular software player, a pause
button is included with the other video controls.
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Discovering Math: Arithmetic
Teacher’s Guide
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Video Index—Here the video is divided into chapters indicated by title. Each chapter is then
divided into four sections indicated by video thumbnail icons; brief descriptions are noted for each
section. To play a particular segment, press Enter on the remote for TV playback; on a computer,
click once to highlight a thumbnail and read the accompanying text description and click again to
start the video.
Quiz—Each chapter has four interactive quiz questions correlated to each of the chapter’s
four sections.
Standards Link—Selecting this option displays a single screen that lists the national academic
standards the video addresses.
Teacher Resources—This screen gives the technical support number and Web site address.
Video Index
I.
Addition and Subtraction (6 min.)
Addition and Subtraction: Introduction
Adding birds to groups or subtracting birds from groups changes the sizes of the
groups, or the numbers of birds in them.
Example 1: Adding Flamingos
The size of a group of flamingos increases when more flamingos enter the group.
Number sentences for addition and the plus and equals signs are presented.
Example 2: Subtracting Penguins
The size of a group of penguins decreases when penguins leave the group. Number
sentences for subtraction and the minus sign are presented.
Example 3: Adding and Subtracting
Adding and subtracting birds changes the number of birds in the group, unless the
number added or subtracted is zero. Subtracting all the birds leaves zero.
II.
Go Figure: Using Addition and Subtraction (6 min.)
Using Addition and Subtraction: Introduction
Everyday problems and questions often involve addition and subtraction. Ranchers
keep track of the number of their cattle: how many they bring to market, how many they
buy or sell, and how many remain.
Example 1: Adding One-Digit Numbers
Larry adds tomato slices to a pizza he is making, providing a simple addition problem
with one-digit numbers.
Example 2: Subtracting One-Digit Numbers
Charles collects conch shells, and then subtracts some to give to people on the beach.
This provides a simple subtraction problem with one-digit numbers.
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Teacher’s Guide
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Example 3: Adding One- and Two-Digit Numbers
Sea turtles laying eggs add to a number of eggs. Park rangers collecting eggs to protect
add them to their collection. This provides an addition problem adding a one-digit
number to a two-digit number.
III.
Estimating Strategy (6 min.)
Estimation Strategy: Introduction
Estimation is a method to figure out amounts when an exact answer is more difficult
to get or not important. An example is estimating the total number of books in several
piles.
Example 1: Estimating Group Size
Scientists estimate the large number of caribou in Alaska by photographing groups and
counting, then figuring out the approximate total. A small example of counting a sample
of caribou and estimating a total is provided.
Example 2: Estimating Measurements
The height of horses is measured in hands. A Clydesdale’s height is measured by first
estimating how many hands would reach halfway to its shoulder, then calculating the
total estimated height.
Example 3: Front-End Estimation
Karen and Margaret estimate how much three items cost, using rounding and front-end
estimation.
IV.
Undoing Addition and Subtraction (5 min.)
Undoing Addition and Subtraction: Introduction
Addition and subtraction undo one another. If the same number is added to and
subtracted from a group, the original number is restored. A small group of horses
provides an example.
Example 1: Subtraction Undoes Addition
Adding the number of Galápagos harbor seals to a group, then subtracting the same
number results in the original number. Subtraction of a number undoes addition of the
same number.
Example 2: Addition Undoes Subtraction
Subtracting African elephants from a group, then adding the same number results in the
original number. Addition of a number of items undoes subtraction of the same number.
Example 3: Addition and Subtraction – Inverse Operations
Addition and subtraction undo each for temperature. If the temperature goes up, then
down the same amount, it ends up where it started. It works the same way for going
down first, then up.
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Discovering Math: Arithmetic
Teacher’s Guide
Quiz
I.
Addition and Subtraction
1. Three flamingos stand in the water. Then four more flamingos enter the water. What
is the total number of flamingos in the water?
A. 1
B. 5
C. 7
D. 12
Answer: C
2. Five penguins play on the ice. Three penguins leave. How many penguins are left
playing on the ice?
A. 1
B. 2
C. 5
D. 8
Answer: B
3. 7 + 0 = _____
A. 0
B. 7
C. 17
D. 70
Answer: B
II.
Go Figure: Using Addition and Subtraction
1. 3 + 3 = _____
A. 0
B. 3
C. 6
D. 33
Answer: C
2. 8 – 3 = _____
A. 2
B. 4
C. 5
D. 11
Answer: C
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Discovering Math: Arithmetic
Teacher’s Guide
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3. 15 + 3 = _____
A. 2
B. 8
C. 12
D. 18
Answer: D
III.
Estimation Strategy
1. Sara wants to know how many blocks she has in a large pile. What can she do to come
up with a number that is close to the total number of blocks she has?
A. estimate
B. subtract
C. play with the blocks
D. put the blocks in groups
Answer: A
2. Bruce sees two groups of dogs. Each group appears to have about five dogs. About how
many dogs are in both groups?
A. 5
B. 10
C. 15
D. 55
Answer: B
3. Mark is almost 4 feet tall. John is about one foot taller than Mark. About how tall
is John?
A. 3 feet
B. 4 feet
C. 5 feet
D. 6 feet
Answer: C
4. Tara wants to buy three new books. Each book costs $9. 89. About how much money
does Tara need to buy all three books?
A. $10
B. $20
C. $30
D. $40
Answer: C
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Discovering Math: Arithmetic
Teacher’s Guide
IV.
10
Undoing Addition and Subtraction
1. Four horses play in the water. One more horse goes into the water. Then two horses get
tired and leave the water. How many horses are left in the water?
A. 2
B. 3
C. 5
D. 7
Answer: B
2. Eight seals are playing together. Five more seals come to play. Then five swim away.
How many seals are playing?
A. 5
B. 8
C. 13
D. 18
Answer: B
3. Five elephants are eating leaves. One elephant walks away. Another elephant joins the
group. How many elephants are eating leaves?
A. 4
B. 5
C. 6
D. 7
Answer: B
4. The temperature outside is 90 degrees Fahrenheit. When it starts to rain the temperature
goes down 10 degrees. What is the new temperature?
A. 10 degrees
B. 70 degrees
C. 80 degrees
D. 100 degrees
Answer: C
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Teacher’s Guide
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Addition Problem-Solving Challenges
1. Samantha collects rocks. She finds four new rocks at the beach and seven new rocks
at the park. How many new rocks did Samantha find in all?
Show Work:
Number Sentence: ___________________________ Answer: ________________
2. Nicholas is playing with his toy trains. He has two red train cars and eight blue train cars.
How many train cars does Nicholas have in all?
Show Work:
Number Sentence: ___________________________ Answer: ________________
3. Tamika read nine pages of her book on Monday and eight pages of her book on Tuesday.
How many pages of her book did Karen read in all?
Show Work:
Number Sentence: ___________________________ Answer: ________________
4. Thomas bought four new comic books in January, eight new comic books in February, and
five new comic books in March. How many new comic books did Thomas buy in all?
Show Work:
Number Sentence: ___________________________ Answer: ________________
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Discovering Math: Arithmetic
Teacher’s Guide
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Subtraction Problem-Solving Challenges
1. There are 15 students standing in the front of Ms. Smith’s classroom. She asks 7 students to
sit down. How many students are left standing in the front of the classroom?
Show Work:
Number Sentence: ___________________________ Answer: ________________
2. John bought nine oranges at the store. He gave four oranges away. How many oranges
does John have left?
Show Work:
Number Sentence: ___________________________ Answer: ________________
3. Joshua made 12 snowballs. Three of the snowballs melted. How many snowballs does
Joshua have left?
Show Work:
Number Sentence: ___________________________ Answer: ________________
4. Lara has 18 stickers. She gives 5 stickers to Rob. She gives 3 stickers to Lisa. How many
stickers does Lara have left?
Show Work:
Number Sentence: ___________________________ Answer: ________________
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