**Children's Literature**

—CarolRaker Collins, Ph.D.

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Make Learning Math Fun With This Hands-on Resource from Everyone's Favorite math and Science Teacher!

Now you can help students develop their math skills while fostering a long-term love for mathematical exploration. In Janice VanCleave's Teaching the Fun of Math, the award-winning teacher and popular children's author gives you a wealth of teaching techniques for

—CarolRaker Collins, Ph.D.

- ISBN-13:
- 9780471331049
- Publisher:
- Wiley
- Publication date:
- 02/25/2005
- Edition description:
- Grades 3-8
- Pages:
- 208
- Sales rank:
- 1,086,555
- Product dimensions:
- 8.64(w) x 11.04(h) x 0.57(d)

All right reserved.

* A number* is a symbol used to represent a *quantity* (an amount). *Operations* are processes that are performed on numbers. Operations and *operational symbols* (figures representing math operations) include addition (+), subtraction (-), multiplication (×), and division (÷). An understanding of operations and the order in which they are to be performed gives kids the tools they will need later to discover the value of unknown variables in algebraic equations. Since some mathematical problems require more calculations than others, the use of a technological tool-the calculator-can speed up the process of finding the answer. The common operations of addition, subtraction, multiplication, and division are needed to solve problems containing fractions as well as to find unknown variables in algebraic equations.

*1 Addition and Subtraction *

* TEACHING TIPS *

* *

* Benchmarks*

*By the end of grade 5, students should be able to*

Demonstrate an understanding of operation patterns and properties.

Use addition and subtraction to solve problems connected to everyday experiences.

*By the end of grade 8, students should be able to*

Represent operations with models, words, and numbers.

Compare and order integers.

*In this chapter, students are expected to*

Use number lines to evaluate addition and subtraction expressions.

Analyze word problems to choose an operation and write and evaluate an expression for the problem.

*Preparing the Materials*

*Activity 1: Addition and Subtraction*

Make a copy of the Addition and Subtraction activity sheet for each student.

*Activity 2: Problem Solving*

Make a copy of the Problem Solving activity sheet for each student.

*Presenting the Math Concepts *

* 1.* Introduce the new terms:

*addends* Numbers that are added together.

*addition* The operation of adding together two or more numbers called addends, which are combined into a resulting number called the sum.

*analyze* To separate information into individual parts, examine those parts, and organize them to solve a problem.

*commutative property for addition* When numbers are added, the order of the addends may be changed without changing the sum.

*equal (=)* Symbol used to compare equal numbers or expressions.

*equation* A mathematical sentence that uses an equal symbol to show that two expressions are equal.

*expression* Numbers or letters or numbers and letters combined with one or more operational symbols.

*inverse operations* Operations that undo each other. Addition and subtraction are inverse operations.

*number line* A line divided into equal parts with one point chosen as the 0 point, or origin.

*numerical expression* Numbers combined with one or more operational symbols.

*operations* Processes such as addition and subtraction that are performed on numbers.

*subtraction* The operation that involves finding the difference between two numbers.

*sum* The number that is the result of adding two or more addends.

*whole numbers* Counting numbers and 0.

*word problem* A math problem using only words; a problem written in sentence form that needs to be solved using math.

*2.* Explore the new terms:

Whole numbers are counting numbers and 0, which include 0, 1, 2, 3, 4, ...

Sometimes commas are used to write whole numbers with more than three digits to make the number easier to read. To place a comma in a whole number, count digits from the right-hand end and place a comma after every three digits. For example, the whole number 2307456 can be written as 2,307,456.

Commas are also used when words are used to name a number. Thus, the name of 2,307,456 would be two million, three hundred seven thousand, four hundred fifty-six.

The symbol for the operation of addition is the plus sign (+).

The symbol for the operation of subtraction is the minus sign (-).

Addition and subtraction are inverse operations, which means that if you start with any number and then add and subtract the same number to it, the result is the original number. For example, if you begin with the number 10, add 4, and then subtract 4, the result is 10. 10 + 4 - 4 = 10.

The commutative property for addition for real numbers *a* and *b* would be expressed as *a* + *b* = *b* + *a*.

Examples of numeral expressions are 3 + 4 and 5 + 4 - 2.

An equation uses the symbol = to compare equal numbers or expressions. For example: 2 + 3 = 5 or 2 + 3 = 4 + 1.

To solve a word problem, you must first analyze it to determine what you know (the facts), what you want to know, and what operations are needed. You then write an expression in sentence form to find the answer.

*EXTENSION*

1. Introduce the terms *negative numbers, positive numbers*, and *signed numbers*. Negative numbers are numbers with a value less than 0 and are found to the left of 0 on a horizontal number line. Positive numbers have a value geater than 0 and are found to the right of 0 on a horizontal number line. Signed numbers are numbers with a positive or negative sign. Negative numbers must have a negative sign, such as -5. But positive numbers can be written with or without a positive sign, for example, +4 or 4.

2. When using arrows to show addition of signed numbers, such as in the figure below, the length of the arrow represents the value of the number. On a horizontal number line, an arrow for a positive number points to the right and an arrow for a negative number points to the left. For example, using arrows and a number line to find the sum of 4 + (-3) would be:

Prepare an activity sheet for the addition of signed numbers, providing a number line for each problem as shown. For each problem, students can use a pencil to draw directed arrows on a number line to find the sum of each problem. Example problems:

Number Line

1. (-2) + (-1) *Answer:* (-3)

2. 6 + (-4) *Answer:* (2)

3. 7 + (-2) + (-4) *Answer:* (1)

4. 4 + (-2) + 1 + (-5) *Answer:* (-2)

5. (+3) + (-2) + (-6) *Answer:* (-5)

*ANSWERS *

* Activity 1: Addition and Subtraction *

* 1. *

* Answer:* 8 - 3 = 5

*2. *

* Answer:* 9 + 1 - 7 = 3

*3. *

* Answer:* 4 + 2 - 1 + 5 = 10

*4. *

* Answer:* 3 - 2 + 6 - 4 = 3

*Activity 2: Problem Solving *

* 1. a.* Total customers = 15 Customers given away = 7

*b.* How many customers did Kimberly keep?

*c.* Subtraction

*d.* 15 - 7

*e.* 15 - 7 = 8

*2. a.* Time Lacey has already spent baby-sitting = 2 hours

Time until parents return = 3 hours

*b.* Total time Lacey will baby-sit

*c.* Addition

*d.* 2 hours + 3 hours

*e.* 2 hours + 3 hours = 5 hours

*3. a.* Total miles to run = 4 miles Miles left to run = 1 mile

*b.* How many miles has Ginger left to run?

*c.* Subtraction

*d.* 4 miles - 1 mile

*e.* 4 miles - 1 mile = 3 miles

*4. a.* Money paid to cut lawn = $15.00 Money paid to trim hedges = $10.00 Money paid to rake leaves = $5.00

*b.* How much did Travis earn in all?

*c.* Addition

*d.* $15.00 + $10.00 + $5.00

*e.* $15.00 + $10.00 + $5.00 = $30.00

*ACTIVITY 1 *

* Addition and Subtraction*

*Operations* are processes that are performed on numbers, including addition and subtraction. *Addition* is the operation of adding together two or more numbers called *addends*, which are combined into a resulting number called the *sum*. You can change the order of the addends without changing the sum. This property of addition is called the *commutative property for addition. Subtraction* is an operation that involves finding the difference between two numbers. Since addition is an operation that adds and subtraction is an operation that takes away, they are *inverse operations,* and they undo each other. A *number* line, which is a line divided into equal parts in which all points correspond to a number, can be used to show that addition and subtraction are inverse operations. An *expression* consists of numbers or letters or numbers and letters combined with one or more operational symbols. A *numerical expression* is an expression of numbers combined with one or more symbols. The *equal (=)* symbol is used to show that numbers or expressions are equal. An *equation* is a mathematical sentence that uses an equal symbol to show that two expressions are equal. In this activity *whole numbers,* which are counting numbers and 0, will be used.

*Practice Problems *

* 1.* Use a number line to find the sum of 4 + 5.

*Think!*

4 + 5 is an expression involving addition.

Addition is represented on a number line by arrows that move to the right.

Begin the first arrow at a point above the 0 on the number line. Use a pencil and ruler to draw the 4 arrow going toward the right. The length of the arrow is 4 divisions to the right on the number line, from 0 to 4. The head of the arrow is above the 4 on the number line.

Starting at the 4 on the number line, count to the right 5 more divisions, from 4 to 9 on the number line. Use the pencil and ruler to draw the arrow from the tip of the first arrow 5 divisions to the right, so the head of the arrow is now above the 9 on the number line.

*Answer:* 4 + 5 = 9

*2.* Use a number line to find the solution of 3 + 6 - 4.

*Think!*

3 + 6 - 4 is a number expression involving addition and subtraction.

Begin the first arrow at a point above the 0 on the number line. Use a pencil and ruler to draw the arrow going 3 spaces to the right, so the head of the arrow is above the 3 on the number line.

Starting at the tip of the arrow that ends at the number 3, use the pencil and ruler to draw an arrow pointing 6 more spaces to the right. The head of the arrow is now above the 9 on the number line.

Starting directly above the tip of the arrow that ends at the number 9, draw an arrow pointing 4 spaces to the left, from 9 to 5 on the number line.

The tip of the last arrow is above the 5 on the number line.

*Answer:* 3 + 6 - 4 = 5

*On Your Own*

Use a ruler and the number line to find the sum of each problem.

*1.* 6 + 4

*Answer:* __________________

*2.* 8 - 3

*Answer:* __________________

*3.* 9 + 1 - 7

*Answer:* __________________

*4.* 4 + 2 - 1 + 5

*Answer:* __________________

*5.* 3 - 2 + 6 - 4

*Answer:* __________________

*ACTIVITY 2 *

* Problem Solving*

To *analyze* means to separate information into its individual parts, examining those parts and organizing them to solve a problem. A *word problem* is a math problem using only words; it is a problem written in sentence form that needs to be solved using math. To solve a word problem, you analyze it to determine what you know (the facts), what you want to know, and what operations are needed. Using this information, you write an expression. You solve the word problem by evaluating (or solving) the expression.

*Practice Problems*

Analyze each word problem, write an expression for the problem, then evaluate the expression.

*1.* Jennifer had 120 stuffed animals. She had so many animals that she gave away 50. How many animals did Jennifer keep?

*Think!*

What do you know?

Jennifer started with 120 stuffed animals and gave away 50 of them.

What do you want to know?

How many animals Jennifer kept.

What operation is needed?

Since Jennifer is *giving away* stuffed animals, the operation is subtraction.

What expression represents the problem?

120 animals - 50 animals

Evaluate the expression.

120 animals - 50 animals = ?

*Answer:* Jennifer kept 70 animals.

*2.* David watched television for 1 hour. His parents then left the house and said they'd be back in 2 hours. If David watches television until his parents return, how long will he have watched television?

*Think!*

What do you know?

David watched television for 1 hour, and will watch for another 2 hours.

What do you want to know?

Total time watching television

What operation is needed?

Since the question is about a *total* amount of time, the operation is addition.

What expression represents the problem?

1 hour + 2 hours

Evaluate the expression.

1 hour + 2 hours = ?

*Answer:* David will have watched television for 3 hours.

*On Your Own*

Analyze each word problem, write an expression for the problem, then evaluate the expression.

1. Kimberly watched dogs for 15 customers. This was more dogs than she could handle, so she gave 7 customers to Lauren. How many customers did Kimberly keep?

*a.* What do you know? ________________________________________________________

*b.* What do you want to know? ________________________________________________

*c.* What operation is needed? ________________________________________________

*d.* What expression represents the problem? __________________________________

*e.* Evaluate the expression. _________________________________________________

2. Lacey has been baby-sitting Jacob for 2 hours. Jacob's parents will be home in 3 hours. How long will Lacey have baby-sat Jacob by the time his parents return?

*a.* What do you know? ________________________________________________________

*b.* What do you want to know? ________________________________________________

*c.* What operation is needed? ________________________________________________

*d.* What expression represents the problem? __________________________________

*e.* Evaluate the expression. _________________________________________________

*3.* Ginger has 1 mile left to run. If she wants to run 4 miles, how many miles has she already run?

*a.* What do you know? ________________________________________________________

*b.* What do you want to know? ________________________________________________

*c.* What operation is needed? ________________________________________________

*d.* What expression represents the problem? __________________________________

*e.* Evaluate the expression. _________________________________________________

*4.* Travis was paid $15.00 to cut the lawn, $10.00 to trim the hedges, and $5.00 to rake leaves. How much did he earn in all?

*a.* What do you know? ________________________________________________________

*b.* What do you want to know? ________________________________________________

*c.* What operation is needed? ________________________________________________

*d.* What expression represents the problem? __________________________________

*e.* Evaluate the expression. _________________________________________________

*(Continues...)*

Excerpted fromJanice VanCleave's Teaching the Fun of MathbyJanice Van CleaveCopyright © 2005 by John Wiley & Sons, Inc. . Excerpted by permission.

All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.

Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

**JANICE VANCLEAVE** is a former science and math teacher who now spends her time writing and giving educational workshops. She is the author of more than forty children’s science and math books that have sold over two million copies and a resident science fair authority on **discovery.com.**

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