Graph Challenge
Select from one of the several types of graph
challenges below. Hold Ctrl and click on one of the icons to begin.
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Pie |
Bar |
Line |
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Typical Family Budget |
Minimum Wage |
Temperature versus Altitude |
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Average Animal Life Span |
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Swimming Times of Boys and Girls |
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Try some of these graph resource to help you
tackle the challenges above:
Line Graph Tutorial
This tutorial provides step by step instruction on how to create a line graph.
If you have a Macintosh, it will even speak to you.
Bar Graph Maker
Here's a project in working progress. Simply specify a few conditions, input
your information, and click a couple of buttons and presto! You've got a bar
graph.
Identifying the extra information.
Directions:
Tell students that today you will be solving problems that contain extra information. Explain that sometimes when you are given information to solve a problem, the person giving the information gives you too much and you have to determine which facts are the most important to answer the question.
Tell students that today you will be figuring out word problems based on things
that you would find in a grocery store. Put the attached transparency on the
overhead and go through each problem with students, underlining important facts
and crossing out the extra information given. Then ask students to come up with
a number sentence to solve the problem.
Just the Facts
Look at the following word problems. Determine which facts are important to answer the questions and which are just extra information. Underline the important facts and cross out the extra information.
1. Jane was shopping in the grocery store. The grocery store had a sale on green beans. The cans were 10 ounces. One can used to cost 45¢, now it is on sale for 35¢. She bought 3 cans. How much money did she save on each can?
2. Rick went to the department store to buy a new shirt. He bought two shirts that were on sale for $10.00 a piece and one shirt that was on sale for $15.00. How many shirts did he buy?
3. John wanted to buy a new yo-yo at the store. He looked through his wallet and found $1.50. The yo-yo was on sale for 30% off the original price. He needed 40¢ more to buy the yo-yo. How much did the yo-yo cost?
4. Terri bought 4 flowers for her mother that cost 30¢ a piece. She put them in a vase that cost $3.00. How much did she spend on the flowers?
Order of operations
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Problem: |
Evaluate the following arithmetic expression: 3 + 4 x 2 |
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Solution: |
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It seems that each student interpreted the problem differently, resulting in two different answers. Student 1 performed the operation of addition first, then multiplication; whereas student 2 performed multiplication first, then addition. When performing arithmetic operations there can be only one correct answer. We need a set of rules in order to avoid this kind of confusion. Mathematicians have devised a standard order of operations for calculations involving more than one arithmetic operation.
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Rule 1: |
First perform any calculations inside parentheses. |
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Rule 2: |
Next perform all multiplications and divisions, working from left to right. |
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Rule 3: |
Lastly, perform all additions and subtractions, working from left to right. |
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Example 1: |
Evaluate each arithmetic expression using the rules for order of operations. |
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a) |
6 + 7 x 8 |
= 6 + 56 |
= 62 |
Multiplication (Rule 2), then addition (Rule 3). |
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b) |
16 ÷ 8 - 2 |
= 2 - 2 |
= 0 |
Division (Rule 2), then subtraction (Rule 3). |
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c) |
(25 - 11) x 3 |
= 14 x 3 |
= 42 |
Parentheses (Rule 1), then multiplication (Rule 2). |
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d) |
6 x (5 + 4) ÷ 3 - 7 |
= 6 x 9 ÷ 3 - 7 |
Parentheses (Rule 1). |
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6 x 9 ÷ 3 - 7 |
= 54 ÷ 3 - 7 |
Perform multiplication before division since multiplication is to the left of division in the problem (Rule 2). |
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54 ÷ 3 - 7 |
= 18 - 7 |
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18 - 7 |
= 11 |
Subtraction (Rule 3). |
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In Example 1(d), you will notice that multiplication and division were performed from left to right. According to Rule 2, since multiplication occurred first in the problem, it was performed first. Let's look at another example.
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Example 2: |
Evaluate each arithmetic expression using the rules for order of operations. |
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a) |
150 ÷ (6 + 3 x 8) - 5 |
= 150 ÷ (6 + 24) - 5 |
Evaluate operations within parenthesis first (Rule 1). Perform multiplication first (Rule 2), then addition (Rule 3). |
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150 ÷ (6 + 24) - 5 |
= 150 ÷ 30 - 5 |
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150 ÷ 30 - 5 |
= 5 - 5 |
Perform division (Rule 2). |
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5 - 5 |
= 0 |
Perform subtraction (Rule 3). |
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b) |
8 x 7 + 28 ÷ (12 + 16) - 3 |
= 8 x 7 + 28 ÷ 28 - 3 |
Parentheses (Rule 1). |
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8 x 7 + 28 ÷ 28 - 3 |
= 56 + 28 ÷ 28 - 3 |
Perform multiplication before division since multiplication is to the left of division in the problem (Rule 2). |
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56 + 28 ÷ 28 - 3 |
= 56 + 1 - 3 |
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56 + 1 - 3 |
= 57 - 3 |
Perform addition before subtraction since addition is to the left of subtraction in the problem (Rule 3). |
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57 - 3 |
= 54 |
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c) |
9 - 5 ÷ (8 - 3) x 2 + 6 |
= 9 - 5 ÷ 5 x 2 + 6 |
Parentheses (rule 1). |
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9 - 5 ÷ 5 x 2 + 6 |
= 9 - 1 x 2 + 6 |
Perform division before multiplication since division is to the left of multiplication in the problem (Rule 2). |
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9 - 1 x 2 + 6 |
= 9 - 2 + 6 |
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9 - 2 + 6 |
= 7 + 6 |
Perform subtraction before addition since subtraction is to the left of addition in the problem (Rule 3). |
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7 + 6 |
= 13 |
In Example 2, multiplication and division are performed in the order in which they occur in the problem (Rule 2). The same thing holds for addition and subtraction (Rule 3).
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Example 3: |
Evaluate the arithmetic expression below: |
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Solution: |
When a problem includes a fraction bar (also called a vinculum), perform all calculations above and below the fraction bar BEFORE the division. |
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Example 4: |
Write an arithmetic expression for this problem. Then evaluate the expression using the order of operations. |
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Mr. Smith charged Jill $32 for parts and $15 per hour for labor to repair her bicycle. If he spent 3 hours repairing her bike, how much does Jill owe him? |
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32 + 3 x 15 = 32 + 3 x 15 = 32 + 45 = 77 |
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Solution: |
Jill owes Mr. Smith $77. |
Summary:
When evaluating arithmetic expressions, the order of operations is:
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1: |
Simplify all operations inside parentheses. |
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2: |
Perform all multiplications and divisions, working from left to right. |
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3: |
Perform all additions and subtractions, working from left to right. |
Exercises
Directions: Complete each exercise by
applying the rules for order of operations. Show your work.
1.
9
+ 6 x (8 - 5)
2.
(14
- 5) ÷ (9 - 6)
3.
5
x 8 + 6 ÷ 6 - 12 x 2
4.
5.
A
caterer charges a setup fee of $50, and $20 per person. How much will the
caterer charge if 35 people attend the party, and the customer has a coupon for
$100 off the total?