Problem Solving Strategy: Working Backwards

7.13C: Selecting the appropriate problem solving strategy.

Mr. Brewer’s 7th Grade MathSeptember 9, 2009

A. 21

B. 24

C. 19

D. 2795

Alto, Texas has a population of 1407 people. New Summerfield, Texas has a population of 1388 people. What is the difference between the two towns’ populations?

A. 7

B. 9

C. 6

D. 2

The Texas Rangers had an incredible start to the year. They scored 387 runs during the first 43 games. If they scored the same amount of runs every game, how many points did they score per game?

A. 5

B. 3

C. 17

D. 4

The zoo uses a total of 268 pounds of food every day for the 67 animals they keep. If each animal ate the same amount of food, how many pounds of food does each animal eat?

A. 378

B. 252

C. 48

D. 53

The Liberty Middle School 7th grade football team scored 63 points in each of their first four football games. How many total points did they score in their first four games?

Copy these numbers in your ‘Warm Up’ section and order them from least to greatest. There are four sets

of numbers to order: Set A, Set B, Set C, and Set D.

A. 567 356 0 867 -23

B. 1.2 1.55 1.58 1.9 0

C. 5.65 56.5 0 565 -565

D. -7 5 0 -5 7 24 -24

Warm-Up

Comparing and Ordering Integers

7.1A: Compare and order integers and positive rational numbers.

Mr. Brewer’s 7th Grade MathSeptember 9, 2009

Reviewing Vocabulary

• Integers – The set of all whole numbers, their opposite numbers, and zero (what’s on the number line (-8, 0, 4, -8 etc…))

• Negative numbers – The set of all real numbers less thanless than zero (-8, -4, -2, etc…)

• Rational numbers – Any number that can be written as a fraction (3/4, 8, -8, .40)

Reviewing Vocabulary• Integers – Give an example of an integer?– Give an example of something that is not an integer?

• Negative numbers– Give an example of a negative number?– Give an example of something that is not a negative?

• Rational numbers – – Give two examples of a rational number?– Give an example of something that is not a rational

number?

The opposite of a number is the samedistance from 0 on a number line as the

original number, just in the opposite direction.

1 2 3 4 5 • •

–5–4–3–2–1 0

–4 and 4 are opposites

–4 4

Negative integers Positive integers

0 is neither positivenor negative

What’s an Opposite?

Graph the integer 7 and its opposite on a number line.

The opposite of –7 is 7.

1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0

7 units 7 units

Graph the integer 5 and its opposite on a number line.

The opposite of –5 is 5.

1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0

5 units 5 units

The Number Line – Key Understandings

• Negative integers closer to zero have a greater value than those numbers further from zero.

• From any point on a number line, an integer’s value increases as you move right and decreases as you move left.

1 2 3 4 5 6 7 –7 –6 –5 –4 –3 –2 –1 0

The Number Line

Order the following numbers using the number line.

6 -7 8 3 0 -2 -3 6

1 2 3 4 5 6 7 –7 –6 –5 –4 –3 –2 –1 0

The Number Line

1. What two whole numbers fall between 4 & 7 on the number line?2. Negative 3 lies the right or left of zero?3. Tell me three numbers less than -2 on the number line?

1 2 3 4 5 6 7 –7 –6 –5 –4 –3 –2 –1 0

Signs of Comparison

• Less Than ‹ 4 ‹ 8• “Four is less than eight”

• Greater Than › 8 › 4• “Eight is greater than eight”

• Equal To = 8 = 8• “Eight is equal to eight”

‹

›

=

Which Sign?

< > =

Which Sign?

< > =

Which Sign?

< > =

Which Sign?

< > =

4 5

Which Sign?

< > =

-8 -5

Which Sign?

10 6

Copy these numbers into your notes section and determine the appropriate sign.

2 -2-6 -8

Where do we see negative integers in the real world?

Do we see negative integers in sports?

What about in geography?

Highest and Lowest, USA

Mt. McKinley

20,320 Ft.

Death Valley

- 282 Ft.

Credit Cards

Temperature?

AltitudeThere are four people out on the

ocean.

1. Floating on a raft2. Scuba diving at -32 ft3. In a boat 5 feet above the

water. 4. Snorkeling at -1 ft

Who is the highest, who is the lowest?

Comparison: Altitude

<>=

Sports

Which is the better play?

A. Sack for 9 yardsB. Run for 5 yardsC. Incomplete for 0 yardsD. Run, lose 1 yardE. Pass for 35 yards

Comparison: Sports

<>=

BusinessWhich business would you be least likely to buy? Most

likely?

A. A car wash that makes $500 per week.B. A restaurant that loses $200 per week.C. A diner that makes $200 per week.D. A CD store that loses $450 per week.

Order these stores from best to worst (greatest to least).

Credit Cards

Who has less money?

A. Bob owes $30B. Mary owes $40C. Mark owes $0D. Marty owes $100E. Dom owes $85

Order Least to Greatest

Temperature Temperatures– All in degrees F

• McAllen, TX 75• Mexico City 85• Fairbanks, AK -10• Athol, MA 28• The Forks, ME -5• Whitefish, MT -15 Order these temperatures

from least to greatest.

• Put the following lists of numbers in order from greatest to least:

-19, -20, 20, 19, -23, 34, -1

130, -25, 87, -125, 52, -94, 2

• Put the following lists of numbers in order from least to greatest:

-9, -11, -15, -13, -7, -17, 0

-13, 12, -11, 10, -9, 8, -7, 6, -5

Integer Exercise

• Instructions: Give 5 examples of positive and negative integers found in the real world.

• For each example, describe in full sentences which integer is least in value and which is greatest in value and why?