Grade 7-8 Pre-Algebra Curriculum Map



Grade 7-8 Pre-Algebra Curriculum Map.pdf

Tools for Algebra

Short Answers:

Sarah and Jacob compared their total bowling scores. Sarah’s total score was 109 points greater than Jacob’s total score. Write an expression that represents Jacob’s total score based onS, Sarah’s total score.

 

[pic]

Integers

Open Responses:

| |Carrie recorded the temperature outside her school at the same time each day for four days. |

| |On Monday, the temperature was 11°F. |

| |On Tuesday, the temperature was 15°F less than the temperature on Monday. |

| |On Wednesday, the temperature was 3°F greater than the temperature on Tuesday. |

| |On Thursday, the temperature was 4°F greater than the temperature on Wednesday. |

a. In your Student Answer Booklet, copy and complete the table below using the information Carrie recorded. Show or explain how you got each of your answers.

|Temperatures Outside |

|Carrie's Schools |

|Day |

|Temperature |

| |

|    Monday |

|11°F |

| |

|    Tuesday |

|  |

| |

|    Wednesday |

|  |

| |

|    Thursday |

|  |

| |

b. What was the difference, in degrees Fahrenheit, between the temperature on Monday and the temperature on Wednesday? Show or explain how you got your answer.

| |Carrie also recorded the temperature outside her school on Friday. She calculated that the mean temperature for the 5 days, |

| |Monday through Friday, was 2°F. |

c. What was the temperature, in degrees Fahrenheit, on Friday? Show or explain how you got your answer.

 Short Answers:

The maximum temperature on the planet Mercury is 950°F. The minimum temperature is —346°F. What is the difference, in degrees Fahrenheit, between the maximum and minimum temperatures on Mercury?

[pic]

Equations

Short Answers:

What is the solution to the equation below? [pic]

[pic] [pic] 3x + 9 = -6

|What is the value of x that makes the equation below true? |

|2x – 3 = 11 |

[pic]

Inequalities

Open Responses:

Ms. Gleason is opening a new restaurant.

• She has enough booths to seat up to 40 people.

• She is ordering tables to fill the rest of the seating space.

• Each table can seat up to 6 people.

a. If t represents the number of tables Ms. Gleason orders, write an expression to show the total number of people that can be seated at booths and tables.

b. Write an inequality that could be used to determine t, the number of tables Ms. Gleason needs to order so that she has enough seating at booths and tables for at least 125 people.

c. Solve the inequality from part (b) to determine the number of tables Ms. Gleason needs to order. Show or explain how you got your answer.

Short Answers:

What is the solution to the inequality below?

5 + 2x [pic] 13

≥

[pic]

Exploring Factors and Fractions

[pic]

Rational Numbers with addition and subtraction

Open Responses:

Jerry wants to copy five files onto a compact disc (CD). The CD can hold a total of 700 megabytes of data. The size, in megabytes, of each of Jerry’s files is shown in the chart below.

Sizes of Jerry’s Files

|File Number |Size of File |

| |(megabytes) |

|1 |   47.76 |

|2 |  58.32 |

|3 |178.99 |

|4 |110.55 |

|5 |  96.75 |

a. What is the difference, in megabytes, between the largest and smallest of the five files? Show or explain how you got your answer.

b. Jerry estimated that the total number of megabytes in the five files was about 500 megabytes. Do you agree or disagree with Jerry’s estimate? Show or explain how you got your answer.

c. Based on Jerry’s estimate, what percent of the 700 total megabytes that the CD can hold will be left after Jerry copies these five files to the CD? Show or explain how you got your answer.

[pic]

Rational Numbers with multiplication and division

Short Answers:

Mr. Johnson noted that [pic] of the students at his school were in the band. He also noted that [pic]of the students in the band were girls. What fractional part of the students at the school were girls in the band?⅜½

[pic]

Functions and Graphing (slope and intercepts)

Open Responses:

| |

|Lisa bought a silver chain. She wants to buy glass beads to put on the chain. The equation below can be used to determine y, |

|Lisa's total cost, in dollars, to buy a silver chain and x glass beads. |

y = 2x + 10

a. In your Student Answer Booklet, copy the table below and complete it using the equation. Show or explain how you got each of your answers.

|Total Cost of |

|Silver Chain and Beads |

|Number of Beads |

|(x) |

|Total Cost |

|(y) |

| |

|0 |

|$10 |

| |

|5 |

|$20 |

| |

|10 |

|  |

| |

|15 |

|  |

| |

|[pic] |

|[pic] |

| |

|25 |

|  |

| |

|[pic] |

|[pic] |

| |

|40 |

|  |

| |

b. What does the 2 in the equation represent? Explain your reasoning.

c. What does the 10 in the equation represent? Explain your reasoning.

|Marisa drank one cup of milk and ate x small vanilla cookies for a snack. The linear equation below represents y, the total number|

|of calories in Marisa’s snack. |

|y = 12x + 120 |

|a. |What is the y-intercept of the line represented by this equation? |

|b. |Explain what the y-intercept tells us about Marisa’s snack. |

|c. |What is the slope of the line represented by this equation? |

|d. |Explain what the slope tells us about Marisa’s snack. |

|e. |If Marisa eats 9 small vanilla cookies, what is the total number of calories in her snack? Show or explain how you got your |

| |answer. |

Currently, Irina exercises a total of 135 minutes during each week. She is planning to begin the following new exercise program.

• The exercise program will last 6 weeks.

• During each week of the program, she will exercise 15 minutes more than she exercised the previous week.

a. Copy the table below into your Student Answer Booklet. In the table, week 0 shows the number of minutes per week Irina exercised before she started the new program. Complete your table to show the number of minutes that Irina will exercise during each of the 6 weeks if she follows her new exercise program.

Minutes of Exercise

During Each Week

|Week (w) |Number of |

| |Minutes (n) |

|0 |135 |

|1 |  |

|2 |  |

|3 |  |

|4 |  |

|5 |  |

|6 |  |

a. For the data shown in the table, write an equation that shows the relationship betweenw and n.

b. Based on the equation you wrote in part (b), what is the total number of minutes Irina will exercise in week 20 if she continues her exercise program beyond 6 weeks? Show or explain how you got your answer.

 

[pic]

Ratio, Proportion and Percents

Open Responses:

A florist sells bouquets of carnations. He creates bouquets of different sizes by using 4 white carnations for every 3 pink carnations in a bouquet.

|a. |Write a proportion that can be used to find p, the number of pink carnations in a bouquet with w white carnations. |

|b. |What is the number of pink carnations in a bouquet with 16 white carnations? Show or explain how you got your answer. |

|c. |The florist made a bouquet with a total of 35 carnations in it. |

| |What is the total number of pink carnations in the bouquet? |

| |What is the total number of white carnations in the bouquet? |

| |Show or explain how you got your answers. |

Short Answers:

Mr. Jamison is the principal at a new school with an enrollment of 430 students. He surveyed 10% of the students at his school to find out which colors they would like as the school colors.What is the number of students in the sample size of the principal’s survey?

James drove 200 miles in 4 hours. At this rate, what is the total number of hours it will take him to drive 150 miles?

[pic]

Statistics and Probability

Open Responses:

Daniel has a spinner divided into two congruent sections, as shown below.

[pic]

a. Daniel will spin the arrow on the spinner one time. What is the probability that the arrow will stop in the gray section? Show or explain how you got your answer.

b. Daniel will spin the arrow two times. What is the probability that the arrow will stop in the gray section both times? Show or explain how you got your answer.

c. Daniel will spin the arrow three times. In your Student Answer Booklet, construct a tree diagram that shows all the possible outcomes that can occur.

d. Based on your diagram from part (c), what is the probability that the arrow will stop in the white section at least one time when Daniel spins the arrow three times? Show or explain how you got your answer.

| |

|The manager of a car dealership is ordering a new car. The options for the new car are shown in the table below. |

|Options for New Car |

|Categories |

|Options |

| |

| |

|  Color |

|    white |

|    red |

|    silver |

| |

|  Roof style |

|    hard top |

|    convertible |

| |

|  Number of doors |

|    2 doors |

|    4 doors |

| |

| |The manager decides to let his computer randomly select one option for each of the three categories in the table. |

a. Based on the table, what is the total number of combinations of 1 color, 1 roof style, and 1 number of doors that can be selected for the new car? Show or explain how you got your answer.

b. What is the probability that the computer will select a hard top for the new car? Show or explain how you got your answer.

c. What is the probability that the computer will not select white for the new car's color? Show or explain how you got your answer.

d. What is the probability that the computer will select for the new car to both be silver and have 2 doors? Show or explain how you got your answer.

 

|Brad made the Venn diagram below to show the number of cars in a parking lot that were red, had four doors, had a sunroof, or had |

|any combination of those features. He left one number off his Venn diagram. |

|[pic] |

|a. |

|Describe what the 6 represents in the Venn diagram. |

| |

|b. |

|A total of 20 cars in the parking lot were red, had four doors, had a sunroof, or had any combination of those features. What |

|number should Brad put in place of the "?" in the center section of his Venn diagram? Show or explain how you got your answer. |

| |

|c. |

|What was the total number of cars in the parking lot that were red? Show or explain how you got your answer. |

| |

The individual weights, in pounds, of the members of a school’s wrestling team are shown in the box below.

|180 |

|171 |

|180 |

|162 |

|163 |

|177 |

|203 |

|155 |

|165 |

|191 |

|196 |

|178 |

|165 |

|168 |

|175 |

|195 |

| |

a. What is the range of the weights? Show or explain how you got your answer.

b. Copy the diagram below into your Student Answer Booklet. Use the diagram to make a stem-and-leaf plot of the data above. Be sure to title your plot and provide a key.

| |[| |

| |p| |

| |i| |

| |c| |

| |]| |

| | | |

| | | |

| | | |

|tens | |Ones |

|[pic] |

|  | |[pic] |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | |Mr. Turner surveyed the students in his class to find out |

| | |if they had read the front page, the |

| | |comics, the sports, or any combination of those sections of|

| | |the previous day’s newspaper. He |

| | |recorded the results in the Venn diagram below. |

| | |Sections of Newspaper |

| | |Read by Students |

| | |[pic] |

| | |Based on the Venn diagram, what was the total number of |

| | |students who had read the front |

| | |page of the previous day’s paper? |

c. What is the median weight for the data in your stem-and-leaf plot from part (b)? Show or explain how you got your answer.

Lorna swam 30 laps per day for the first 6 days of swim practice. She swam 40 laps per day for the next 4 days of practice. What was the mean number of laps that Lorna swam per day for these 10 days?

The stem-and-leaf plot below shows the number of laps walked by 15 students in a walk-a-thon.

|Number of |Key |

|Laps Walked | |

| |1 | 8 represents 18 |

|[pic] | |

| | |

|1   | |

| | |

|2   | |

| | |

|3   | |

| | |

|4   | |

|[pic] | |

|  2   4   4   6   7 | |

| | |

|  0   0   0   3   5   8 | |

| | |

|  0   2   6 | |

| | |

|  2 | |

| | |

What is the total number of students who walked more than 29 laps?

 

 

[pic]

Geometry/Measurement

Open Responses:

Michael stacked cubes to make the structure shown below.

[pic]

a. Draw the right side view of Michael's structure. Be sure to label your drawing "right side view."

Michael used a total of 14 cubes to make his structure.

b. Draw the front view of Michael's structure. Be sure to label your drawing "front view."

c. Draw one possible top view for Michael's structure. Be sure to label your drawing "top view." Show or explain how you got your answer.

|Mora bought a box of cereal that was a rectangular prism with a length of 7.5 inches, a width of 2.5 inches, and a height of 11 |

|inches, as shown below. |

|[pic] |

|a. |What is the total number of vertices of Mora’s cereal box? Show or explain how you got your answer. |

|b. |What is the total number of faces of Mora’s cereal box? Show or explain how you got your answer. |

|c. |In your Student Answer Booklet, draw a net (flat pattern) that can be folded to form a box with the same dimensions as Mora’s|

| |cereal box. Be sure to label your drawing of the net with the lengths, in inches, of the line segments. |

Chelsea drew triangle ABC so that the vertices are at points A (4,−2), B (2,−5), and C (5,−6), as shown on the coordinate grid below.

[pic]

a. Copy the coordinate grid and triangle ABC onto the grid in your Student Answer Booklet. Draw the reflection of triangle ABC across the x-axis to form triangle A'B'C'. List the coordinates for point A', point B', and point C'.

b. On the same coordinate grid, draw the refl ection of triangle A'B'C' across the y-axis to form triangle A"B"C". List the coordinates for point A", point B", and point C".

c. David drew [pic] on a coordinate plane, as shown below.

Short Answers:

[pic]

David reflected [pic] over the x-axis. What are the coordinates of the image of point A?

The figure below shows [pic]PQR and two of its angle measures.

[pic]

What is the degree measure of [pic]P ?

Parallelogram PQRS and the coordinates of point Q are shown on the coordinate plane below.

[pic]

What are the coordinates of the image of point Q after parallelogram PQRS is translated

6 units to the left?

 

In the figure below, parallel lines l and m are intersected by transversal p.

[pic]

If the measure of [pic]1 is 50°, what is the degree measure of [pic]2?

A large jet has a wingspan of 87[pic] yards, as shown below.

[pic]

What is the wingspan, in feet, of the jet?

 

Triangle DEF is similar to triangle ABC.

[pic]

What is the measure, in degrees, of [pic]F?

 

[pic]

Area and Volume

Open Responses:

A cafeteria has a recycling container for cans. The recycling container has a lid that is in the shape of a circle with an opening in the center that is also in the shape of a circle. The lid and some of its dimensions are shown in the diagram below.

[pic]

The shaded part of the diagram represents the opening in the lid.

a. What is the circumference, in inches, of the lid of the recycling container? Show or explain how you got your answer. (Use 3.14 for π.)

b. What is the area, in square inches, of the lid, including the opening? Show or explain how you got your answer. (Use 3.14 for π.)

c. What is the area, in square inches, of the lid, not including the opening? Show or explain how you got your answer. (Use 3.14 for π.)

| |

|Erika has a cylindrical container with a diameter of 6 inches and a height of 1.5 feet, as shown below. |

|[pic] |

a. What is the height, in inches, of the container? Show or explain how you got your answer.

b. What is the volume, in cubic inches, of the container? Show or explain how you got your answer. (Use 3.14 for π.)

c. Erika filled the container with 250 cubic inches of sand. What is the approximate height, in inches, of the sand that Erika put in the container? Show or explain how you got your answer.

A rancher has two water tanks.

• Each water tank is in the shape of a cylinder.

• The base of each water tank is in the shape of a circle.

Diagrams of the two water tanks are shown below.

|[pic] |

|a. |What is the circumference, in feet, of the base of Water Tank 1? Show or explain how you got your answer. (Use 3.14 for π.) |

|b. |The circumference of the base of Water Tank 2 is 6.28 feet longer than that of Water Tank 1. What is the diameter, in feet, |

| |of the base of Water Tank 2? Show or explain how you got your answer. (Use 3.14 for π.) |

|c. |How many more square feet does the base of Water Tank 2 cover than the base of Water Tank 1? Show or explain how you got your|

| |answer. (Use 3.14 for π.) |

The diagram below shows the circular surface of a pond being designed for a park and a walkway around the pond. The diameter of the surface of the pond will be approximately 200 feet.

[pic]

a. Based on the diameter, what will be the circumference, in feet, of the surface of the pond? Show or explain how you got your answer. (Use 3.14 for [pic].)

b. What will be the area, in square feet, of the surface of the pond? Show or explain how you got your answer.

c. As the diagram shows, a walkway 10 feet wide is being designed to go around the pond. What will be the area, in square feet, of the walkway? Show or explain how you got your answer.

 Short Answers:

|A shipping box is in the shape of a rectangular prism, as shown below. |

|[pic] |

|It has a length of 12 inches. |

|It has a width of 6 inches. |

|It has a volume of 288 cubic inches. |

|What is the height, in inches, of the shipping box? |

[pic]

Real Numbers and Pythagorean Theorem

Open Responses:

Danielle measured two of the computer screens in her school’s computer lab. The two screens and some of their dimensions are shown below.

[pic]

a. What is the area, in square inches, of Screen 1? Show or explain how you got your answer.

b. What is x, the diagonal length in inches of Screen 1? Show or explain how you got your answer.

c. Which computer screen, Screen 1 or Screen 2, has the greater area? Show your work or explain how you got your answer.

d. For an art project, Calvin drew a rectangle inscribed in circle C, as shown below.

Short Answers:

The rectangle is 8 centimeters long and 6 centimeters wide.

e. [pic]

What is the diameter, in centimeters, of circle C?

On the real number line, between what two consecutive integers is [pic]?

[pic]

Polynomials

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