2025-2026 2024-2025 Math Essentials- Benchmark 3- Spring 2024

1

Solve for x:

x+7=4

1

Solve for n:

n-17=5

1

Solve for u:

8u=56

1

Solve for t:

\frac{t}{6}=-3

1

There are 30 students in a drama club. They are carpooling in 6 vans to perform a play. They want each van to carry an equal number of students. Let s be the number of students in each van. Write an equation to find the number of students in each van.

1

Solve for x:

3x+1=16

1

Solve for x:

x/4-3=2

1

Solve for x:

2/3x+7=13

1

Solve for x:

4x+13-x=40

1

Solve for x:

-2(x-6)=-18

1

Solve for x:

3(2x-4)-10=20

1

Solve for x:

3(x-4)-1=x-15

1

Determine the number of solutions.

1

There are 7 ushers and 11 technicians helping at the Harper Middle School fall play. What is the ratio of technicians to all helpers?

1

Anya’s team won 5 out of every 7 games this season. If the team played 28 games this season, how many games did they win?

1

Complete the table of equivalent ratios.

Make a graph that illustrates the equivalent ratios shown in the table. Add the next three points.

Instructions

Click the graph tab.
Click on the graph background to add a point. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

1

Which pay is equivalent to a rate of $16 per hour?

1

A cook makes vegetable barley soup by mixing 2 pounds of barley into 7 quarts of vegetable broth. Assume that the cook continues to use the same rate to make more batches of soup. How many pounds of barley should the cook mix with 35 quarts of broth?

1

Two trains are traveling at a constant rate. Which train has the greater speed?

1

Which graph shows a line with the slope of 3/2?

1

The points (80, 20) and (120, 30) for a proportional relationship. What is the slope of the line that passes through these points?

1

Graph the equation y= -1/2 x

Instructions

Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

1

The graph relates the number of gallons of white paint to the number of gallons of red paint Jess used to make the perfect pink. Write an equation that describes the relationship.

1

Find the rate of change and initial value for the linear function.

The rate of change is _______ 

The initial value is _______ 

1

What is the y-intercept for each of the linear relationships shown?

What is an equation for the line shown?

1

Graph the line with equation y= 1/3 x -5

Instructions

Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

1

Choose the equation for the line in slope-intercept form

1

	No Solution	Infinite Solutions	One Solution

	No Solution	Infinite Solutions	One Solution

2025-2026 2024-2025 Math Essentials- Benchmark 3- Spring 2024

Solve for x:x+7=4

Solve for n:n-17=5

Solve for u:8u=56

Solve for t:\frac{t}{6}=-3

There are 30 students in a drama club. They are carpooling in 6 vans to perform a play. They want each van to carry an equal number of students. Let s be the number of students in each van. Write an equation to find the number of students in each van.

Solve for x:3x+1=16

Solve for x:x/4-3=2

Solve for x:2/3x+7=13

Solve for x:4x+13-x=40

Solve for x:-2(x-6)=-18

Solve for x:3(2x-4)-10=20

Solve for x:3(x-4)-1=x-15

Determine the number of solutions.

There are 7 ushers and 11 technicians helping at the Harper Middle School fall play. What is the ratio of technicians to all helpers?

Anya’s team won 5 out of every 7 games this season. If the team played 28 games this season, how many games did they win?

Make a graph that illustrates the equivalent ratios shown in the table. Add the next three points.

Which pay is equivalent to a rate of $16 per hour?

A cook makes vegetable barley soup by mixing 2 pounds of barley into 7 quarts of vegetable broth. Assume that the cook continues to use the same rate to make more batches of soup. How many pounds of barley should the cook mix with 35 quarts of broth?

Two trains are traveling at a constant rate. Which train has the greater speed?

Which graph shows a line with the slope of 3/2?

The points (80, 20) and (120, 30) for a proportional relationship. What is the slope of the line that passes through these points?

Graph the equation y= -1/2 x

The graph relates the number of gallons of white paint to the number of gallons of red paint Jess used to make the perfect pink. Write an equation that describes the relationship.

The graph relates the number of gallons of white paint to the number of gallons of red paint Jess used to make the perfect pink. Write an equation that describes the relationship.

What is an equation for the line shown?

Graph the line with equation y= 1/3 x -5

Choose the equation for the line in slope-intercept form

Tickets to a baseball game cost $22 each and parking costs $10. What is the equation of the line that represents the cost of attending the game?

Solve for x:x+7=4

Solve for n:n-17=5

Solve for u:8u=56

Solve for t:\frac{t}{6}=-3

There are 30 students in a drama club. They are carpooling in 6 vans to perform a play. They want each van to carry an equal number of students. Let s be the number of students in each van. Write an equation to find the number of students in each van.

Solve for x:3x+1=16

Solve for x:x/4-3=2

Solve for x:2/3x+7=13

Solve for x:4x+13-x=40

Solve for x:-2(x-6)=-18

Solve for x:3(2x-4)-10=20

Solve for x:3(x-4)-1=x-15

Determine the number of solutions.

There are 7 ushers and 11 technicians helping at the Harper Middle School fall play. What is the ratio of technicians to all helpers?

Anya’s team won 5 out of every 7 games this season. If the team played 28 games this season, how many games did they win?

Make a graph that illustrates the equivalent ratios shown in the table. Add the next three points.

Which pay is equivalent to a rate of $16 per hour?

A cook makes vegetable barley soup by mixing 2 pounds of barley into 7 quarts of vegetable broth. Assume that the cook continues to use the same rate to make more batches of soup. How many pounds of barley should the cook mix with 35 quarts of broth?

Two trains are traveling at a constant rate. Which train has the greater speed?

Which graph shows a line with the slope of 3/2?

The points (80, 20) and (120, 30) for a proportional relationship. What is the slope of the line that passes through these points?

Graph the equation y= -1/2 x

The graph relates the number of gallons of white paint to the number of gallons of red paint Jess used to make the perfect pink. Write an equation that describes the relationship.

The graph relates the number of gallons of white paint to the number of gallons of red paint Jess used to make the perfect pink. Write an equation that describes the relationship.

What is an equation for the line shown?

Graph the line with equation y= 1/3 x -5

Choose the equation for the line in slope-intercept form

Tickets to a baseball game cost $22 each and parking costs $10. What is the equation of the line that represents the cost of attending the game?

Solve for x:

x+7=4

Solve for n:

n-17=5

Solve for u:

8u=56

Solve for t:

\frac{t}{6}=-3

Solve for x:

3x+1=16

Solve for x:

x/4-3=2

Solve for x:

2/3x+7=13

Solve for x:

4x+13-x=40

Solve for x:

-2(x-6)=-18

Solve for x:

3(2x-4)-10=20

Solve for x:

3(x-4)-1=x-15

Solve for x:

x+7=4

Solve for n:

n-17=5

Solve for u:

8u=56

Solve for t:

\frac{t}{6}=-3

Solve for x:

3x+1=16

Solve for x:

x/4-3=2

Solve for x:

2/3x+7=13

Solve for x:

4x+13-x=40

Solve for x:

-2(x-6)=-18

Solve for x:

3(2x-4)-10=20

Solve for x:

3(x-4)-1=x-15