Michael Was Mixing Blue Paint and Red Paint in the Ratio of 2:3 to Make Purple Paint. He

GRADE 6

Michael was mixing blue paint and red paint in the ratio of 2:3 to make purple paint. He wants to make 45 quarts of purple paint. He began to make a table to help him think about the problem, but is unsure of what to do next.

Quarts of Blue Paint / Quarts of Red Paint / Quarts of Purple Paint
2 / 3 / 5
4 / 6 / 10

1. Complete the table and explain in your own words how to complete the table.

1. Write an explanation to Michael explaining how he can use the table to determine how many quarts of each color he needs to make 45 quarts of purple.

1. Create at least one other mathematical model to represent this problem. You may use a tape diagram, a double-number line or a graph.

Possible Extensions:

GRADE 7

Michael was mixing blue paint and red paint in the ratio of 2:3 to make purple paint. He wants to make 45 quarts of purple paint. He began to make a table to help him think about the problem, but is unsure of what to do next.

Quarts of Blue Paint / Quarts of Red Paint / Quarts of Purple Paint
2 / 3 / 5
4 / 6 / 10

1. Complete the table and explain in your own words how to complete the table.

1. Create a graph showing (quarts of blue, quarts of red). Do the two quantities represent a proportional relationship? Explain how you know.

1. Identify the constant of proportionality. What does it mean in the context of the problem?

1. Write an explanation in words to Michael about how he can use your graph to determine how many quarts of each color he needs to make 45 quarts of purple.

Possible Extensions:

GRADE 8

A professional typist can type 50 words per minute.

1. Graph the relationship described above. Be sure to label your axes.

1. Write an equation relating the number of words typed in terms of the time in minutes. What information does the coefficient in the equation represent?

1. The graph below represents the number of words typed by Sarah over a 60 minute period of time. Write an equation relating the number of words typed in terms of the time in minutes.

1. Determine if the following statements are true or false. Provide evidence based on the context of the problem that shows why the statements are true or false. Explain your reasoning in words.
2. A person can decide if Sarah types faster or slower than the professional typist by comparing her graph to the professional’s graph.
3. A person can decide if Sarah types faster or slower than the professional typist by comparing her equation to the professional’s equation.

Similar Triangles

Brian and Maddie used different triangles to determine the slope of the line shown below.

Brian started at (0, –1) and drew a right triangle going up 2 units and right 3 units. / Maddie started at (–3, –3) and drew a right triangle going up 6 units and right 9 units.

1. Draw and label both triangles on the graph above. Use blue to draw Brian’s triangle and red to draw Maddie’s triangle.

1. Describe how the two triangles are related.

1. Find the slope of the line using Brian’s triangle and Maddie’s triangle. Show all work.

1. Justify how the triangles relate to the slope of the line. Why can you find the slope using any two points on the line?

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