Grade 7 ratios and proportional relationships: what it is and what to check

What it is

The state standards group this domain under one idea: analyze proportional relationships and use them to solve real-world and mathematical problems. In plain terms, grade 7 covers:

• Unit rates, including rates with fractions (NY-7.RP.1), like "3/4 of a mile in 1/2 an hour".
• Deciding whether two quantities are in a proportional relationship, finding the constant of proportionality (the unit rate) in a table, graph, equation or picture, and writing the equation (NY-7.RP.2).
• Explaining what a point on the graph means, with special attention to (0, 0) and (1, r) (NY-7.RP.2d).
• Multistep ratio and percent problems: discounts, tax, tips, interest, percent change (NY-7.RP.3).

Grade 7 ratio work leans on fractions and division. A child who is shaky there will struggle here even if they understand ratios.

Five things to check

1. Equivalent ratios: can they fill in a missing number in 3 : 5 = 12 : ?, and say why it works?
2. Unit rate from a table: given cost for 4 items, 6 items and 10 items, can they find the cost of one?
3. Percent of a number: what is 15% of 80, and how did they get it?
4. Percent steps: a price drops 25% and then tax is added. Do they apply each step to the right amount?
5. Meaning: ask what the number 12 means in "12 miles per hour". A child who says "how far in one hour" understands the idea.

Sample questions, with answers

Each question was checked by two separate programs. The other answers are the ones a child gets from a typical slip.

1. A pancake batter uses 4 eggs for every 5 cups of milk. At this rate, how many cups of milk are needed for 20 eggs?

   • A. 30 cups
   • B. 100 cups
   • C. 25 cupsAnswer
   • D. 21 cups
   What the other answers come from

   • 30 cups: One Batch Too Many. Count how many times the first amount fits, and use exactly that many.
   • 100 cups: Skipped the Divide. Find the amount for one by dividing, then multiply for the new amount.
   • 21 cups: Adding Both Sides. Ratios grow by multiplying. Find what you multiply by, then use it on both.

2. A pancake batter uses 5 eggs for every 3 cups of milk. At this rate, how many cups of milk are needed for 25 eggs?

   • A. 15 cupsAnswer
   • B. 18 cups
   • C. 75 cups
   • D. 23 cups
   What the other answers come from

   • 18 cups: One Batch Too Many. Count how many times the first amount fits, and use exactly that many.
   • 75 cups: Skipped the Divide. Find the amount for one by dividing, then multiply for the new amount.
   • 23 cups: Adding Both Sides. Ratios grow by multiplying. Find what you multiply by, then use it on both.

3. A grocery store sells apples by the pound. The table shows this relationship.

   Weight (pounds)	Total Cost
   5	$25.50
   9	$45.90
   11	$56.10

   What is the cost per pound of apples?

   • A. $5.10 per poundAnswer
   • B. $20.50 per pound
   • C. $25.50 per pound
   • D. $20.40 per pound
   What the other answers come from

   • $20.50 per pound: Minus Trap. Rates come from dividing. Divide the total by the amount.
   • $25.50 per pound: Grabbed a Total. That's a total from the table. Divide total by amount to get the rate for one.
   • $20.40 per pound: Row Gap. Subtracting two rows won't give the amount for one. Divide total by amount.

4. A craft store sells ribbon by the yard. The table shows this relationship.

   Ribbon (yards)	Total Cost
   4	$4.40
   10	$11.00
   15	$16.50

   What is the cost per yard of ribbon?

   • A. $6.60 per yard
   • B. $0.40 per yard
   • C. $1.10 per yardAnswer
   • D. $4.40 per yard
   What the other answers come from

   • $6.60 per yard: Row Gap. Subtracting two rows won't give the amount for one. Divide total by amount.
   • $0.40 per yard: Minus Trap. Rates come from dividing. Divide the total by the amount.
   • $4.40 per yard: Grabbed a Total. That's a total from the table. Divide total by amount to get the rate for one.

What a gap looks like

• Adding the same amount to both parts of a ratio instead of multiplying: 2 : 3 becomes 4 : 5 rather than 4 : 6.
• Setting up the unit rate upside down: dividing the number of items by the cost instead of the cost by the number of items.
• Taking a percent off, then adding the same percent back, and expecting to end where they began.

Most of these trace to multiplication and division facts, or to fractions. If you see them, look backward first: how to find math gaps in a 7th grader.

Keep reading

• NYS grade 7 math test: format, topics and calculator
• How to find math gaps in a 7th grader