Ratio table and double number line

What the tool shows

A ratio compares two amounts, such as 3 cups of flour for every 2 eggs. This tool keeps the two amounts together in a ratio table. Choose a story, set the two numbers, then build new rows with × 2, × 3, ÷ 2 or by adding one more batch. Every row is also drawn on a double number line, with one quantity on each line, so equal ratios line up. The readout gives the unit rate both ways, such as 1.5 cups of flour per egg, and a dashed purple mark shows where the unit rate sits on the lines.

Why a table helps

Ratio problems are easy to get wrong by adding instead of multiplying. If 3 cups of flour go with 2 eggs, a student might say 4 cups go with 3 eggs, adding 1 to each. A table shows that every new row comes from multiplying or dividing both amounts by the same number, or from adding a whole batch, and the double number line shows that the rows stay in proportion. Unit rates then appear naturally: halve 3 : 2 and you get 1.5 : 1.

Common mix-ups

• Adding the same number to both amounts. 3 : 2 and 4 : 3 are not equivalent. Check by looking for one number that multiplies both.
• Changing only one amount. Doubling the flour without doubling the eggs changes the recipe.
• Mixing up the order. 3 : 2 here means 3 cups of flour to 2 eggs, not 3 eggs to 2 cups. The table headings keep the order fixed.
• Expecting unit rates to be whole numbers. 3 cups for 2 eggs is 1.5 cups per egg, and that is a perfectly good rate.

A 10-minute activity

• Minutes 1 to 3: choose Baking. Ask the child to predict the next row before pressing × 2, then do the same with × 3.
• Minutes 4 to 5: press Start again, then ÷ 2. Ask what 1.5 cups of flour for 1 egg means in the kitchen.
• Minutes 6 to 8: press Missing value. The child builds rows until one matches the question, then types the answer and presses Check.
• Minutes 9 to 10: switch to Apples, where 4 apples cost 3 dollars, and ask how much 1 apple costs. Compare the child's answer with the readout.

Where it fits by grade

• Grade 6: ratio language (Common Core 6.RP.A.1), unit rates (6.RP.A.2), and tables of equivalent ratios, tape diagrams and double number lines for finding missing values and solving rate problems (6.RP.A.3a and 6.RP.A.3b).
• Grade 7: proportional relationships, including unit rates that involve fractions (7.RP.A.1 and 7.RP.A.2).
• Grade 5: students who know their multiplication facts well can use the table as a preview of ratios.
• England: Year 6 pupils solve problems about the relative sizes of two quantities where missing values come from multiplication and division facts, and ratio continues through Key Stage 3.

Learning more

Ratios and proportions is a skill on Eurekami's skill map, and lessons build ratio tables like this one from the numbers in each question. For word problems that feel stuck, the AI tutor asks the next useful question rather than handing over the answer.