Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A ratio compares two quantities by saying how much of one there is for a certain amount of the other. If a fruit bowl holds 6 apples and 4 pears, the ratio of apples to pears is 6 to 4, which can be written 6:4, and students learn to say it in words: for every 3 apples there are 2 pears. Sixth grade is where this way of thinking becomes a named idea, and it underpins most of the proportional reasoning in grades 6 to 8.
Order matters. Apples to pears (6:4) is not the same comparison as pears to apples (4:6). Students also meet the difference between part-to-part ratios (apples to pears) and part-to-whole ratios (apples to all the fruit, 6:10). Being able to describe a situation in ratio language, and to read a ratio statement back as a picture or a table, is the whole goal here. Calculations come later in the cluster, so the emphasis is on precise wording and on seeing that 6:4 and 3:2 describe the same relationship.
Asked for the ratio of boys to girls, students often write the girls first. Have them label each number with its unit (12 boys : 15 girls) until the habit sticks.
A ratio of 2:3 apples to pears does not mean 2/3 of the fruit is apples. Apples make up 2 parts out of 5 in total, so they are 2/5 of the fruit.
A 3:1 ratio of water to juice does not mean there are exactly 3 cups of water. It describes how the amounts compare; the mix could be 6 cups to 2 cups.
Some students describe 8 cats and 4 dogs by saying there are 4 more cats. That is a difference, not a ratio. The ratio says there are 2 cats for every dog.
A class has 12 students who walk to school and 18 who ride the bus. Write the ratio of walkers to bus riders, a simpler equivalent ratio, and the ratio of walkers to all students.
Answer: Walkers to bus riders is 12:18, or 2:3. Walkers to the whole class is 12:30, or 2:5.
Start with real counts from the room (pencils to erasers, windows to doors) and have students say the ratio sentence aloud before writing anything. Tape diagrams and colored counters help students see that 4:6 and 2:3 are the same relationship grouped differently.
Assessment items for this standard are often matching tasks: choose the statement that correctly describes a picture, or decide whether a ratio is part-to-part or part-to-whole. Expect students to explain their choice in words.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: A) 8:5
Tulips are named first, so their count comes first: 8 tulips to 5 roses, or 8:5.
Answer: 10
4 + 6 = 10 marbles. The part-to-whole ratio of red marbles to all marbles is 4:10.
Answer: C) The ratio of drummers to singers is 3:1
'3 drummers for every 1 singer' is the ratio of drummers to singers, 3:1. Reversing the order describes a different comparison.
Answer: B) 10:16
The whole is all games played: 10 + 6 = 16. Wins to all games is 10:16, which compares a part to the whole.
Answer: 3
Split 9 dogs and 3 cats into 3 equal groups: each group has 3 dogs and 1 cat. So there are 3 dogs for every cat.
Answer: D) 5 more boys than girls
'5 more boys than girls' compares by subtracting. The other three compare by saying how much of one quantity goes with a set amount of the other.
A full lesson with slides, activities and an exit ticket on understanding ratios, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 6.RP.A.1 with an answer key, ready in about a minute.
Make a worksheet βTurn understanding ratios into a quiz students answer online that marks itself, with a class summary for you.
Build a test βSixth graders can describe how two amounts compare using ratio language, such as 'for every 2 red tiles there are 5 blue tiles', and can write that relationship as 2:5 or 2 to 5.
Not exactly. A part-to-whole ratio can be written as a fraction, but a part-to-part ratio such as 2 cats to 3 dogs does not describe a fraction of one whole. Students should know which kind they are using.