6.RP.A.1Common CoreMathRatios and Proportional RelationshipsGrade 6
6.RP.A.1: Understanding Ratios and Ratio Language
In plain English: 6.RP.A.1 is the Common Core grade 6 math standard that asks students to understand what a ratio is and to use ratio language, such as "3 to 2", "3:2" or "for every 3 there are 2", to describe how two quantities are related. Students write part-to-part and part-to-whole ratios and learn that order matters. It starts the grade 6 unit on ratios and rates.
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."
Common Core State Standards for Mathematics · Domain: Ratios and Proportional Relationships (RP) · Cluster: Understand ratio concepts and use ratio reasoning to solve problems. Also written as 6.RP.1 · Official standard
Students meet the idea of a ratio: a comparison of two quantities that says how many of one there are for a certain number of the other. They learn three ways to write and say a ratio: with a colon (3:2), with the word "to" (3 to 2), and with ratio language such as "for every 3 cups of flour there are 2 cups of milk". They see that the order of the numbers matters, and they tell apart part-to-part ratios (one part of a group compared with another part) and part-to-whole ratios (one part compared with the whole group).
The lesson works through both official examples: the wings and beaks in a zoo bird house (a 2:1 ratio) and an election in which candidate C received nearly three votes for every vote candidate A received. Students also learn why a ratio is different from a difference: "12 more students than laptops" and "3 students for every laptop" say different things. Unit rates (6.RP.A.2) and ratio tables (6.RP.A.3) come next; here the focus is on understanding what a ratio says and describing it clearly. All quantities are whole numbers.
Learning Objectives
By the end of this lesson, students will be able to:
Explain what a ratio is and write it three ways: a:b, a to b, and "for every a ..., there are b ..."
Write part-to-part and part-to-whole ratios from a picture, a list or a story
Explain why the order of the quantities in a ratio matters
Tell the difference between comparing two quantities with a ratio and comparing them with a difference
Use words such as "nearly" or "about" to describe a ratio relationship that is close to a whole-number ratio
Prior Knowledge Required
Students should already be comfortable with:
Comparing quantities with multiplication, such as "3 times as many" 4.OA.A.14.OA.A.2
Understanding a fraction as parts of a whole 3.NF.A.1
Recognizing equivalent fractions such as 2/3 = 4/6 4.NF.A.1
Multiplying and dividing whole numbers with basic facts
Show the class a pet store fish tank (a picture or a drawing on the board) and pose the question:
Warm-Up Prompt
"A fish tank has 4 goldfish and 12 guppies. Write two different sentences that compare the number of goldfish with the number of guppies."
Collect sentences and sort them into two columns on the board. Some students will subtract: "There are 8 more guppies than goldfish." Others will multiply or group: "There are 3 times as many guppies as goldfish" or "For every 1 goldfish there are 3 guppies." Explain that the second kind of sentence describes a ratio, and that this lesson is about that kind of comparison. Ask: if the store adds 4 goldfish and 12 guppies, which sentence is still true? (For every 1 goldfish there are still 3 guppies, because 8 goldfish and 24 guppies keep the same groups. The difference changes from 8 to 16.)
Direct Instruction15-20 minutes
Part 1: What a ratio is. A ratio is a comparison of two quantities that tells how many of one quantity there are for a certain number of the other. We write the ratio of goldfish to guppies as 4:12 (read "4 to 12") or as 4 to 12. Because the fish can be split into 4 equal groups of 1 goldfish and 3 guppies, 4:12 describes the same relationship as 1:3. In ratio language: for every 1 goldfish there are 3 guppies. The order matters: the ratio of guppies to goldfish is 12:4, or 3:1.
Official example: wings to beaks
The bird house at the zoo has 14 birds. Each bird has 2 wings and 1 beak. What is the ratio of wings to beaks, and what does it mean?
Equation: 14 × 2 = 28 wings and 14 beaks, so wings to beaks is 28:14, the same relationship as 2:1, because for every 2 wings there is 1 beak
Official example: nearly three votes
In a town election, candidate A received 120 votes, candidate B received 95 votes and candidate C received 350 votes. Compare the votes for candidates A and C.
Equation: A to C is 120:350. Three votes for each of A's votes would be 3 × 120 = 360, and 350 is just under 360, so for every vote candidate A received, candidate C received nearly three votes
Part to part and part to whole
A bag holds 8 blue marbles and 12 white marbles. Write a part-to-part ratio in each order and a part-to-whole ratio.
Equation: Blue to white 8:12 (the same as 2:3); white to blue 12:8 (the same as 3:2); blue to all marbles 8:20 (the same as 2:5)
One ratio, several descriptions
A school garden has 5 rows of beans and 3 rows of corn. Describe the relationship in as many ways as you can.
Equation: Beans to corn is 5:3, or 5 to 3: for every 5 rows of beans there are 3 rows of corn. Corn to beans is 3:5. Beans to all rows is 5:8
A ratio is not a difference
Room 12 has 6 laptops for 18 students. Room 14 has 10 laptops for 22 students. Both rooms have 12 more students than laptops. Do they have the same ratio?
Equation: Room 12: 6:18, the same as 1:3 (for every 1 laptop, 3 students). Room 14: 10:22, the same as 5:11 (for every 5 laptops, 11 students). Same difference, different ratios
Part 2: Ratio language. Put these sentence frames on the board and use them for every example: "The ratio of ___ to ___ is ___:___"; "For every ___ ___, there are ___ ___"; "For each ___ there are ___"; and, when one number is a multiple of the other, "There are ___ times as many ___ as ___". Work the official wings example with a tape diagram, a drawing of bars split into equal boxes where every box stands for the same amount (Diagram 2): wings get 2 boxes and beaks get 1 box, and each box is 14.
Part 3: Part to part, part to whole, and "nearly". Use Diagram 1 to show that the same bag gives a part-to-part ratio (blue to white) and a part-to-whole ratio (blue to all marbles). Point out that the whole, 20, is found by adding the parts. Then discuss the official election example. Real counts are not always an exact number of groups, so ratio language allows words like "nearly" and "about". Candidate C did not get exactly 3 votes for each of A's votes, but 350 is close to 360, so "nearly three" is an honest description. Ask why "about three" would also be fine, but "exactly three" would not.
Guided Practice15 minutes
Pairs solve three problems on mini whiteboards. After each one, two pairs read their sentences aloud and the class checks the order of the quantities.
Problem 1: a basket at the class party. Write four ratios from the table, in the order asked.
Item
Count
Juice boxes
6
Water bottles
9
Answers to Problem 1: juice boxes to water bottles is 6:9, the same as 2:3 (for every 2 juice boxes there are 3 water bottles); water bottles to juice boxes is 9:6, or 3:2; juice boxes to all drinks is 6:15, or 2:5; water bottles to all drinks is 9:15, or 3:5. Problem 2: a soccer team won 10 games and lost 4, with no ties. Write the ratio of wins to losses and of losses to games played. (10:4, the same as 5:2; 4:14, the same as 2:7.) Problem 3: on Saturday the library lent 198 fiction books and 51 nonfiction books. Complete: "For every nonfiction book, the library lent nearly ___ fiction books." (4, because 4 × 51 = 204 is close to 198, and 3 × 51 = 153 is far away.) Listen for pairs who write the numbers in the order they appear in the story instead of the order the question asks for.
Independent Practice10-15 minutes
Students work alone on four problems. (1) A box has 16 crayons, and 4 of them are shades of green. Write the ratio of green crayons to the other crayons, and of green crayons to all crayons. (4:12, the same as 1:3; 4:16, the same as 1:4.) (2) A parking lot has 20 cars and 5 vans. Which statements are true? "For every 4 cars there is 1 van." "The ratio of cars to vans is 1:4." "The ratio of vans to all vehicles is 1:5." (The first and third are true; the second has the order reversed.) (3) Write a story about any two quantities that have the ratio 7:2, and describe it with "for every". (4) A school orchestra has 32 string players and 11 brass players. Describe the ratio of string players to brass players with the word "about". (About 3 string players for every brass player, since 3 × 11 = 33.)
Closure5 minutes
Exit ticket: (1) A shelf holds 3 math books and 7 science books. Write the ratio of math books to science books and of science books to all books. (3:7 and 7:10.) (2) At a school carnival there are 5 adults and 40 children. Write a "for every" sentence that uses 1 adult. (For every 1 adult there are 8 children.) (3) In one sentence, explain the difference between "35 more children than adults" and "8 children for every adult".
Differentiation Strategies
For Struggling Students
Give counters or snap cubes so students can build each ratio and physically sort the objects into equal groups before writing the numbers
Provide a sentence-frame card ("The ratio of ___ to ___ is ___:___" and "For every ___ there are ___") and have students underline the first quantity named in the question before they write
Color-code the quantities: students write each number in the same color as the object it counts, so the order of the ratio is visible
For Advanced Students
Ask for three different situations that all have the ratio 2:5, one with people, one with money and one with a recipe
Give a group of 30 students in which the ratio of students who walk to students who ride is 2:3, and ask how many walk and how many ride (a preview of 6.RP.A.3, labeled as going further)
Ask students to find real election or sports results in a newspaper and describe one comparison with "nearly" or "about", explaining why their word choice is honest
Assessment Guidance
What to Look For
Check that students write the quantities in the order the question names them and label them ("blue to white", not just "8:12"). Listen for ratio language ("for every", "to") instead of difference language ("more than") when a ratio is asked for. Ask students to point to the part and the whole in a part-to-whole ratio and to explain how they found the whole. When numbers do not form exact groups, students should use "nearly" or "about" and be able to say which whole-number ratio the counts are close to.
02
Classroom Activities
3 Activities
1
Ratio Language Card Match
15 minPairs
Each pair receives 12 cards: 4 situation cards, 4 ratio cards and 4 sentence cards. Pairs make 4 sets of three cards that describe the same ratio relationship, then explain each set to another pair.
Situation Cards (4 cards)
S1: A basketball team has 4 coaches and 12 players.
S2: A pack of pens has 10 red pens and 4 black pens.
S3: In a class of 21 students, 9 wear glasses.
S4: A wildlife park has 6 zebras and 8 giraffes.
Ratio Cards (4 cards)
R1: coaches to players is 1:3
R2: red pens to black pens is 5:2
R3: students who wear glasses to all students is 3:7
R4: giraffes to zebras is 4:3
Sentence Cards (4 cards)
For every 3 players there is 1 coach.
For every 5 red pens there are 2 black pens.
For every 7 students in the class, 3 wear glasses.
For every 3 zebras there are 4 giraffes.
Procedure
Shuffle the cards and spread them face up
Take turns choosing a situation card and finding its ratio card and sentence card; the partner must agree before the set is kept
For each set, check the order: the ratio card must name the quantities in the same order as its numbers
Write one more ratio for each situation in the opposite order
Discussion Questions
Which set is a part-to-whole ratio? How can you tell? (S3: 21 is the whole class)
Card R4 names the giraffes first, but situation S4 names the zebras first. Why does R4 still match S4?
In S2, there are 6 more red pens than black pens. Why is "6" not a ratio?
Modification for Distance Learning
Put the 12 cards on a shared slide. Pairs drag the cards into three-card rows in breakout rooms, then paste a screenshot of their rows into the class chat before the discussion.
2
Class Survey: Ratios About Us
20 minGroups of 4
Each group asks every classmate one yes-or-no question, tallies the answers, and writes four ratio statements about the class. Groups then check each other's statements for order and for the right kind of ratio.
Survey Questions (one per group)
Do you have at least one brother or sister?
Did you eat breakfast today?
Do you play on a sports team?
Is your first name longer than 5 letters?
Procedure
Record every answer on the tally sheet; the "yes" and "no" counts must add up to the number of students present
Write four statements: yes to no, no to yes, yes to all students surveyed, and one "for every" sentence
If the counts do not form exact groups, write a "nearly" or "about" sentence, like the official election example
Trade statements with another group, which checks the order and marks each statement "part to part" or "part to whole"
Sample Results (invented, for the teacher)
In an invented class of 26 students, 17 have a brother or sister and 9 do not. Statements: "The ratio of students with a sibling to students without one is 17:9." "The ratio of students without a sibling to all students is 9:26." "For every student without a sibling, nearly 2 students have one" (2 × 9 = 18, close to 17).
Discussion Questions
Why must the "yes" and "no" counts add up to the class size?
Which of your statements would change if one more student joined the class and answered "yes"?
When is "nearly" a better word than "exactly"?
3
Build It with Snap Cubes
15 minPairs
Partner A reads a ratio card and builds a train of snap cubes in two colors to match it. Partner B describes the finished train in three ways: with a colon, with "to", and with "for every". Partners switch roles for each card.
Ratio Cards (4 cards)
Card 1: For every 2 blue cubes there are 3 yellow cubes. Use 15 cubes in all. (6 blue, 9 yellow)
Card 2: The ratio of yellow cubes to all cubes is 1:4. Use 12 cubes in all. (3 yellow, 9 blue)
Card 3: For every 1 blue cube there are 5 yellow cubes. Use 18 cubes in all. (3 blue, 15 yellow)
Card 4: The ratio of blue cubes to yellow cubes is 4:3. Use 14 cubes in all. (8 blue, 6 yellow)
Procedure
Build the train in repeating groups (for Card 1: 2 blue, 3 yellow, 2 blue, 3 yellow, ...) until you reach the number of cubes on the card
Partner B counts each color and writes the ratio three ways
Both partners color the train on grid paper, one square per cube
Discussion Questions
Which card's train had the most yellow cubes? (Card 3, with 15)
On which two cards did the train have more blue cubes than yellow cubes? (Cards 2 and 4)
Card 2 gives a part-to-whole ratio. How did you find the number of blue cubes?
Challenge Variation
Pairs write their own ratio card with a total number of cubes, trade with another pair, and check whether the total can really be built from whole groups (for example, a 2:3 train cannot have exactly 12 cubes).
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Part-to-Part and Part-to-Whole Ratios in One Bag
The 8 blue and 12 white marbles split into 4 equal groups of 2 blue and 3 white. The same bag gives two part-to-part ratios, blue to white (8:12) and white to blue (12:8), and a part-to-whole ratio, blue to all 20 marbles (8:20).
Diagram 2: A Tape Diagram for the Official Wings and Beaks Example
A tape diagram uses bars of equal boxes. For 14 birds, the wings bar has 2 boxes and the beaks bar has 1 box, and every box stands for 14. So there are 28 wings and 14 beaks, and the ratio of wings to beaks is 2:1.
04
Homework Assignment
~30 min
6.RP.A.1 Homework: Writing and Describing Ratios
Directions: Label every ratio with the quantities it compares, in order (for example, "apples to oranges"). Use ratio language in your sentences, and show how you found any whole.
Part 1: Writing Ratios (Problems 1-2)
A fruit bowl has 5 apples and 7 oranges. (a) Write the ratio of apples to oranges in three ways: with a colon, with the word "to", and with a "for every" sentence. (b) Write the ratio of oranges to apples. (c) Write the ratio of apples to all the fruit in the bowl.
A bike shop has 36 bikes and 12 scooters on display. Write the ratio of bikes to scooters. Then write a "for every" sentence that uses 1 scooter, and explain how you found it.
Part 2: Order, Parts and Wholes (Problems 3-4)
A class has 13 boys and 15 girls. (a) Write the ratio of girls to all students. (b) Write the ratio of boys to girls. (c) Explain why 13:15 and 15:13 describe different relationships.
A necklace has 30 beads. Its pattern repeats 4 blue beads, then 1 white bead. (a) How many blue beads and how many white beads does it have? (b) Write the ratio of blue beads to white beads. (c) Write the ratio of white beads to all beads.
Part 3: Describing Ratio Relationships (Problems 5-6)
In a vote for student council, Ali received 41 votes and Ben received 162 votes. Write a sentence like the official example: "For every vote Ali received, Ben received nearly ___ votes." Explain how you chose the number and why the word "nearly" is needed.
An animal shelter has 12 dogs and 18 cats. Decide whether each statement is true or false, and explain: (a) The ratio of dogs to cats is 2:3. (b) For every 3 cats there are 2 dogs. (c) The ratio of cats to all the animals is 3:5. (d) There are 6 more cats than dogs, so the ratio of cats to dogs is 6.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Writing Ratios
Ratios written correctly in all three forms and labeled
Correct numbers but one form missing or unlabeled
Ratios missing or incorrect
Order of Quantities
Every ratio lists the quantities in the order asked, with an explanation of why order matters
One ratio reversed
Several ratios reversed
Part to Part and Part to Whole
Wholes found correctly and part-to-whole ratios correct
Whole found but one ratio incorrect
Parts and wholes confused
Ratio Language
Clear "for every" and "nearly" sentences that match the numbers
Sentences correct but unclear or with a small error
Uses differences instead of ratios
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
A desk drawer holds 3 rulers and 5 glue sticks. What is the ratio of rulers to glue sticks?
Answer: C
The question names rulers first, so the ratio is 3 rulers to 5 glue sticks, or 3:5. Choice A reverses the order and gives glue sticks to rulers. Choice B compares the rulers with all 3 + 5 = 8 items, which is a part-to-whole ratio. Choice D compares all 8 items with the glue sticks.
Question 2 of 20 · Multiple Choice
A garden has 6 tomato plants and 10 pepper plants. What is the ratio of pepper plants to all the plants in the garden?
Answer: A
The whole garden has 6 + 10 = 16 plants, so pepper plants to all plants is 10:16 (the same relationship as 5:8). Choice B compares pepper plants with tomato plants, a part-to-part ratio. Choice C compares the tomato plants with all plants. Choice D reverses the order and gives all plants to pepper plants.
Question 3 of 20 · Multiple Choice
At a homework club, the ratio of students to tutors is 4:1. Which sentence means the same thing?
Answer: B
In 4:1, the first number counts students and the second counts tutors, so there are 4 students for every 1 tutor. Choice A reverses the order. Choice C describes a difference, not a ratio: 8 students and 2 tutors have a 4:1 ratio but 6 more students. Choice D uses the group of 4 + 1 = 5 people, but in that group 1 person is a tutor, not a student.
Question 4 of 20 · Multiple Choice
A tricycle has 3 wheels and 1 seat. A daycare has 7 tricycles. What is the ratio of wheels to seats?
Answer: D
7 tricycles have 7 × 3 = 21 wheels and 7 seats, so wheels to seats is 21:7, the same relationship as 3:1: for every 3 wheels there is 1 seat. Choice A reverses the order and gives seats to wheels. Choice B is also seats to wheels, written with one tricycle. Choice C counts the wheels on all 7 tricycles but the seat on only one.
Question 5 of 20 · Multiple Choice
In a basketball game, the Red team scored 26 points and the Blue team scored 9 points. Which completes the sentence? "For every point the Blue team scored, the Red team scored ___."
Answer: C
Three points for each of Blue's points would be 3 × 9 = 27, and 26 is just under 27, so "nearly 3 points" describes the ratio 26:9. Choice A is too far off: 2 × 9 = 18 is 8 points short of 26. Choice B uses the difference 26 - 9 = 17 instead of a ratio. Choice D uses the total 26 + 9 = 35.
Question 6 of 20 · Multiple Choice
A chess club has 12 boys and 16 girls. Which statement is NOT correct?
Answer: D
Statement D reverses the order: the club has more girls than boys, so it cannot have 4 boys for every 3 girls. Statement A is correct as written. Statement B is correct because 12 boys and 16 girls form 4 groups of 3 boys and 4 girls. Statement C is correct because the club has 12 + 16 = 28 members.
Question 7 of 20 · Multiple Choice
At an animal shelter, the ratio of cats to dogs is 2:5. Which could be the number of cats and dogs?
Answer: B
6 cats and 15 dogs make 3 groups of 2 cats and 5 dogs, so for every 2 cats there are 5 dogs. Choice A adds 2 to both numbers of 2:5, which changes the relationship. Choice C reverses the order. Choice D reads 2:5 as 2 cats out of 5 animals, which is a part-to-whole reading of a part-to-part ratio.
Question 8 of 20 · Multiple Choice
Ana has 8 stickers and Ben has 12 stickers. Which sentence uses ratio language to compare them correctly?
Answer: C
8 and 12 split into 4 equal groups of 2 and 3, so for every 2 stickers Ana has, Ben has 3. Choice A is true, but it compares with a difference, 12 - 8 = 4, not a ratio. Choice B adds the two amounts. Choice D reverses the order and would mean Ana has more stickers.
Question 9 of 20 · Multiple Choice
A pizza is cut into 8 equal slices, and 3 slices have mushrooms. What is the ratio of slices without mushrooms to all slices?
Answer: A
8 - 3 = 5 slices have no mushrooms, and there are 8 slices in all, so the part-to-whole ratio is 5:8. Choice B uses the slices with mushrooms. Choice C compares the two parts, slices without mushrooms to slices with them. Choice D reverses the order.
Question 10 of 20 · Multiple Choice
A tape diagram shows a paint mix. The blue bar has 3 equal boxes, the white bar has 2 boxes of the same size, and each box stands for 4 cups. How many cups of white paint are in the mix?
Answer: D
The white bar has 2 boxes of 4 cups, so there are 2 × 4 = 8 cups of white paint. The ratio of blue to white is 12:8, the same as 3:2. Choice A is the blue paint, 3 × 4 = 12 cups. Choice B counts the boxes instead of the cups. Choice C is all the paint, 5 × 4 = 20 cups.
Question 11 of 20 · Multiple Choice
In a choir, the ratio of sopranos to altos is 3:2. Which statement must be true?
Answer: A
The ratio 3:2 means 3 sopranos for every 2 altos, in any number of groups. Choice B treats the ratio as the actual count; a choir of 12 sopranos and 8 altos also has the ratio 3:2. Choice C uses 3 + 2 = 5, the size of one group, as the number of altos. Choice D reverses the order.
Question 12 of 20 · Multiple Choice
Each ant in an ant farm has 6 legs and 2 antennae. What is the ratio of legs to antennae?
Answer: C
Each ant has 6 legs and 2 antennae, and 6:2 is the same relationship as 3:1: for every 3 legs there is 1 antenna. The count of ants does not change this. Choice A reverses the order. Choice B compares legs with all 6 + 2 = 8 legs and antennae. Choice D compares all 8 legs and antennae with the antennae.
Question 13 of 20 · Multiple Choice
A rice recipe says: "For every 2 cups of rice, use 3 cups of water." What is the ratio of water to rice?
Answer: B
The question names water first, so the ratio is 3 cups of water to 2 cups of rice, or 3:2. Choice A is rice to water, the order used in the recipe sentence. Choice C compares the water with all 2 + 3 = 5 cups. Choice D compares all 5 cups with the rice.
Question 14 of 20 · Multiple Choice
For the class trip, 92 students voted for the museum and 31 voted for the aquarium. Which statement describes the votes best?
Answer: D
Three museum votes for each aquarium vote would be 3 × 31 = 93, and 92 is just under 93, so "nearly 3" fits, with the museum as the larger group. Choice A reverses the two groups. Choice B says "exactly", but 3 × 31 = 93, not 92. Choice C is too far off: 2 × 31 = 62.
Question 15 of 20 · Short Answer
A bakery box has 8 chocolate cupcakes and 4 vanilla cupcakes. Write (a) the ratio of chocolate to vanilla cupcakes, (b) the ratio of vanilla to chocolate cupcakes, (c) the ratio of chocolate cupcakes to all the cupcakes, and (d) one "for every" sentence.
(a) 8:4, the same relationship as 2:1. (b) 4:8, or 1:2. (c) The box holds 8 + 4 = 12 cupcakes, so chocolate to all is 8:12, or 2:3. (d) For example: for every 2 chocolate cupcakes there is 1 vanilla cupcake, because 8 and 4 make 4 groups of 2 and 1.
Question 16 of 20 · Short Answer
A classroom has 6 tables with 5 chairs at each table. Write the ratio of chairs to tables, and explain what it means with a "for every" sentence.
There are 6 × 5 = 30 chairs and 6 tables, so chairs to tables is 30:6, the same relationship as 5:1. For every 1 table there are 5 chairs. The order matters: tables to chairs would be 6:30, or 1:5.
Question 17 of 20 · Short Answer
In a vote for the school mascot, the Eagles received 44 votes and the Owls received 15 votes. Complete the sentence and explain your choice: "For every vote the Owls received, the Eagles received nearly ___ votes."
Nearly 3 votes. Three votes for each of the Owls' votes would be 3 × 15 = 45, and 44 is just under 45. The word "nearly" is needed because the Eagles did not get exactly 3 votes for each Owls vote. The difference, 44 - 15 = 29, is not the answer, because the sentence asks for a ratio.
Question 18 of 20 · Short Answer
A box has 10 red tiles and 15 blue tiles. Jo says, "The ratio of red tiles to blue tiles is 5, because 15 - 10 = 5." Explain Jo's mistake and write the correct ratio.
Jo found a difference, not a ratio. A ratio compares the two quantities by groups: 10 red and 15 blue tiles make 5 groups of 2 red and 3 blue, so red to blue is 10:15, the same relationship as 2:3. For every 2 red tiles there are 3 blue tiles. A ratio always has two numbers, written in the order the question names the quantities.
Question 19 of 20 · Short Answer
In a class, 11 students walk to school and 14 students ride the bus. Every student does one or the other. Write the ratio of walkers to all students in the class and the ratio of bus riders to walkers. Label each as part to part or part to whole.
The class has 11 + 14 = 25 students. Walkers to all students is 11:25 (part to whole). Bus riders to walkers is 14:11 (part to part). Neither ratio can be written with smaller whole numbers, because 11 and 25 share no factor other than 1, and neither do 14 and 11.
Question 20 of 20 · Short Answer
A punch recipe uses 1 cup of juice for every 4 cups of water. Draw a tape diagram for the recipe. If a pitcher of punch has 3 cups of juice, how many cups of water does it have, and what is the ratio of juice to all the punch?
Draw 1 box for juice and 4 boxes of the same size for water. With 3 cups of juice, each box is 3 cups, so the water is 4 × 3 = 12 cups. The punch has 3 + 12 = 15 cups in all, so juice to all punch is 3:15, the same relationship as 1:5.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 6.RP.A.1 mean?
6.RP.A.1 means students understand what a ratio is and can describe one with ratio language. A ratio compares two quantities, such as 2 cups of sugar for every 5 cups of flour. Students write it as 2:5 or "2 to 5", say it with "for every", and explain what it tells about the two quantities.
Is 6.RP.A.1 a grade 6 standard, and what comes after it?
Yes, 6.RP.A.1 is the first grade 6 ratio standard. Right after it, students learn unit rates (6.RP.A.2) and solve ratio problems with tables, tape diagrams and double number lines (6.RP.A.3). In grade 7, ratios grow into proportional relationships (7.RP.A.2), and later into slope and linear functions in grade 8 and Algebra I.
What is a ratio in simple terms?
A ratio is a way to say how much of one thing there is for a certain amount of another thing. A soccer team on the field has 1 goalkeeper for every 10 field players, so the ratio of goalkeepers to field players is 1:10. The ratio stays the same if you look at several teams together, because each team adds the same group.
What is the difference between a part-to-part and a part-to-whole ratio?
A part-to-part ratio compares two parts of a group, and a part-to-whole ratio compares one part with the whole group. In a class of 9 students who play an instrument and 16 who do not, the part-to-part ratio is 9:16 and the part-to-whole ratio of players to the class is 9:25. To find the whole, add the parts.
Does the order of numbers in a ratio matter?
Yes, the order must match the order of the quantities you name. "Cats to dogs is 3:4" means 3 cats for every 4 dogs, while 4:3 would mean more cats than dogs. Students should always label a ratio with words, such as "cats to dogs", so the order is clear.
How is a ratio different from saying one amount is more than another?
A ratio compares by groups (multiplication), while "more than" compares by subtraction. 5 teachers and 20 students, and 15 teachers and 30 students, both have 15 more students than teachers, but the first has 4 students for every teacher and the second has only 2. The ratio tells you how the two amounts are related, not just how far apart they are.
How do you write a ratio?
You can write a ratio with a colon (7:3), with the word "to" (7 to 3), or in a sentence such as "for every 7 red tulips there are 3 yellow tulips". Some books also write ratios as fractions; this lesson uses the colon and "to" forms, which keep the two quantities of a ratio clearly separate. All three forms give the quantities in the same order.
What does "nearly three votes" mean in the 6.RP.A.1 example?
It means the two vote counts are close to, but not exactly, a 1:3 ratio. If candidate A got 200 votes and candidate C got 590, three votes for each of A's votes would be 600, and 590 is just below that. Words like "nearly" and "about" let students describe real data honestly when the counts do not form exact groups.
What are common mistakes with ratios?
A common mistake is writing the numbers in the order they appear in a story instead of the order the question asks. Another is giving a difference ("the ratio is 4") instead of two numbers. Students also mix up parts and wholes, for example writing 3:5 for "3 out of 5" when the question asked for a part-to-part ratio of 3 to 2.
How can parents help with ratios at home?
Look for ratios in everyday life and ask your child to say them in words. Recipes ("2 eggs for every cup of flour"), sports scores, and the number of forks and spoons in a drawer all work. Ask for both orders and for a part-to-whole ratio, and ask whether the ratio would stay the same if you doubled the recipe.
07
Related Standards
5 standards
These standards connect to 6.RP.A.1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
4.OA.A.2Prerequisite
Multiply or divide to solve word problems involving multiplicative comparison
Lesson coming soon
3.NF.A.1Prerequisite
Understand a fraction a/b as a parts of size 1/b of a whole
Lesson coming soon
Alongside
6.RP.A.2Parallel
Understand a unit rate a/b for a ratio a:b and use rate language
