Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.1

Lesson 3.13.1 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can write and describe a ratio that compares two quantities — one step at a time, with support.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
RatioSpanish: Razón A way to compare two amounts, like 3 to 2. 3 to 5 ■■■ □□□□□
ComparisonSpanish: Comparación Looking at two or more amounts to see how they are related. 5 eggs vs. 3 eggs — which recipe uses more?
Part-to-partSpanish: Parte a parte A ratio comparing one part of a group to another part. apples to oranges
Part-to-wholeSpanish: Parte a todo A ratio comparing one part to the whole group. apples to all the fruit
Colon notationSpanish: Notación con dos puntos Writing a ratio with two dots between the numbers, like 3:2. 3 to 2 can be written as 3:2
Tape diagramSpanish: Diagrama de cintas A bar cut into equal parts that shows how two amounts in a ratio compare, and how they make up the whole. 3 equal parts of apple juice beside 2 equal parts of sparkling water — 5 parts of fruit drink in all.

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

  1. Count each group. pens = 10 pencils = 4
  2. Write them in the order the question asks — pens FIRST.
  3. Write all three forms: 10 to 4 · 10 : 4 · 10/4
  4. Simplify: divide both terms by 2. 10 : 4 → 5 : 2

Answer: The ratio of pens to pencils is 5 : 2 in simplest form.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A bowl has 4 apples and 1 orange. Write the ratio of apples to oranges. Then write the ratio of apples to all the fruit.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The ratio of to is .
  • This means for every , there are .
  • The order matters because .
  • I simplified by dividing both terms by .

Word bank ratiotermcomparefor everypartwholetotalsimplest formdivideorderfirstsecond

Watch outA common mistake

A common mistake in Understand Ratios is writing the ratio in the wrong order: when asked for the ratio of apple juice to sparkling water in a recipe that uses 3 cups of apple juice for every 2 cups of sparkling water, some students write 2:3 (sparkling water to apple juice) because they list the ingredients in whatever order comes to mind rather than the order the question asks for. The two ratios describe different drinks — 3:2 means 3 cups of juice for every 2 cups of water, while 2:3 would mean only 2 cups of juice for every 3 cups of water. Always match the order of your ratio to the order named in the question: "apple juice to sparkling water" means the apple juice number comes first, giving 3:2.

Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.1

Lesson 3.13.1 Small Group · Group 1

Group 1Supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target With my small group, I can write and describe a ratio that compares two quantities — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    Grapes5Strawberries2
    The counts from the problem, in order.

    A fruit cup has 5 grapes for every 2 strawberries. Write the ratio of grapes to strawberries.

    1. 1Which fruit do the words name first?
    2. 2Read the table. Grapes to strawberries is 5 to ?. What is the missing number?
    3. 3Write the ratio with a colon.
    Final answer:
  2. 2Complete each step, then write the final answer.
    Boys5Girls6Total players?
    The Total row is all the players.

    A team has 6 girls and 5 boys. Write the ratio of boys to all the players.

    1. 1Add to fill the Total row. How many players are there?
    2. 2Which number goes first: the boys or all the players?
    3. 3Write boys to all the players with a colon.
    Final answer:
  3. 3Complete each step, then write the final answer.
    Green marblesRed marbles________

    A bag has 3 red marbles and 8 green marbles. The ratio of green marbles to red marbles is ? : 3. What is the missing number?

    Show your work

    Hint Green comes first in this ratio. How many green marbles are there?

    Final answer:
  4. 4Complete each step, then write the final answer.
    Apple juice (cups)Sparkling water (cups)Total drink (cups)________

    Chef Reyes mixes 4 cups of apple juice with 3 cups of sparkling water. The ratio of apple juice to the whole drink is 4 to ?. What is the missing number?

    Show your work

    Hint The whole drink is the juice and the water together.

    Final answer:
  5. 5Complete each step, then write the final answer.
    Blue crayonsRed crayonsTotal crayons________

    A box has 12 crayons. 5 are red and the rest are blue. The ratio of blue crayons to red crayons is ? : 5. What is the missing number?

    Show your work

    Hint First find how many crayons are blue. 12 is all the crayons.

    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.
    DogsCats________

    Lily has 3 cats and 4 dogs. Ben says the ratio of dogs to cats is 3:4. Which ratio of dogs to cats is correct?

    1. A4:3
    2. B3:4
    3. C4:7
    4. D3:7

    Hint Which animal do the words name first? Its number goes first.

    Show your work

Explain your thinkingBen wrote 3:4 for dogs to cats. Why does the order of the numbers matter in a ratio?

Sentence starter Dogs to cats is ___ because the words say ___ first. · If I switch the order, the ratio compares ___ to ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help