Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.4

Lesson 2.82.8 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can determine the mean of a data set, use a target mean to find a missing value, and explain the mean as the fair share and the balance point of the data — 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
MeanSpanish: Media The average of a data set. Add all the values, then divide by how many values there are. Add, then divide by the count
AverageSpanish: Promedio Another word for the mean — the amount each value would be if the total were shared equally. A typical amount
Measure of centerSpanish: Medida de centro A single number used to describe the middle, or typical value, of a whole data set. Mean and median are both
Balance pointSpanish: Punto de equilibrio The value where the total distance of the data above it equals the total distance below it. The mean is the balance point. The mean balances the set
Data setSpanish: Conjunto de datos The whole collection of values that were gathered or measured. 8, 15, 11, 6
Target meanSpanish: Media objetivo The mean a person is trying to reach. A goal average of 29 points.

How it worksWorked examplefinding the mean of a data set

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

Five afternoons of dog walking earned 14, 21, 17, 19, and 24 dollars. Find the mean.

  1. Add every value. The five amounts give a total of 95 dollars.
  2. Count the values. There are five of them.
  3. Share the total evenly: divide it by the count of values.
  4. Check: the mean should land between the least and the greatest value.

Answer: The mean is 19 dollars — what each afternoon would earn if the money were shared evenly.

Now you trySame steps, your turn

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

Five bowling scores are 46, 52, 38, 44, and 50. Find the mean score.

  1. Add every value: Total:
  2. How many values are there?
  3. Share the total evenly by dividing it by the count. Mean:
  4. Check: does your mean sit between the least and greatest value?
Answer:mean score

Say it and write itSentence starters

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

  • The total of all the values is .
  • There are values, so I divided by .
  • The mean is , which means .
  • The mean must fall between and .

Word bank meanaveragetotalsumdividecountfair sharebalance pointcentertypicaldata setvalue

Watch outA common mistake

The most common mistake with the mean is adding correctly and then dividing by the wrong number — or not dividing at all. Students report the total (for 8, 10, 6, 12 they say the mean is 36) or they divide by a count that does not match the data, such as dividing a 4-value total by 5, or skipping a zero when counting the values. Before you finish, do two things: count the values in the data set out loud, and check that your mean lands between the smallest and largest value. A mean of 36 for data that never goes above 12 is impossible.

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.4

Lesson 2.82.8 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 determine the mean of a data set, use a target mean to find a missing value, and explain the mean as the fair share and the balance point of the data — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    345678910Cats per week
    The mean is between the smallest and largest values.

    A shelter takes in 7, 4, 9 and 8 cats in 4 weeks. Find the mean number of cats per week.

    1. 1Add the values. What is the total?
    2. 2How many values are there?
    3. 3Divide the total by the number of values. What is the mean?
    Final answer:
  2. 2Complete each step, then write the final answer.
    5 games?????? points
    The total shared equally by 5 games.

    Jada scored 12, 15, 10, 18 and 20 points in 5 games. Find her mean score.

    1. 1Add the five scores. What is the total?
    2. 2This time there are 5 values. What do you divide by?
    3. 3Share the total equally. What is the mean?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the mean of 4, 6, 8, 10, 12.

    Show your work

    Hint Add all five values. Then divide the total by 5.

    Final answer:
  4. 4Complete each step, then write the final answer.

    Ruby earned $14, $22, $18 and $26 babysitting on 4 days. What is the mean amount per day?

    Show your work

    Hint Find the total money first. Then share it equally among the 4 days.

    Final answer:
  5. 5Complete each step, then write the final answer.

    Three friends picked 2, 5 and 11 pounds of apples. They share all the apples equally. How many pounds does each friend get?

    Show your work

    Hint Put all the apples together. Then split the total into 3 equal parts.

    Final answer:
  6. 6Complete each step, then write the final answer.

    Omar finds the mean of 6, 9, 3 and 10. He adds them and gets 28. He says the mean is 28. What is the mean?

    Show your work

    Hint Omar found the total. Is 28 between the smallest and largest values? What step is missing?

    Final answer:

Explain your thinkingOmar said the mean was 28. Why is the total not the mean? Use the idea of a fair share.

Sentence starter The total is ___, but the mean is ___ because ___. · If every value were the same, each one would be ___.

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