Grade 6

Readiness Check

Check Your Readiness
1.

Calculate each quotient.

  1. 125÷5125 \div 5
  2. 800÷16800 \div 16
  3. 3.5÷23.5 \div 2
  4. 21.4÷1021.4 \div 10

Answer:

  1. 25
  2. 50
  3. 1.75
  4. 2.14

Teaching Notes

This item is about general number sense and understanding of division. Students will need to make calculations like this when they calculate the mean or MAD of a data set, and they will frequently need to efficiently divide by 2 when calculating the median.

If most students struggle with this item, plan to add extra practice in the weeks before Lesson 11. There are practice problems in Lesson 4 of this unit and in lessons throughout Unit 5 that can be used. Those problems and the problems here can also be used as a quick Number Talk.

2.

Evaluate each expression.

  1. 16−2.216 - 2.2
  2. 3−0.263 - 0.26
  3. 11.26+5.3411.26 + 5.34
  4. 2.06+3.942.06 + 3.94
  5. 51−0.0751 - 0.07

Answer:

  1. 13.8
  2. 2.74
  3. 16.6
  4. 6
  5. 50.93

Teaching Notes

Students will need to make calculations like the following in order to calculate mean absolute deviation (MAD).

If most students struggle with this item, plan to add extra practice in the weeks before Lesson 11. There are practice problems in both Lesson 4 and Unit 5 that can be used. Those problems and the problems here can also be used as a quick Number Talk.

3.

The bar graph shows how many students are in grades 6, 7, and 8 at a school.

  1. About how many total students are in these three grades?
  2. Which grade has the most students?

  3. About how many more sixth graders are there than eighth graders?

Bar graph. X-axis labeled grade 6, grade 7 and grade 8. Y axis 0-200 by 100's.
Bar graph. X-axis labeled grade 6, grade 7 and grade 8. Y axis 0-200 by 100's. The bar labeled grade 6 has an approximate height between 225 and 235. The bar labeled grade 7 has an approximate height between 215 and 220. The bar labeled grade 8 has an approximate height of 195.

Answer:

  1. About 650
  2. Sixth grade
  3. Sample response: Between 30 and 40

Teaching Notes

Students interpret a bar graph. Students are not required to judge the exact values assigned to each bar, so the problem is more about general understanding, interpretation, and estimation. If students answer incorrectly, it is possible that they have made arithmetic errors, but it is more likely that they are having difficulty interpreting the bar graph.

If most students struggle with this item, plan to do the optional activity in Lesson 3, "Favorite Summer Sports." This is an opportunity to think about bar graphs and compare them to dot plots and histograms. Students can also plan their own data collection and bar graph development as needed.

4.

A pet store has 11 lizards, with these lengths in inches:

  • 5125\frac{1}{2}
  • 5345\frac{3}{4}
  • 5345\frac{3}{4}
  • 5785\frac{7}{8}
  • 5785\frac{7}{8}
  • 6
  • 6186\frac{1}{8}
  • 6186\frac{1}{8}
  • 6186\frac{1}{8}
  • 6146\frac{1}{4}
  • 6386\frac{3}{8}

Draw a line plot for this data.

A blank line plot labeled length in inches. There are equally spaced tick marks every quarter from 5 to 7.

 

Answer:

<p>Dot plot. Length in inches. </p>

Teaching Notes

Students create a line plot showing fractional values. They will need to find a common denominator for the fractions and label the values on the number line correctly.

If most students struggle with this item, plan to support their understanding by creating the dot plot with the students in Activity 1, "Pencils on a Plot." Amplify the steps as the dot plot is created, including partitioning equally and labeling. 

5.

Diego drew this line plot showing the width, in inches, of all the bolts in a storage bin. Select all the true statements.

Dot plot from 0 to one and one fourth by one fourths. Width in inches. 
Dot plot from 0 to one and one fourth by one fourths. Width in inches. Beginning at one fourth, number of dots above each increment is 1, 3 dots at three eighths, 2, 4 dots at five eighths, 0, 1 dot at seven eighth, 0, 1.

A.

There are 12 bolts in the storage bin.

B.

The widest bolt is 78\frac 7 8 inches wide.

C.

Half of the bolts are less than 12\frac 1 2 inch wide.

D.

None of the bolts is exactly 28\frac 2 8 inches wide.

E.

None of the bolts is exactly 68\frac 6 8 inches wide.

F.

The difference between the maximum and minimum width of the bolts is 1 inch.

Answer: A, E, F

Teaching Notes

Students who don’t select Choice A may not recall that multiple marks in the same column refer to multiple instances. Students who select Choice C are probably misinterpreting the meaning of “less than” because half of the bolts are less than or equal to 12\frac 1 2 inch wide. Students who select Choice D probably failed to recognize that 28\frac 2 8 is equivalent to 14\frac 1 4.

If most students struggle with this item, plan to do Activity 1, "Pencils on a Plot," allowing for extra time for students to share their understandings. For extra practice, make a class number line showing zero to 2 and add fractions to it.

6.

This line plot shows the amount of time, in seconds, that it took 20 sixth graders to run a 50-meter dash.

Dot plot from 7 to 0 by 0 point 1's. Time in seconds. Beginning at 7 point 1, dots above each increment is 1, 0, 4, 3, 2, 2, 2, 3, 2, 1.

Select all the true statements.

A.

The fastest time was 7.0 seconds.

B.

No runner recorded a time of 7.2 seconds.

C.

The fastest 5 students’ total time was 36.3 seconds.

D.

Exactly half of the students were faster than 7.7 seconds.

E.

The difference between the fastest and slowest times was 0.9 seconds.

Answer: B, C, E

Teaching Notes

In addition to reading the line plot, students must also add and subtract decimal values in context.

If most students struggle with this item, plan to adapt Lesson 5 by using the data collected in Lesson 1 Activity 2 Question 12 to create and interpret a line plot. This data will allow for questions that require adding and subtracting decimal values in context.

7.

Calculate each percentage.

  1. 25% of 50
  2. 25% of 60
  3. 50% of 60
  4. 75% of 60
  5. 75% of 30
  6. 100% of 22.5
  7. 10% of 22.5
  8. 50% of 45.7

Answer:

  1. 12.5
  2. 15
  3. 30
  4. 45
  5. 22.5
  6. 22.5
  7. 2.25
  8. 22.85

Teaching Notes

Students calculate several benchmark percentages, notably 25%, 50%, and 75%. This skill will be essential when they find quartiles. Whole number values and decimal values are both included, because students require both skills in this unit.

If most students struggle with this item, plan to explicitly share the strategies used by students to determine percentages in Lesson 4 Activity 3. In addition, here are two percentage questions that could be added to the lesson synthesis: What percentage of dogs weighed 15 kg or more? What percentage of dogs weighed less than 15kg?