One of These Things Is Not Like the Others
5 min
Teacher Prep
Setup
Narrative
This activity prompts students to reason about equivalent ratios on a double number line and think of reasonable scenarios for these ratios. This is a review of their work in grade 6.
Launch
Arrange students in groups of 2. Give students 2 minutes of quiet work time followed by partner discussion. As students discuss their answers and reasoning with their partner, select students to share during the whole-class discussion.
Student Task
-
Complete the double number line diagram with the missing numbers.
A double number line with 11 evenly spaced tick marks. For the top number line, a dashed box represents the title and the number 0 is on the first tick mark, 2 on the third, 7 on the eighth, and 10 on the eleventh. For the bottom number line, a dashed box represents the title and the number 0 is on the first tick mark, 1 on the third, and 5 on the eleventh. -
What could each of the number lines represent? Invent a situation and label the diagram.
Make sure your labels include appropriate units of measure.
Sample Response
-
The top number line counts by 1 while the bottom number line counts by 21 or equivalent.
- Sample responses:
- number of wheels and number of bicycles
- pints of sauce and quarts of sauce
- chocolate powder (tablespoons) and milk (cups)
Activity Synthesis (Teacher Notes)
Display the double number line for all to see with correct values filled in. It does not matter whether the bottom line is labeled with fractions, decimals, or mixed numbers.
Invite selected students to share the situations they came up with and the units for each quantity. After each student shares, invite others to agree or disagree with the reasonableness of the diagram representing that situation. For example, is it really reasonable to say that 7 wheels make 321 bicycles?
Advances: Speaking
Math Community
After the Warm-up, display the revisions to the class Math Community Chart that were made from student suggestions in an earlier exercise. Tell students that over the next few exercises, this chart will help the class decide on community norms—how they as a class hope to work and interact together over the year. To get ready for making those decisions, students are invited at the end of today’s lesson to share which “Doing Math” action on the chart is most important to them personally.
Anticipated Misconceptions
Students may struggle thinking of a scenario with a 1:2 ratio. For those students, ask them if they can draw a picture that would represent that ratio and label each line accordingly.
Standards
- 6.RP.A·Understand ratio concepts and use ratio reasoning to solve problems.
- 6.RP.A·Understand ratio concepts and use ratio reasoning to solve problems.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
One of These Things Is Not Like the Others
5 min
Teacher Prep
Setup
Narrative
This activity prompts students to reason about equivalent ratios on a double number line and think of reasonable scenarios for these ratios. This is a review of their work in grade 6.
Launch
Arrange students in groups of 2. Give students 2 minutes of quiet work time followed by partner discussion. As students discuss their answers and reasoning with their partner, select students to share during the whole-class discussion.
Student Task
-
Complete the double number line diagram with the missing numbers.
A double number line with 11 evenly spaced tick marks. For the top number line, a dashed box represents the title and the number 0 is on the first tick mark, 2 on the third, 7 on the eighth, and 10 on the eleventh. For the bottom number line, a dashed box represents the title and the number 0 is on the first tick mark, 1 on the third, and 5 on the eleventh. -
What could each of the number lines represent? Invent a situation and label the diagram.
Make sure your labels include appropriate units of measure.
Sample Response
-
The top number line counts by 1 while the bottom number line counts by 21 or equivalent.
- Sample responses:
- number of wheels and number of bicycles
- pints of sauce and quarts of sauce
- chocolate powder (tablespoons) and milk (cups)
Activity Synthesis (Teacher Notes)
Display the double number line for all to see with correct values filled in. It does not matter whether the bottom line is labeled with fractions, decimals, or mixed numbers.
Invite selected students to share the situations they came up with and the units for each quantity. After each student shares, invite others to agree or disagree with the reasonableness of the diagram representing that situation. For example, is it really reasonable to say that 7 wheels make 321 bicycles?
Advances: Speaking
Math Community
After the Warm-up, display the revisions to the class Math Community Chart that were made from student suggestions in an earlier exercise. Tell students that over the next few exercises, this chart will help the class decide on community norms—how they as a class hope to work and interact together over the year. To get ready for making those decisions, students are invited at the end of today’s lesson to share which “Doing Math” action on the chart is most important to them personally.
Anticipated Misconceptions
Students may struggle thinking of a scenario with a 1:2 ratio. For those students, ask them if they can draw a picture that would represent that ratio and label each line accordingly.
Standards
- 6.RP.A·Understand ratio concepts and use ratio reasoning to solve problems.
- 6.RP.A·Understand ratio concepts and use ratio reasoning to solve problems.