Setting the Stage: / Guiding Questions
1. Students should be prepared to work independently during this activity.
2. After students attempt the first two boxes on their own, discuss the key points as a class:
- 4 equal parts = 3 equally spaced lines
- Equivalent ratios – same “for every” relationship
- Equivalent ratios – variety of strategies
3. As students bring up ways of finding equivalent ratios, highlight any errors with absolute (additive) comparisons. Introduce the idea of double number lines and tape diagrams just as a way to organize their thoughts about a relative (multiplicative) comparison.
4.
Explore the Concept: / Guiding Questions
1. Go through the double number line example with the students. Stress the need to label the diagram appropriately. Use student-generated responses to the questions below to help guide student thinking about the problem. Focus should be:
- Equal divisions – match up equivalent ratios
- Side labels (wool/hats) necessary – otherwise numbers without meaning
- Relative (multiplicative) comparison – would adding/subtracting make sense in this case?
2. Allow students to attempt the “On your own!” problem. Discuss result as a class. Focus students on the need to fully label their diagram to fully understand the problem.
3. Go through the tape diagram example with students. Stress the need to label the diagram appropriately. Use student-generated responses to the questions below to help guide student thinking about the problem. Focus should be:
- Tape segments = “for every” thinking
- Label operation between known values
- Apply the same to the unknown values
- Relative comparison – “for every” – does adding make sense?
4. Allow students to attempt the “On your own!” problem. Discuss result as a class. Focus students on the need to fully label their diagram to fully understand the problem.
5. Students further explore both diagram types on the back of the worksheet. Encourage students to label the diagram and verbally describe the relationship between values. / ·
Reflection: / Guiding Questions
1. Give students time to independently reflect and respond to the questions at the end of the worksheet. Hold students accountable for writing down their thoughts about these questions.
2. Use the thinking/reflection questions as a starting point for a class discussion about the function / usefulness of these diagram types.
EXTENSION
3. Use key vocabulary of the unit to describe what happens when using a tape diagram or double number line.
4. Discuss how the final Challenge! problem dealing with Andy’s speed was more challenging. Discuss what mental math made the problem easier. / ·
Setting the Stage
