standard_description: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
problem_activity: Narrative
The purpose of this activity is for students to locate fractions on the number line, and find pairs of fractions that are equivalent. Students can use a separate number line for each denominator, but they can also place fractions with different denominators on the same number line to show equivalence. Focus explanations about why fractions are equivalent on the fact that they share the same location. In the synthesis, discuss how one number line or two can be used to compare fractions.
Engagement: Develop Effort and Persistence.
Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Attention, Organization
Launch
Groups of 2
Activity
“Work independently to locate these numbers on the number line. Then, find 4 pairs of fractions that are equivalent. Be prepared to explain your reasoning.”
3–5 minutes: independent work time
“Now, share the pairs of fractions you wrote with your partner and explain how you know they are equivalent.”
2–3 minutes: partner discussion
Monitor for students who compare fractions on a single number line and those who compare fractions on separate number lines.
Student Facing
Locate and label the following numbers on a number line. You can use more than one number line if you wish.
\(\frac{1}{2}\)
,
\(\frac{1}{3}\)
,
\(\frac{1}{4}\)
,
\(\frac{2}{3}\)
,
\(\frac{2}{6}\)
,
\(\frac{3}{8}\)
,
\(\frac{3}{4}\)
,
\(\frac{4}{6}\)
,
\(\frac{4}{8}\)
,
\(\frac{6}{8}\)
,
\(\frac{7}{8}\)
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Find 4 pairs of fractions that are equivalent. Write equations to represent them.
\(\underline{\hspace{1 cm}} = \underline{\hspace{1 cm}}\)
\(\underline{\hspace{1 cm}} = \underline{\hspace{1 cm}}\)
\(\underline{\hspace{1 cm}} = \underline{\hspace{1 cm}}\)
\(\underline{\hspace{1 cm}} = \underline{\hspace{1 cm}}\)
If you have time: Use the number lines to generate as many equivalent fractions as you can.
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Student Response
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Activity Synthesis
Select previously identified students to display how a single number line or separate number lines can be used to show equivalent fractions.
“When might it make sense to use a single number line and when might it be helpful to use two number lines?“ (One number line might make sense if one fraction can be partitioned to get to another, like halves to fourths. If a number line is too crowded or has fractions that could be hard to partition together, like halves and thirds, it might be helpful to use two number lines.)


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