Predict how a multiplier below, equal to or above one changes a quantity.
Teaching companion · Version 2.0.0
Compare the product with a positive starting quantity by comparing its factor with one.
The original lesson PDFs remain version 1.0.0. This supplement adds diagnostic probes, teaching responses, and question-specific rubrics. Use the supplement below for the updated guidance.
Ask for an explanation or drawing before choosing a response. A wrong answer alone does not identify its cause.
Before computing, predict whether 3/4 × 1/2 is below or above 3/4.
Look for: Below 3/4, because it takes half of that positive amount; the product is 3/8.
If you observe: Predicts a larger result because the operation is multiplication.
Respond: Fold a 3/4-length segment in half and compare the folded share with the full starting segment.
Predict how multiplying 7/8 by 1 and by 4/3 changes the starting amount.
Look for: A factor of 1 preserves 7/8; a factor of 4/3 makes it larger.
If you observe: Uses the numerator or denominator separately rather than comparing the whole factor with one.
Respond: Represent 4/3 as one full copy plus another third-copy of the starting 7/8.
Check independently: Without computing the exact product, compare 5/6 × 2/5 with 5/6.
The product is smaller because the positive factor 2/5 is below one.
Use the scaling short intervention if the difficulty persists. Return to this check before repeating the exit ticket.
e1 meets its criterion: e1 gives 3/8 for 3/4 × 1/2. e2 also meets its criterion: e2 states the positive-factor cases below one, equal to one, and above one.
Continue to the linked next lesson. Use size predictions when a fractional amount is divided into equal smaller shares.
Next lesson: Unit Fraction Sharinge1 does not yet meet this criterion: e1 gives 3/8 for 3/4 × 1/2.
Ask the learner to explain the attempt, then use the matching diagnostic probe to identify the difficulty. Work through the focused reteach below and its check. Use the linked short intervention if the difficulty persists; retry e1 and e2 before moving on.
Open the linked short interventione1 meets its criterion, but e2 does not yet show this evidence: e2 states the positive-factor cases below one, equal to one, and above one.
Use three sketches with the same starting strip and factors 1/2, 1, and 2. Ask the learner to state all three e2 cases and connect the first to e1.
Open the linked short interventionUse these as follow-up prompts, then examine the learner’s model or explanation. Open responses may differ from the sample while satisfying the criteria.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Look for in the response:
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Look for in the response:
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Look for in the response:
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Look for in the response:
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Look for in the response:
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Eight core questions and a two-question exit ticket. Print one set per student.
Recognize a whole and count equal parts.
Look at the first model or task. What is the whole? What do you notice?
Start with a 3/4 meter ribbon. Predict the result of scaling by 1/2, 1 and 2.
Model each product and compare it with the original length.
Partners write a rule based on the multiplier, then test a new ribbon length.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Calculate 3/4 × 1/2. Show a model or your reasoning. State the scaling rule for positive amounts.
Assumes multiplication always enlarges a positive amount.
Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Teacher answer key. Open responses include a rubric and one valid sample.
3/4 × 1/2 = 3/8. Multiply the numerators and denominators; interpret the groups or overlap.
3/4 × 1 = 3/4. Multiply the numerators and denominators; interpret the groups or overlap.
3/4 × 2 = 3/2. Multiply the numerators and denominators; interpret the groups or overlap.
2/3 × 3/4 = 1/2. Multiply the numerators and denominators; interpret the groups or overlap.
2/3 × 3/2 = 1. Multiply the numerators and denominators; interpret the groups or overlap.
5/6 × 2/5 = 1/3. Multiply the numerators and denominators; interpret the groups or overlap.
4/5 × 5/4 = 1. Multiply the numerators and denominators; interpret the groups or overlap.
7/8 × 4/3 = 7/6. Multiply the numerators and denominators; interpret the groups or overlap.
1/2 × 1/2 = 1/4. Multiply the numerators and denominators; interpret the groups or overlap.
1/2 × 1 = 1/2. Multiply the numerators and denominators; interpret the groups or overlap.
1/2 × 2 = 1. Multiply the numerators and denominators; interpret the groups or overlap.
3/4 × 1/2 = 3/8. Multiply the numerators and denominators; interpret the groups or overlap.
Taking half of a positive amount makes it smaller.
1/2 × 1/2 = 1/4, smaller than 1/2.
Its value stays unchanged.
It exceeds it because the multiplier 4/3 is above one.
3/4 × 1/2 = 3/8. Multiply the numerators and denominators; interpret the groups or overlap.
A factor below one shrinks, one preserves, and above one enlarges the amount.
Use the whole and equal-part prompts before moving to independent practice. Some items revisit the core concept with simpler models.
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
Designed for Grade 5. Predict how a multiplier below, equal to or above one changes a quantity.
5.NF.B.5b curriculum reference
Version 1.0.0. Original, AI-assisted lesson content. Free local classroom use; public reuse terms have not yet been assigned.
These lessons have not yet been field-tested in classrooms. Use the exit ticket and student explanations to decide what to revisit.