Add unlike fractions by renaming both ingredients in common units.
Teaching companion · Version 2.0.0
Preserve both addends while renaming them in common fractional units.
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.
A learner writes 1/3 + 1/4 = 2/7. What is wrong with the units?
Look for: Thirds and fourths are different sizes; rename as 4/12 + 3/12 = 7/12.
If you observe: Combines numerator and denominator counts directly.
Respond: Place a third piece beside a fourth piece and ask what equal-sized piece can measure both; partition the common whole into twelfths.
Could 2/7 be the sum of the positive amounts 1/3 and 1/4?
Look for: No. 2/7 is less than 1/3, while adding a positive amount must increase 1/3.
If you observe: Accepts the computed answer without checking its size.
Respond: Mark 1/3 on a line and show that a positive addition moves right; compare 2/7 = 6/21 with 1/3 = 7/21.
Check independently: Find 1/2 + 1/3 and state why the denominator is not five.
3/6 + 2/6 = 5/6. The two amounts are counted in sixths, not fifths.
Use the unlike estimation short intervention if the difficulty persists. Return to this check before repeating the exit ticket.
e1 meets its criterion: e1 gives 7/12 for 1/3 + 1/4. e2 also meets its criterion: e2 explains that numerator counts can be combined only when they name the same fractional unit.
Continue to the linked next lesson. Use the same common-unit structure to remove an amount and check by addition.
Next lesson: Fraction Difference Traile1 does not yet meet this criterion: e1 gives 7/12 for 1/3 + 1/4.
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 explains that numerator counts can be combined only when they name the same fractional unit.
Ask the learner to point to one third and one fourth, then to the twelfth-piece used to count both. Require that unit explanation in e2.
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: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Adds, subtracts, or multiplies a denominator when combining counts of the same fractional unit.
Try: Place three eighth-size pieces beside five eighth-size pieces. Count eight pieces without recutting any of them. Write 8/8 and explain why 8/16 would describe smaller pieces than the ones on the table.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Look for in the response:
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Look for in the response:
Watch for: Changes one part of a fraction without scaling numerator and denominator by the same factor.
Try: Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.
Look for in the response:
Watch for: Chooses an operation from the numbers without identifying whether the task combines, takes a part, shares, or counts groups.
Try: Ask the learner to finish “I know …; I need …” with units. Act out the quantity: combine disjoint colors, overlap two fractional selections, share one amount, or count fixed-size pieces. Write an equation only after the action is identified.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Look for in the response:
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
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?
Model one third cup plus one fourth cup using equal-sized cup diagrams.
Repartition both into twelfths and count seven twelfths in all.
Partners prepare a second recipe and estimate before adding.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Calculate 1/3 + 1/4. Show a model or your reasoning. Why must the pieces have the same size before adding?
Combines numerator counts before making the fractional units alike.
Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Teacher answer key. Open responses include a rubric and one valid sample.
1/3 + 1/4 = 7/12. Use equal-sized parts before combining or removing them.
2/5 + 1/2 = 9/10. Use equal-sized parts before combining or removing them.
3/4 + 1/6 = 11/12. Use equal-sized parts before combining or removing them.
1/2 + 2/3 = 7/6. Use equal-sized parts before combining or removing them.
5/8 + 1/4 = 7/8. Use equal-sized parts before combining or removing them.
2/3 + 3/5 = 19/15. Use equal-sized parts before combining or removing them.
1/6 + 3/8 = 13/24. Use equal-sized parts before combining or removing them.
3/10 + 2/5 = 7/10. Use equal-sized parts before combining or removing them.
1/2 + 1/4 = 3/4. Use equal-sized parts before combining or removing them.
1/3 + 1/6 = 1/2. Use equal-sized parts before combining or removing them.
1/4 + 1/8 = 3/8. Use equal-sized parts before combining or removing them.
1/5 + 2/5 = 3/5. Use equal-sized parts before combining or removing them.
Four twelfths plus three twelfths gives seven twelfths.
The pieces have different sizes; the denominators cannot simply be added.
12 and 24 both work and produce equivalent sums.
Use 1/2 cup of oats, 1/4 cup of seeds and 1/4 cup of dried fruit: the total is one cup.
1/3 + 1/4 = 7/12. Use equal-sized parts before combining or removing them.
A numerator counts units; both counts must refer to the same fractional unit.
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. Add unlike fractions by renaming both ingredients in common units.
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.