One garden plot is split equally among 5 neighbors. What fraction of a whole plot does each neighbor receive? Verify by multiplying the share by the neighbor count.
Application-and-critique task: 2 identical community garden plots are shared equally among 4 neighbors. What fraction of a whole plot does each neighbor receive? Verify by multiplying the share by the neighbor count. Independently prepare a fraction strip defining the reference whole and every equal recipient; do not simply repeat the first application question’s computation. A student wrote this solution: “2 ÷ 4 = 2. I reversed the dividend and divisor.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.
An irrigation tank receives 3/5 L in the morning and 5/6 L later. How many liters were added altogether? Show a common partition.
Application-and-critique task: A greenhouse measuring jug receives 1/6 L in the morning and 1/3 L later. How many liters were added altogether? Show a common partition. Independently prepare two matching denominator partitions with a labeled liter whole; do not simply repeat the first application question’s computation. A student wrote this solution: “For 1/6 and 1/3, my answer is 2/9; I added both numerators and denominators without making equal parts.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.
After measuring 1/3 m of fabric, a tailor cuts off 1/5 m. How much remains? Defend the order of subtraction.
Application-and-critique task: During a sewing workshop, after measuring 7/8 m of fabric, a tailor cuts off 1/2 m. How much remains? Defend the order of subtraction. Independently prepare aligned equal-size fraction strips showing the subtracted segment; do not simply repeat the first application question’s computation. A student wrote this solution: “For 7/8 and 1/2, my answer is 4/5; I added both numerators and denominators without making equal parts.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.
Two rolls of ribbon have lengths 1 1/4 m and 2 1/4 m. How long are they together? Present a correct fractional exchange where needed.
Application-and-critique task: An art installation joins ribbons measuring 3 1/3 m and 1 1/3 m. How long are they together? Present a correct fractional exchange where needed. Independently prepare whole bars plus fractional subdivisions at a common denominator; do not simply repeat the first application question’s computation. A student wrote this solution: “For 10/3 and 4/3, my answer is 7/3; I added both numerators and denominators without making equal parts.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.
Two rolls of ribbon have lengths 1 2/3 m and 1 1/2 m. How long are they together? Present a correct fractional exchange where needed.
Application-and-critique task: A gift-wrapping team combines ribbon lengths of 1 3/4 m and 2 1/2 m. How long are they together? Present a correct fractional exchange where needed. Independently prepare a mixed-number bar model including any regrouped whole; do not simply repeat the first application question’s computation. A student wrote this solution: “For 7/4 and 5/2, my answer is 2; I added both numerators and denominators without making equal parts.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.
A shop has 8 5/6 kg of a material and ships 1 2/3 kg. How many kilograms remain? Show the unit-whole exchange if the smaller fractional part is subtracted from a larger one.
Application-and-critique task: A community pantry stores 7 1/2 kg of a material and ships 1 1/4 kg. How many kilograms remain? Show the unit-whole exchange if the smaller fractional part is subtracted from a larger one. Independently prepare a subtraction strip with before, removed, and remaining quantities; do not simply repeat the first application question’s computation. A student wrote this solution: “For 15/2 and 5/4, my answer is 10/3; I added both numerators and denominators without making equal parts.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.
A shop has 8 1/8 kg of a material and ships 2 5/8 kg. How many kilograms remain? Show the unit-whole exchange if the smaller fractional part is subtracted from a larger one.
Application-and-critique task: A farm cooperative stocks 5 1/8 kg of a material and ships 2 3/4 kg. How many kilograms remain? Show the unit-whole exchange if the smaller fractional part is subtracted from a larger one. Independently prepare an explicit one-whole exchange chart; do not simply repeat the first application question’s computation. A student wrote this solution: “For 41/8 and 11/4, my answer is 13/3; I added both numerators and denominators without making equal parts.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.
Answer from first principles. Include a model where requested. These questions are distinct from taught worked examples.
Locate 1/3 using six equal intervals. Which tick?
Calculation items: 2 points for correct mathematics and units plus 1 for valid working. Notebook diagnosis tasks: 4 points, one each for identifying a specific faulty step, explaining the repair, solving accurately, and checking units/logic. Targeted transfer tasks: 4 points with detailed anchors in private teacher keys. Equivalent exact representations accepted; reviewers must examine explanations.