Open family activity
Depth, Not Speed Lab
Start with one familiar problem your child has already entered. Then choose one more turn that changes the thinking, not the workload.
This activity stores no response, profile, score, or personal note.
Need a starting idea?
Choose one if it interests your child. These are starting ideas, not grade levels or an ability ladder. You can pass or stop.
Change the parts
Put 8 drawn dots into two groups. Parent says, “I made 3 and 5. Can you change both groups without changing the total?” Examples: 2 + 6, 1 + 7, 4 + 4. Your child can move, point, draw, or explain. Keep all 8 dots accounted for while your child changes groups; then swap.
Test an always claim
Make two rows of 4 marks. Parent says, “I think splitting 8 marks into two groups always gives equal groups. Can you find a way that changes my mind?” This is the pretend parent's guess, not a fact. 3 and 5 is a counterexample: the total stays 8 and the group sizes differ. If your child makes 4 and 4, say, “That one has equal groups. Want to try moving one mark, or stop here?”
Change a condition
Draw rectangles on square paper with 12 unit squares inside. A 3-by-4 rectangle and a 2-by-6 rectangle both work. If your child chooses to compare boundaries, the lengths are 14 and 16 unit edges. A 1-by-12 rectangle has 26 unit edges. Ask, “Same number of squares inside. Does the edge have to stay the same?” Count edges together; no formula or prior multiplication is required. Choose a different starter if this doesn't fit your child's present entry.
Depth, Not Speed Lab, readable version
Need a starting idea?
Choose one if it interests your child. These are starting ideas, not grade levels or an ability ladder. You can pass or stop.
Change the parts
Put 8 drawn dots into two groups. Parent says, “I made 3 and 5. Can you change both groups without changing the total?” Examples: 2 + 6, 1 + 7, 4 + 4. Your child can move, point, draw, or explain. Keep all 8 dots accounted for while your child changes groups; then swap.
Test an always claim
Make two rows of 4 marks. Parent says, “I think splitting 8 marks into two groups always gives equal groups. Can you find a way that changes my mind?” This is the pretend parent's guess, not a fact. 3 and 5 is a counterexample: the total stays 8 and the group sizes differ. If your child makes 4 and 4, say, “That one has equal groups. Want to try moving one mark, or stop here?”
Change a condition
Draw rectangles on square paper with 12 unit squares inside. A 3-by-4 rectangle and a 2-by-6 rectangle both work. If your child chooses to compare boundaries, the lengths are 14 and 16 unit edges. A 1-by-12 rectangle has 26 unit edges. Ask, “Same number of squares inside. Does the edge have to stay the same?” Count edges together; no formula or prior multiplication is required. Choose a different starter if this doesn't fit your child's present entry.
Choose one depth move: Explain one decision and ask which decision mattered most. Test one claim with another example or a counterexample. Change one condition and predict what changes and what stays true.
Notice the response: Explains and keeps going; has an idea but needs support; or wants to stop. No choice is a score or child label.
If thinking keeps going: ask one: What convinced you? Would that work every time? What did the change affect? One genuine follow-up is enough.
If support would help: Clarify one word or direction; provide objects or drawing space; solve one small part together; allow explanation without every written step; or ask what information is missing. Record what the support unlocked.
If your child wants to stop: Say, “We can stop here.” Ask one optional question, accept “I don't know” or silence, and do not force another turn. A respectful stop is information, not failure.
Which part should we keep for another time? Passing ends it; no answer or written note is required.
Reflect together, if you want: What changed after the first answer? What helped you keep thinking? What would make a problem like this more interesting or workable next time?
One useful observation: Keep a concrete sentence about what you saw or heard. Spoken, built, sketched, pointed, acted, or written answers all count. Do not turn the observation into a label.
This activity stores no response, profile, score, or personal note. Copying or printing stays under your control.