For parents
Missing number puzzles: hide a few blocks
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In 4 + □ = 7, the total is already known: seven. The puzzle asks for one missing part. A few blocks and a sheet of paper make the empty box meaningful, without guessing or learning rules about moving numbers across an equals sign.
Read the whole equation
Gather ten large blocks, paper for covering them and a pencil. Read 4 + □ = 7 as four and some more make seven. The equals sign says that both sides have the same value. Writing 7 = 4 + □ gives the same puzzle. The NCETM resource below discusses missing parts and the relationship between addition and subtraction.
Build the total and hide a part
Line up seven blocks and count them together. Move four to the left and cover the remaining blocks. Ask how many are hidden. Your child can count on from four: five, six, seven. That is three steps, so the missing number is 3. Uncover the blocks and check by reading 4 + 3 = 7.
Find how many were taken away
Write 9 − □ = 5 and set out nine blocks. Move blocks one at a time into a separate pile until five remain. Four blocks have moved: that is the missing number. Check 9 − 4 = 5. The question asks how many were removed, rather than how many are left on the table.
Find the starting amount
For □ − 3 = 5, you know the amount removed and the amount left. Put out five blocks, then return the three that were taken away. There were eight at the start. Replace the box and check the original equation: 8 − 3 = 5. Simply subtracting the two visible numbers would answer a different question.
Play hidden cargo
Pretend the blocks are cargo for a toy vehicle. Agree on a total, such as eight. One player shows five blocks and covers the rest; the other writes 5 + □ = 8 and explains the answer. Swap roles. Change the visible part in the next round while keeping eight blocks altogether. Leave everything visible if the hiding makes it too difficult.
Four questions and their checks
Try 2 + □ = 6; 8 − □ = 3; □ − 2 = 7; and 6 = □ + 1. The answers are 4, 5, 9 and 5 respectively. Check: 2 + 4 = 6, 8 − 5 = 3, 9 − 2 = 7 and 6 = 5 + 1. Each separate puzzle has its own missing number. Ask your child to model one answer with blocks.
Notice the reasoning
When counting on, count the steps without counting the starting number as a step. From four to seven takes three steps. If your child adds every visible number, return to the whole and its parts. Keep the activity unhurried. A parent can later choose addition or subtraction in Otto Math on iPhone or iPad. The first five routes in each book are free; further routes require Otto Plus.