How to Help With Missing Numbers Without Guessing

The blank stands for a number

In 8 + ___ = 13, the blank is not an empty answer box at the end of a calculation. It stands for the number that makes the complete equation true.

The mistake makes sense. The visible numbers attract attention, and the plus sign can seem to say, “Add these.” Instead, read the whole line aloud: “Eight plus what makes thirteen?” This turns the printed symbols into a clear question.

The same idea works when the blank moves. ___ − 4 = 7 asks, “What number minus four makes seven?” In 3 × ___ = 18, it asks, “Three times what makes eighteen?”

Work through the kitchen-table problem

Use one short routine

Cover the written guess. Point to the blank, then to the total. Ask the child to say the question in words before touching a pencil.

Next, let the child use a suitable tool. Small numbers can be shown with counters, fingers or quick marks. With bigger numbers in an adding question, take the number you know away from the total. In a times question, ask which times fact gives the total.

Finally, put the number back into the blank and read the completed equation. If both sides do not match, the answer needs another look. This check matters more than finishing quickly.

What to do next

1. 1. Can the child turn the equation into a spoken question?

   • Yes: go to question 2
   • No: Cover any written guess. Point to the blank and read the full equation slowly, replacing the blank with the word “what.”

2. 2. Is the equation using addition or subtraction?

   • Yes: go to question 3
   • No: go to question 4

3. 3. Can the numbers be shown comfortably with counters, fingers or marks?

   • Yes: Build the known part, then add or remove items until the equation is true. Count what changed.
   • No: Look at where the blank is. 34 + ___ = 71: take 34 from 71 to get 37. 15 − ___ = 9: take 9 from 15 to get 6. ___ − 4 = 7: add 7 and 4 to get 11. Then put the answer in the blank and check.

4. 4. Is it a times question, as in 4 × ___ = 28?

   • Yes: Ask which times fact makes 28 (4 × 7). If needed, work out 28 ÷ 4.
   • No: It is a sharing question. In ___ ÷ 6 = 7 the blank is the starting number, so work out 6 × 7 = 42.

Match practice to the kind of blank

Pick the page for your child’s grade. Kindergarten and Grade 1 stay with small adding and taking-away blanks. Grade 2 adds bigger numbers and times facts, and Grade 3 adds sharing (division).” Keep any page links that sit on this paragraph.

Start with a short set that contains one kind of blank. Once the child can explain the question and check the answer, mix the positions or operations. This keeps the new difficulty clear.

Avoid turning the blank into a guessing game

Do not ask only, “What is the answer?” That wording can reinforce the idea that the blank is always the final answer spot. Ask what number would make the entire equation true.

Avoid giving several new equation types at once when the first one is still unclear. A page mixing addition, subtraction, multiplication and division can hide the exact point of confusion.

Do not erase an incorrect answer before discussing it. In Tuesday’s problem, 21 shows that the two visible numbers were added. That gives the adult a useful next question: “Does 8 plus 21 equal 13?”

When to talk to the teacher

Talk to the teacher if the child repeatedly cannot explain what the equals sign means, even with small numbers and objects. Also ask for guidance if the method used at home conflicts with the method shown in class.

Bring one or two examples rather than a whole stack. Mark where the child stopped and record what they said. The teacher can then see where it goes wrong: reading the question, remembering a fact, or working it out.

Try three before putting the page away

1. 16 + ___ = 10

   4

   1. 6 + ___ = 10

   Answer: 4

2. 23 + ___ = 8

   5

   2. 3 + ___ = 8

   Answer: 5

3. 37 + ___ = 9

   2

   3. 7 + ___ = 9

   Answer: 2

End by explaining, not racing

Before Tuesday’s sheet is put away, return to 8 + ___ = 13. Ask the child to explain why 5 fits and why 21 does not. A clear explanation shows more than another row of guesses.

If an adult wants to check the rest later, the worksheet page offers “Answer key.” Keep it aside until the child has tried each question and checked it by putting the answer back in.