Early Math · Grade 1

Subtraction and Missing Numbers

Quick answer

Every subtraction asks for a missing part. 10 − 8 asks what goes with 8 to make 10, which is the addition question 8 + □ = 10, and both have the answer 2. The same idea finds a missing number anywhere in a number sentence: decide which number is the whole and which are parts, then add the parts or take a part away from the whole. Putting the answer back in the box checks it.

What you'll learn

  • Subtract by finding the number that adds on to make the whole
  • Find a missing number in an addition or subtraction sentence
  • Check an answer by putting it back in the sentence

Subtract by adding

What is 10−810 - 8? You can take 88 away. Or you can ask a new question: 88 and what make 1010?

Eight in a ten-frame A ten-frame with eight dots. Two boxes are empty.
Eight in a ten-frame

88 dots fill most of the frame. 22 boxes are empty. So 8+2=108 + 2 = 10.

That means 10−8=210 - 8 = 2.

Why subtracting finds a missing part

In 10−810 - 8, the whole is 1010 and one part is 88. Subtracting finds the other part.

Adding up finds that same part. 8+□=108 + \square = 10 asks the same thing as 10−8=□10 - 8 = \square. Both ask for the part that goes with 88 to make 1010.

So you can pick the way that is faster. For 10−810 - 8, adding up from 88 is only 22 steps. Counting back 88 from 1010 is 88 steps.

A missing number can be anywhere

The box can be in any spot:

Number sentenceWhat it asks
6+6=□6 + 6 = \squareWhat do 66 and 66 make?
8+□=118 + \square = 1188 and what make 1111?
□+5=12\square + 5 = 12What and 55 make 1212?
14−□=914 - \square = 9Take what from 1414 to leave 99?
5=□−35 = \square - 3Take 33 from what to leave 55?

To find the box, find the whole first.

  • If the box is a part, take the known part away from the whole.
  • If the box is the whole, add the two parts.

Worked examples

Common mistakes

Practice problems

  1. Find 10−710 - 7 by asking ”77 and what make 1010?”

    Answer

    33

    Full solution

    7+3=107 + 3 = 10, so 10−7=310 - 7 = 3.

  2. Find the box: 9+□=159 + \square = 15.

    Answer

    66

    Full solution

    1515 is the whole and 99 is a part. 9+1=109 + 1 = 10, and 55 more is 1515. That is 66.

  3. Find the box: □+4=12\square + 4 = 12.

    Answer

    88

    Full solution

    1212 is the whole and 44 is a part. 12−4=812 - 4 = 8. Check: 8+4=128 + 4 = 12.

  4. Find the box: 7+7=□7 + 7 = \square.

    Answer

    1414

    Full solution

    Both parts are known, so add. 7+7=147 + 7 = 14 is a double.

  5. Find the box: 16−□=816 - \square = 8.

    Answer

    88

    Full solution

    1616 is the whole and 88 is the part left. 8+8=168 + 8 = 16, so 88 was taken away.

  6. Find the box: 4=□−64 = \square - 6.

    Answer

    1010

    Full solution

    The box is where you start, so it is the whole. 4+6=104 + 6 = 10. Check: 10−6=410 - 6 = 4.

  7. Find 12−912 - 9 by adding up.

    Answer

    33

    Full solution

    9+1=109 + 1 = 10, and 22 more is 1212. That is 1+2=31 + 2 = 3.

  8. Find the box: □−5=7\square - 5 = 7.

    Answer

    1212

    Full solution

    Take 55 away and 77 is left. So the start is 7+5=127 + 5 = 12.

  9. Find the box: 11=3+□11 = 3 + \square.

    Answer

    88

    Full solution

    1111 is the whole and 33 is a part. 11−3=811 - 3 = 8. Check: 3+8=113 + 8 = 11.

  10. For □−4=6\square - 4 = 6, Ava writes 22. What went wrong, and what is the right answer?

    Hint

    Put 22 in the box. Does 2−42 - 4 make 66?

    Answer

    She took away instead of adding. The box is 1010.

    Full solution

    The box is where you start. After taking 44 away, 66 are left, so the start is bigger than 66.

    6+4=106 + 4 = 10. Check: 10−4=610 - 4 = 6.

Frequently asked questions

How can adding help me subtract?

Turn the subtraction into a missing part. 10 − 8 asks what goes with 8 to make 10. Since 8 + 2 = 10, the answer is 2.

How do I find the missing number in 8 + □ = 11?

11 is the whole and 8 is one part. The missing part is 11 − 8 = 3. Check: 8 + 3 = 11.

What about 5 = □ − 3?

The box is where you start, so it is the whole. The parts are 5 and 3, so the box is 5 + 3 = 8. Check: 8 − 3 = 5.

How do I check my answer?

Put your number in the box and work out both sides. If they match, the answer is right.

Can the answer come first, like 9 = 4 + 5?

Yes. The = sign means 'is the same as,' so either side can come first.

What to learn next

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

  • CCSS.MATH.CONTENT.1.OA.B.4Operations and Algebraic ThinkingUnderstand subtraction as an unknown-addend problem.
  • CCSS.MATH.CONTENT.1.OA.D.8Operations and Algebraic ThinkingDetermine the unknown whole number in an addition or subtraction equation relating three whole numbers.
For teachersTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.