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1st Grade algebra · Ages 6–7

The Same As

The most important algebra lesson of all happens in first grade: what the = sign really means.

□the unknown

The one idea

The = sign doesn’t mean “the answer comes next”. It means both sides are worth the same.

Most children leave Grade 1 thinking “=” means “write the answer”. That one misunderstanding causes years of trouble later. Read = out loud as “is the same as” every single time, and 4 + 5 = □ + 6 stops being confusing.

📚 The 4 lessons⚖️ Balance scale✏️ Practice

This page is the right one if they can already…

  • Adds and subtracts within 10
  • Counts on from a number (5… 6, 7, 8)
  • Knows that 3 + 4 and 4 + 3 give the same answer

Not yet? Start at Kindergarten: Make It Fair — algebra only works one rung at a time.

The four 1st Grade algebra lessons

In order — each one leans on the last. Every example is broken into single moves and ends by checking itself.

1

= means “is the same as”

Both sides of = are worth the same. The answer can be on the left or the right.

8
53

Worked example

Is 8 = 5 + 3 true?

  1. 1

    Read it with the words “is the same as”.

    8 is the same as 5 + 3

  2. 2

    Work out the side with the sum.

    5 + 3 = 8

  3. 3

    Compare the two sides.

    8 and 8

Answer: True.

Check: Both sides are 8, so the scale is level.

⚠️ The usual mistake

Says 8 = 5 + 3 is “backwards” or wrong.

Every sum they have seen so far had the answer on the right.

Fix: Write sums both ways round all week: 7 = 4 + 3 as often as 4 + 3 = 7.

💬 Say this

“Read the equals sign as “is the same as”. Is 8 the same as 5 and 3?”

🏠 Try it at home

Write 6 = 4 + 2 and 6 = 6 and 6 = 5 + 2 on sticky notes. Which ones are true? (The last one is a trap.)

2

Find the missing number

If you know the total and one part, count up from the part to the total.

Worked example

3 + □ = 7

  1. 1

    Start at the number you know.

    3

  2. 2

    Count up to 7, putting up a finger each time.

    4, 5, 6, 7

  3. 3

    Count your fingers.

    4 fingers

Answer: □ = 4

Check: 3 + 4 = 7 ✓

⚠️ The usual mistake

Writes 10.

They see a plus sign and add the two numbers they can see.

Fix: Always put the answer back in. Does 3 + 10 make 7? No — so 10 can’t be right.

💬 Say this

“I have 3. I need 7. How many more do I need?”

🏠 Try it at home

Put 3 spoons out. “I want 7 spoons on the table. How many more should you bring?”

3

When the box comes first

The box can be anywhere. Use the numbers you know, and remember subtraction undoes addition.

Worked example

□ + 5 = 12

  1. 1

    The whole is 12. One part is 5.

    12 is made of □ and 5

  2. 2

    Take away the part you know.

    12 − 5

  3. 3

    Work it out.

    12 − 5 = 7

Answer: □ = 7

Check: 7 + 5 = 12 ✓

⚠️ The usual mistake

Writes 17.

Adding feels like the right move when you see a + sign.

Fix: Draw the bar. The whole bar is 12 — the box is only part of it, so it must be less than 12.

💬 Say this

“The whole thing is 12. If one part is 5, how big is the other part?”

🏠 Try it at home

Hide some coins under a cup and leave 5 out. “There are 12 altogether. How many under the cup?”

4

Make both sides the same

When there are sums on both sides, work out the side you can finish, then make the other side match it.

45
□6

Worked example

4 + 5 = □ + 6

  1. 1

    Finish the side with no box.

    4 + 5 = 9

  2. 2

    So the other side must also be worth 9.

    □ + 6 = 9

  3. 3

    Count up from 6 to 9.

    7, 8, 9 → 3

Answer: □ = 3

Check: 4 + 5 = 9 and 3 + 6 = 9. Same ✓

⚠️ The usual mistake

Writes 9 in the box.

They think = means “put the answer here”, so they write the answer to 4 + 5.

Fix: Read it aloud: “4 + 5 is the same as 9 + 6?” 9 is not the same as 15 — the scale tips.

💬 Say this

“The left side is worth 9. What does the right side need so it’s worth 9 too?”

🏠 Try it at home

Two piles of Lego: 4 and 5 bricks in one, 6 in the other. “Make the piles the same.” How many did you add?

⚖️ Keep it fair

Get □ on its own using only fair moves. This is exactly how equations are solved at every grade, right up to Grade 10. Try the wrong button too — see what happens.

Puzzle: □ + 2 = 5

□

□ + 2 = 5

✏️ Practice that never runs out

Every question is new. A wrong answer gets a hint; a second one shows the worked solution, so no one stays stuck.

Find the missing number

The box can be anywhere. Read = as “is the same as”. Check your answer by putting it back in.

What number goes in the box?

17 − □ = 7

The words, in plain English

Equals (=)
Is the same as.
8 = 5 + 3 says 8 is the same as 5 + 3.
Missing number
The number in the box we need to find.
3 + □ = 7, the box is 4.
True
Both sides really are the same.
6 = 4 + 2 is true.
False
The sides are not the same.
6 = 5 + 2 is false.
Part and whole
Parts join to make the whole.
3 and 4 are parts of 7.

🌍 Algebra in an ordinary day

  • “You have 6 stickers and need 10 for the chart. How many more?”
  • Fair swaps: 3 cards and 2 cards for 5 cards
  • Counting up to work out change from 10

🏁 By the end of 1st Grade

  • Reads = as “is the same as” and explains it
  • Says whether an equation like 6 = 5 + 2 is true or false
  • Finds the missing number in any position within 20
  • Solves 4 + 5 = □ + 6 without writing 9

Where this fits

One idea, twelve rungs. The hiding spot just gets cleverer.

  1. Pre-K❓The Hiding Game
  2. K🎁Make It Fair
  3. 1□The Same As
  4. 2?Number Machines
  5. 3nLetters Are Boxes
  6. 4nNumber Recipes
  7. 5xUndo It
  8. 6xBalance and Tip
  9. 7xTwo Steps Back
  10. 8y = mx + bLines and Slope
  11. 9xAlgebra 1
  12. 10f(x)Curves and Functions

← One rung down

Kindergarten: Make It Fair

One rung up →

2nd Grade: Number Machines

All 12 gradesMore maths, grade by grade →

Frequently Asked Questions

What algebra should a 1st Grade child learn?

The = sign doesn’t mean “the answer comes next”. It means both sides are worth the same. By the end of the year they should be able to: reads = as “is the same as” and explains it; says whether an equation like 6 = 5 + 2 is true or false; finds the missing number in any position within 20; solves 4 + 5 = □ + 6 without writing 9.

Isn’t 1st Grade too early for algebra?

Not the way it is taught here. Algebra is finding a number that is hiding, and at this age the hiding spot is □ — something a child can point at. There are no letters, and the ideas match what 1st grade maths already covers.

What is the most common 1st Grade algebra mistake?

Writes 10. They see a plus sign and add the two numbers they can see. The fix: Always put the answer back in. Does 3 + 10 make 7? No — so 10 can’t be right.

What if my child is stuck?

Go down one rung. Every lesson here builds on the Kindergarten page, and the “ready for this page if” list at the top tells you exactly what they need first. In practice, a wrong answer gives a hint, and a second wrong answer shows the full worked solution.

Is it free?

Yes. All 4 lessons, the pictures, the worked examples, the balance scale and the practice questions are free with no signup. The practice never runs out — every question is generated fresh and checked.

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