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Using Known Facts to Add

A 40-minute Grade 1 lesson on the properties that turn one known fact into several — turning the numbers round, adding three in a helpful order, and leaning on doubles.

Using Known Facts to Add is a free 40-minute Grade 1 maths lesson plan for Common Core standard 1.OA.B.3 — use facts you know to work out ones you do not — like knowing 3+8 because you know 8+3. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.

Grade:
Grade 1
Length:
40 minutes
Standard:
1.OA.B.3

Grade 1 · Operations & Algebraic Thinking

1.OA.B.3

Apply properties of operations as strategies to add and subtract.

Objective

Students will be able to use a known addition fact to work out a related one, rather than calculating each fact from scratch.

Students are successful when they can

  • Uses 3 + 9 to answer 9 + 3 without recalculating.
  • Reorders three addends to make ten first.
  • Uses a double to get a near double: 6 + 7 from 6 + 6.

What you need

  • Cubes in two colours, 20 per pair
  • Ten frames, two per pair
  • Fact cards showing pairs like 3 + 9 and 9 + 3
  • The printable practice sheet linked at the end of this plan

The lesson

Warm-up — doubles round

5 min
  1. Rapid-fire the doubles to 10 + 10. These should be quick; if they are not, this lesson has nothing to lean on.
  2. Then ask 6 + 7 and watch what happens. Some will count; some will say 'it is one more than twelve'.

Teach — three ways to reuse a fact

12 min
  1. Build 3 + 9 with cubes: a stick of three and a stick of nine. Ask for the total.
  2. Now swap the sticks over without changing either. Write 9 + 3. Nothing was added or removed, so the total cannot have changed.
  3. Say why it matters: counting on 3 from 9 is three steps, counting on 9 from 3 is nine. Same answer, a third of the work.
  4. Move to three addends: 8 + 5 + 2. Ask which two to do first. Pairing 8 and 2 makes ten, and ten plus five needs no thought.
  5. Finally, doubles: build 6 + 6 and then add one more cube. 6 + 7 is not a new fact, it is a known one plus one.
“You do not have to learn every fact. You have to learn some facts and how to get from them to the others.”

Guided practice — name the strategy

11 min
  1. Pairs take a fact card and answer it, then say which strategy they used.
  2. Insist on the name: turn it round, make ten, near double.
  3. Where two strategies both work, collect both. That is the point rather than a complication.

Independent practice

9 min
  1. Students complete a strategies page.
  2. Look for counting on from the smaller number — that pupil has the answer but is not yet reusing anything.

Close

3 min
  1. Give 7 + 8 and ask for two different ways to get it without counting.
  2. Near double from 7 + 7, or make ten by moving 3 across. Collect both and stop.

What goes wrong, and why

Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.

Treats 9 + 3 and 3 + 9 as two separate facts to learn.

Why: They are written differently and have been met as separate items, so nothing has suggested they are the same fact twice.

Fix: Physically swap two cube sticks without changing them. The identity is a fact about the objects, not a rule to memorise.

Adds three numbers strictly left to right even when a ten is available.

Why: Left to right is how reading works and how every calculation has been modelled so far. Reordering looks like changing the question.

Fix: Do 8 + 5 + 2 both ways and compare the difficulty, not just the answer. Same result, obviously less work, and the pupil chooses the easier route themselves.

Applies the turnaround to subtraction: 3 − 9 for 9 − 3.

Why: A property has been over-generalised, which is what happens when a rule is learned as a manipulation of symbols rather than a fact about quantities.

Fix: Try it with cubes. Nine take away three can be done; three take away nine cannot, with cubes on the table. The property is about joining, and joining is symmetric in a way that removing is not.

If they are not there yet

  • Secure the doubles to 5 + 5 first. Every near-double strategy is worthless without the double it leans on.
  • Use two-colour cubes so the two addends stay visually distinct when the sticks are swapped.

If they finish early

  • Use a near double twice: 6 + 8 from 6 + 6, or from 7 + 7.
  • Add four numbers and find the best pairing.
  • Ask whether the turnaround works for three numbers in any order, and test it.

Exit ticket

You know 4 + 4 = 8. Use it to work out 4 + 5. Then work out 2 + 9 + 8 the easy way.

What to look for: 9, said as one more than 8, and 19 with the 2 and 8 paired first. A pupil who recalculated 4 + 5 from scratch got it right without using the lesson.

Printable practice for 1.OA.B.3

Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.

Questions about Using Known Facts to Add

How long does the Using Known Facts to Add lesson take?

40 minutes, split across 5 timed sections: warm-up 5 min, teach 12 min, guided practice 11 min, independent practice 9 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.

Which standard does Using Known Facts to Add teach?

CCSS.MATH.CONTENT.1.OA.B.3 — 1.OA.B.3, Operations & Algebraic Thinking for Grade 1: “Apply properties of operations as strategies to add and subtract.” In plain terms, use facts you know to work out ones you do not — like knowing 3+8 because you know 8+3.

What do I need to teach this lesson?

Cubes in two colours, 20 per pair, ten frames, two per pair, fact cards showing pairs like 3 + 9 and 9 + 3 and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.

What mistakes should I expect in this lesson?

Three, each a reasoning error rather than carelessness: treats 9 + 3 and 3 + 9 as two separate facts to learn; adds three numbers strictly left to right even when a ten is available and applies the turnaround to subtraction: 3 − 9 for 9 − 3. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.

How do I know whether the lesson worked?

The exit ticket asks: “You know 4 + 4 = 8. Use it to work out 4 + 5. Then work out 2 + 9 + 8 the easy way.” 9, said as one more than 8, and 19 with the 2 and 8 paired first. A pupil who recalculated 4 + 5 from scratch got it right without using the lesson. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.

Is there a worksheet to go with Using Known Facts to Add?

Yes — 2 printable 1.OA.B.3 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.

Is Using Known Facts to Add free to use?

Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 5 September 2026. Please do not resell it or republish it as your own.

Last reviewed 2026-09-05. Aligned to 1.OA.B.3 of the Common Core State Standards for mathematics.