Singapore Math: Grade 1
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Path Steps
Number Bonds to 20
Free PreviewExtend number bond mastery to 20.
Why the path starts here
Grade 1 starts by stretching kindergarten number bonds past 10. Seeing 14 as 10 and 4 is the key idea of the year: it is the bridge to make-10 addition and to tens and ones.
Sets up: Make 10 Strategy
Skills in this step
- Find missing parts for any bond within 20
- Think flexibly about part-whole relationships
- Connect to subtraction as finding a missing part
4 + ? = 19
- A number bond joins two parts to make a whole. The whole is 19 and one part is 4.
- To find the missing part, take the known part away from the whole: 19 − 4.
- So the missing part is 15.
Answer: 15
Make 10 Strategy
Learn the powerful make-10 mental math strategy.
Why this step comes next
With bonds to 20 in place, 8 + 5 can be solved by moving 2 from the 5 to make 10, then adding the 3 that is left. This step teaches that move on its own before the facts to 20 are practised in a mix.
Sets up: Addition Facts to 20
Skills in this step
- Understand the make 10 strategy
- Break apart numbers to make 10
- Add faster using make 10
8 + 3 = ?
- 8 needs 2 more to make 10.
- Split 3 into 2 and 1.
- 8 + 2 = 10.
- 10 + 1 = 11.
Answer: 11
Addition Facts to 20
Master addition facts using mental strategies.
Why this step comes next
Now the make-10 move is used on every sum up to 20. Accuracy comes first; the sheets mix easy and bridging facts so the child has to choose a strategy rather than repeat one.
Sets up: Subtraction Facts to 20
Skills in this step
- Add any single-digit numbers with sums up to 20
- Use multiple strategies (counting on, making 10, doubles)
- Build fluency with all basic addition facts
9 + 3 = ?
- 9 needs 1 more to make 10.
- Split 3 into 1 and 2.
- 9 + 1 = 10.
- 10 + 2 = 12.
Answer: 12
Subtraction Facts to 20
Subtract within 20 using known addition facts and number bonds.
Why this step comes next
Subtraction follows the addition facts because every subtraction fact to 20 is an addition fact read backwards: 13 − 5 asks “what goes with 5 to make 13?”. A child who is secure on the previous step is answering questions she already knows.
Sets up: Place Value: Tens and Ones
Skills in this step
- Subtract any single-digit number from numbers up to 20
- Use multiple strategies (counting back, making 10, think addition)
- Build fluency with all basic subtraction facts
15 − 4 = ?
- Start at 15 on the number line.
- Count backward 4 steps.
- You land on 11.
- Or think: 4 + ? = 15. The answer is 11!
Answer: 11
Place Value: Tens and Ones
Understand place value up to 100.
Why this step comes next
The bonds to 20 already split each teen number into a ten and some ones. This step gives that idea its name, tens and ones, and extends it to every two-digit number.
Sets up: Bar Models Introduction
Skills in this step
- Understand that 2-digit numbers have tens and ones
- Count the tens and ones in a number
- Use place value blocks to show numbers
How many tens and ones are in 16?
- Split 16 into tens and ones.
- 16 has 1 tens and 6 ones.
Answer: 1 tens, 6 ones
Bar Models Introduction
Introduction to bar model problem solving.
Why this step comes next
A bar model is a number bond drawn as rectangles: the whole as one long bar, the parts as pieces of it. It is introduced once the facts are fluent so the child can concentrate on the drawing, not the arithmetic.
Sets up: Word Problems with Bar Models
Word Problems with Bar Models
Solve word problems using bar models.
Why this step comes next
With the drawing familiar, the bar becomes a way to read a story: decide which number is the whole and which is a part, then find the missing piece. It is the same add-and-subtract thinking as before, now hidden inside words.
Sets up: Measurement and Data
Measurement and Data
Compare the lengths and weights of everyday objects.
Why this step comes next
Measurement takes comparison off the page: longer or shorter, heavier or lighter. It comes last because it uses the language of more and less the child has practised with numbers all year.
Skills in this step
- Compare the length of two objects
- Use the words longer and shorter
- Understand relative length
The stick is 9 inches. The crayon is 5 inches. Which is longer?
- Both are measured in inches, so compare the numbers: 9 is more than 5.
- The stick (9 inches) is longer than the crayon (5 inches).
- So the longer one is the stick.
Answer: stick