The Lumenary · K–2

Addition, subtraction and place value to 100

Name: ______________________

Date: ______________________

You will learn to

Add and subtract within 20 by counting on, making ten and using fact families, and within 100 using tens and ones
Explain that the equals sign means "has the same value as", so that $7 = 3 + 4$ and $3 + 4 = 4 + 3$ are both true
Represent two-digit numbers as tens and ones, and use this to compare them
Use the turn-around rule, and explain why taking away undoes adding but subtraction does not turn around

1.
Priya sells 8 mangoes to one customer and 5 mangoes to another. How many mangoes did she sell altogether? ( $8 + 5$ )
2.
Which of these number sentences are true? Choose all that are true.
- A. $7 = 3 + 4$
- B. $3 + 4 = 4 + 3$
- C. $3 + 4 = 8$
- D. $5 + 2 = 7 + 1$
3.
What number goes in the box? $9 + \square = 14$
4.
Amina has 12 shells and Lucas has 7 shells. How many more shells does Amina have than Lucas?
5.
Priya has 52 mangoes. What does the 5 in 52 mean?
- A.5 tens, which is 50 mangoes
- B.5 mangoes
- C.It means 52 is 'five and two', which is 7
6.
Which number is bigger, 47 or 52?
- A.52, because 5 tens is more than 4 tens
- B.47, because 7 is bigger than 2
- C.They are the same size
7.
Work out $38 + 25$ .
8.
Priya has 52 mangoes and sells 27. How many are left? ( $52 - 27$ )
9.
Gideon's game: true or false? "For any two counting numbers, $a - b$ is the same as $b - a$ ."
- A.True, just like $a + b = b + a$
- B.False: $5 - 3 = 2$ , but 5 cannot be taken from 3
10.
Margaret's computer checked $a + b = b + a$ for every $a$ and $b$ from 0 to 10 — all 121 facts — and found no mistakes. Does that prove the turn-around rule for every pair of numbers, even huge ones?
- A.Yes — 121 facts is a lot
- B.No — it checks those 121 facts; a reason is needed for all numbers

Answer key — Addition, subtraction and place value to 100

1.
Make ten: $8 + 5 = 8 + 2 + 3 = 10 + 3 = 13$ . Priya sold 13 mangoes.
2.
A sentence with $=$ is true when both sides have the same value. $7 = 3 + 4$ (7 and 7) and $3 + 4 = 4 + 3$ (7 and 7) are true. $3 + 4 = 8$ (7 and 8) and $5 + 2 = 7 + 1$ (7 and 8) are false.
3.
Count on from 9: ten, eleven, twelve, thirteen, fourteen — 5 steps. So $9 + 5 = 14$ and the box is 5. You can also use a fact family: $14 - 9 = 5$ .
4.
Lucas's 7 shells pair with 7 of Amina's, leaving 5 of hers without a partner. Or use a fact family: $7 + 5 = 12$ , so $12 - 7 = 5$ . Amina has 5 more shells.
5.
In 52 the left digit counts tens and the right digit counts ones. So the 5 means 5 tens = 50, and $52 = 50 + 2$ : five full crates and two loose mangoes.
6.
47 has 4 tens and 52 has 5 tens. Every number with 4 tens (up to 49) is smaller than every number with 5 tens (from 50). So 52 is bigger.
7.
Ones: $8 + 5 = 13 = 1$ ten and 3 ones. Tens: $3 + 2 + 1 = 6$ tens. So $38 + 25$ is 6 tens and 3 ones, which is 63.
8.
Break a ten: 52 is 4 tens and 12 ones. Take away 7 ones: 5 ones are left. Take away 2 tens: 2 tens are left. So $52 - 27 = 25$ . Check by adding: $25 + 27 = 52$ . ✓
9.
The statement is false. $5 - 3 = 2$ , but $3 - 5$ has no answer among the counting numbers: you cannot take 5 away from 3. One counterexample is enough to show that a rule about every pair of numbers is false.
10.
No. The computer checked 121 cases, which is strong evidence for those cases only. The reason that works for every pair is the row of beads: reading it from the left or from the right counts the same beads, so $a + b = b + a$ always. Lean's proof by induction is another reason that covers every number.