Mathematics Grade 1: Addition with Carrying Up to 20

Grade 1 Mathematics: Addition with Carrying (up to 20)

1. The Driving Question

If you have 8 crayons in one box and 7 in another, how do you figure out how many you have total—without counting every single one from scratch? And why does the number sometimes "spill over" into a new ten, like when you pour too much juice into a cup and it overflows into the next one?

2. The Core Idea — Built, Not Listed

Imagine you’re at a lemonade stand with two small cups. One cup has 8 lemons, and the other has 7. You want to pour them both into a bigger cup to count them all at once—but the big cup can only hold 10 lemons before it’s full. When you pour the 8 lemons in, the cup is almost full (8/10). Then you add the 7 lemons from the second cup, but only 2 fit before the big cup is full (10). The leftover 5 lemons spill into a second big cup. Now you have 1 full cup (10) and 5 extra lemons, so your total is 15.

This is what happens when you add numbers and they "carry over" into a new ten. You’re not just counting—you’re grouping the ones into tens to make the number easier to handle.

Key Vocabulary: - Sum – The total number you get when you add two numbers together. Example: If you have 6 marbles and win 5 more in a game, the sum is 11 marbles. - Regroup (or "carry") – When the ones add up to 10 or more, you trade 10 ones for 1 ten. Example: In 9 + 4, you regroup the 13 ones into 1 ten and 3 ones. - Place value – The idea that where a digit sits in a number (ones or tens) tells you its value. Example: In 15, the 1 is worth 10, and the 5 is worth 5. - Addend – One of the numbers you’re adding together. Example: In 7 + 5 = 12, 7 and 5 are addends.

3. Assessment Translation

How this appears in Grade 1 assessments: - Exit tickets: A quick problem like "Solve: 6 + 9 = __" with space to show work (e.g., drawing tens and ones or using a number line). - Short constructed response: "Explain how you solved 8 + 7. Use pictures or words." - Show-your-work problems: "There are 5 apples in one basket and 8 in another. How many apples are there in all? Show how you grouped the apples."

What a "proficient" response looks like: - Numbers: Correct answer (e.g., 15 for 8 + 7). - Work shown: Uses a strategy like: - Drawing tens and ones (e.g., 1 full ten-frame and 5 extra dots). - Writing the equation with a "carry" (e.g., 8 + 7 = 10 + 5 = 15). - Using a number line (jumping from 8 to 10, then 5 more). - Explanation: Says something like, "I knew 8 + 2 = 10, so I took 2 from the 7 to make a ten. Then I had 5 left, so 10 + 5 = 15."

What a "developing" response looks like: - Numbers: Correct answer but no work shown (e.g., just writes "15"). - Work shown: Counts all by ones (e.g., draws 15 individual apples) but doesn’t group into tens. - Explanation: Says, "I counted them all" without showing how.

Model proficient response: Problem: Solve 9 + 6. Show your work. Answer: "I know 9 + 1 = 10, so I take 1 from the 6 to make a ten. Now I have 10 and 5 left, so 10 + 5 = 15. [Draws two ten-frames: one full, one with 5 dots.]"

4. Mistake Taxonomy

Mistake 1: Forgetting to regroup - Question: Solve 7 + 5. - Common wrong answer: "12" (writes 7 + 5 = 12 without regrouping). - Why it loses credit: The student added the ones (7 + 5 = 12) but didn’t trade 10 ones for 1 ten. The answer should be 1 ten and 2 ones (12), but the work doesn’t show the regrouping step. - Correct approach: - Break 5 into 3 and 2. - Add 7 + 3 = 10 (make a ten). - Add the leftover 2: 10 + 2 = 12.

Mistake 2: Regrouping incorrectly - Question: Solve 8 + 6. Show how you made a ten. - Common wrong answer: "14" (writes 8 + 6 = 10 + 4 = 14, but takes 4 from the 6 instead of 2). - Why it loses credit: The student took the wrong number to make a ten. To make 10 from 8, you need 2, not 4. - Correct approach: - 8 + 2 = 10, so take 2 from the 6. - Leftover: 6 – 2 = 4. - Total: 10 + 4 = 14.

Mistake 3: Misplacing the regrouped ten - Question: Solve 9 + 4. Write the sum. - Common wrong answer: "13" (writes 9 + 4 = 10 + 3 = 31). - Why it loses credit: The student regrouped correctly (9 + 1 = 10, leftover 3) but wrote the answer as "31" instead of "13." They put the leftover ones in the tens place. - Correct approach: - 9 + 1 = 10 (take 1 from the 4). - Leftover: 4 – 1 = 3. - Total: 1 ten and 3 ones = 13.

5. Connection Layer

1. Within math: Addition with carrying-Place value in bigger numbers. Why it matters: When you add 28 + 15, you’ll use the same regrouping trick—but now you’re carrying over into the tens place, not just making a new ten. The logic is identical.

2. Across subjects: Addition with carrying-Measuring time in music. Why it matters: In music, beats are grouped into measures (like tens). If you have 7 eighth notes and add 5 more, you "carry over" into the next measure—just like regrouping in math.

3. Outside school: Addition with carrying-Counting money with coins. Why it matters: If you have 8 nickels (40 cents) and earn 7 more (35 cents), you’ll trade 10 nickels for 1 quarter (50 cents) and have 5 nickels left (25 cents). Total: 75 cents. Same regrouping, but with coins!

6. The Stretch Question

If you add three numbers (like 5 + 6 + 7), can you regroup in more than one way? Which way is fastest?

Pointer toward the answer: You can regroup in different orders! For 5 + 6 + 7: - First add 5 + 6 = 11, then 11 + 7 = 18 (regroup once). - Or first add 6 + 7 = 13, then 13 + 5 = 18 (regroup once). - Or look for a ten first: 5 + 7 = 12, then 12 + 6 = 18 (regroup once). The fastest way is usually to look for two numbers that make a ten first (like 5 + 7). Try it with 4 + 8 + 6—what do you notice?