Y.1 Add a multiple of ten and a one-digit number
What is a multiple of ten?
Multiples of ten are numbers that end with a zero. These numbers are made by counting by tens: 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100. You can think of them as groups of ten.
- 10 is one group of ten (10 = 10)
- 20 is two groups of ten (10 + 10 = 20)
- 30 is three groups of ten (10 + 10 + 10 = 30)
- 40 is four groups of ten (10 + 10 + 10 + 10 = 40)
All multiples of ten have a zero in the ones place. This pattern helps us recognize them quickly.
Understanding place value: tens and ones
Place value tells us what each digit in a number means. In two-digit numbers, the left digit shows tens and the right digit shows ones. For example, in the number 37, the "3" means 3 tens (30) and the "7" means 7 ones (7).
- 25 = 2 tens and 5 ones (20 + 5)
- 48 = 4 tens and 8 ones (40 + 8)
- 60 = 6 tens and 0 ones (60 + 0)
- 93 = 9 tens and 3 ones (90 + 3)
When we add a multiple of ten to a one-digit number, we only change the tens place or the ones place, never both at the same time.
Adding a multiple of ten and a one-digit number
When we add a multiple of ten and a one-digit number, we keep the tens digit the same and add the one-digit number to the ones place. Since multiples of ten have zero ones, we simply replace the zero with the one-digit number.
- 30 + 4 = 34 (30 stays as 30, plus 4 ones = 34)
- 50 + 7 = 57 (50 stays as 50, plus 7 ones = 57)
- 80 + 2 = 82 (80 stays as 80, plus 2 ones = 82)
- 20 + 9 = 29 (20 stays as 20, plus 9 ones = 29)
The tens digit never changes when adding a one-digit number to a multiple of ten. Only the ones place changes.
Using models to understand the addition
Models are tools that help us see math problems. We can use base-ten blocks, ten frames, or drawings to show how adding a multiple of ten and a one-digit number works.
- 40 + 6: Show 4 tens rods (40) and 6 single cubes. Together they make 4 tens and 6 ones = 46.
- 70 + 8: Show 7 ten frames completely filled (70) and 8 individual dots. Together they make 7 tens and 8 ones = 78.
- Draw 9 bundles of 10 sticks (90) and 5 single sticks. Together they make 9 tens and 5 ones = 95.
Models help us see that the tens stay separate from the ones. We count the tens first, then add the ones.
Mental math strategy: counting on by ones
Counting on is a mental math strategy where you start with the larger number and count forward by the smaller number. When adding a multiple of ten and a one-digit number, start with the multiple of ten and count up by ones.
- 60 + 3: Start at 60, count forward 3 ones: 61, 62, 63. Answer: 63.
- 30 + 8: Start at 30, count forward 8 ones: 31, 32, 33, 34, 35, 36, 37, 38. Answer: 38.
- 90 + 5: Start at 90, count forward 5 ones: 91, 92, 93, 94, 95. Answer: 95.
Counting on works best when the one-digit number is small. For larger one-digit numbers, it's faster to use place value understanding.
Mental math strategy: place value thinking
Place value thinking is a faster mental math strategy where you recognize that the tens digit stays the same and the ones digit becomes the one-digit number you're adding.
- 40 + 7: Think "4 tens and 7 ones" = 47.
- 20 + 6: Think "2 tens and 6 ones" = 26.
- 80 + 1: Think "8 tens and 1 one" = 81.
- 50 + 9: Think "5 tens and 9 ones" = 59.
This strategy is faster than counting on because you immediately know the answer by just looking at the numbers.
Writing equations horizontally and vertically
Math problems can be written in different ways. Horizontal equations are written across the page (40 + 3 = 43). Vertical equations are written up and down with the numbers aligned by place value.
- Horizontal: 70 + 5 = 75
- Vertical:
70 + 5 ---- 75 - Horizontal: 10 + 8 = 18
- Vertical:
10 + 8 ---- 18
In vertical format, always align the ones digits. The tens digit of the multiple of ten aligns above where the tens digit of the answer will be.
Patterns when adding to multiples of ten
Math has patterns that help us learn faster. When adding one-digit numbers to multiples of ten, there are helpful patterns to notice.
- All answers have the same tens digit as the multiple of ten: 30 + X always has 3 tens.
- The ones digit in the answer is always the one-digit number you added: 60 + 7 always has 7 ones.
- Adding zero to any multiple of ten gives the same number: 40 + 0 = 40.
- Adding to 10 follows the same pattern: 10 + 4 = 14, 10 + 9 = 19.
Recognizing patterns makes math easier. Once you know the pattern, you can solve many problems quickly.
Real-world applications of this skill
We use addition of multiples of ten and one-digit numbers in everyday life. Recognizing these situations helps us understand why this math skill is important.
- Money: If you have 50 cents and find 7 more cents, you have 57 cents.
- Age: If your sister is 20 years old and you are 6 years old, together your ages add to 26 years.
- Collections: If you have 80 baseball cards and get 3 new cards, you have 83 cards total.
- Time: If you read for 30 minutes and then read for 8 more minutes, you read for 38 minutes total.
Math helps us solve real problems. When you see a multiple of ten and need to add a small amount, you can use this skill.
Common mistakes to avoid
Everyone makes mistakes when learning. Knowing common errors helps us avoid them.
- Adding both digits: For 40 + 5, adding 4 + 5 = 9 (wrong) instead of keeping 4 tens and adding 5 ones = 45 (correct).
- Changing the tens digit: Thinking 60 + 4 = 64, but writing 64 as 604 (wrong place value).
- Forgetting the zero: Writing 30 + 2 = 32, but then writing the answer as 32 instead of 32.
- Confusing tens and ones: Thinking 70 means 7 ones instead of 7 tens.
Always check your answer: Does it have the correct tens digit from the multiple of ten? Does it have the one-digit number in the ones place?
Practice strategies for mastery
To become really good at adding multiples of ten and one-digit numbers, try these practice strategies.
- Flashcards: Make cards with problems like "40 + 3" on one side and "43" on the other.
- Number line practice: Use a number line from 0-100 to jump from multiples of ten.
- Verbal practice: Say problems out loud: "Twenty plus four equals twenty-four."
- Writing practice: Write out all the facts for one multiple of ten: 30+0=30, 30+1=31, 30+2=32, up to 30+9=39.
- Game: Roll a dice for the one-digit number and pick a multiple of ten card.
Practice a little each day. Start with easier problems (like 10 + one-digit) and work up to harder ones (like 90 + one-digit).
Connecting to related math skills
Math skills connect to each other. Learning to add multiples of ten and one-digit numbers helps with other important first-grade math concepts.
- Subtraction: If 50 + 6 = 56, then 56 - 6 = 50 and 56 - 50 = 6.
- Adding two-digit numbers: 40 + 3 helps with 43 + 5 (just add to the ones).
- Mental math: Quick thinking with tens and ones helps with all mental math.
- Place value: Understanding that 60 means 6 tens helps with reading and writing all two-digit numbers.
- Counting: Skip counting by tens connects to adding multiples of ten.
Math builds on itself. Mastering this skill makes future math learning easier and faster.
Checking your answers
Good mathematicians check their work. There are several ways to verify if your answer to a multiple of ten plus one-digit problem is correct.
- Use a different strategy: If you used place value thinking, check by counting on.
- Use manipulatives: Build the problem with base-ten blocks or other counters.
- Draw a picture: Draw tens as bundles of sticks and ones as single sticks.
- Use related facts: If 30 + 4 = 34, then 34 - 4 should equal 30.
- Estimate: Know that 60 + 8 should be between 60 and 70, closer to 60 than 70.
Always ask: Does my answer make sense? If I add 8 to 50, I should get a number in the 50s, not the 40s or 60s.
Common Core alignment: CCSS.MATH.CONTENT.1.NBT.C.4 – Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.1.NBT.C.4. Use it for whole-class instruction, independent practice, or homework.
The content systematically builds from foundational concepts (multiples of ten, place value) to the target skill (adding multiples of ten and one-digit numbers), then extends to strategies, applications, and connections. Each section follows the definition-example-note structure for clarity and retention.
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