W.2 Complete subtraction sentences - sums up to 20
What is subtraction
Subtraction is a mathematical operation that represents taking away, removing, or finding the difference between two numbers. When we subtract, we start with a larger number (the whole) and remove a smaller number (the part taken away) to find what remains (the difference).
- If you have 8 apples and eat 3 apples, you have 5 apples left: 8 − 3 = 5
- If you have 12 crayons and give 4 to a friend, you have 8 crayons left: 12 − 4 = 8
- If you count 15 birds and 7 fly away, 8 birds remain: 15 − 7 = 8
Subtraction answers questions like "How many are left?" or "How many more does one group have than another?" The subtraction symbol "−" is called a minus sign.
Parts of a subtraction sentence
A complete subtraction sentence has three main parts: the minuend, the subtrahend, and the difference. These parts work together to show the relationship between numbers in a subtraction problem.
- In 9 − 4 = 5:
- 9 is the minuend (the starting amount)
- 4 is the subtrahend (the amount taken away)
- 5 is the difference (the amount left)
- In 17 − 8 = 9:
- 17 is the minuend
- 8 is the subtrahend
- 9 is the difference
The minuend always comes before the minus sign, and the subtrahend comes after it. The difference appears after the equals sign. Remember: minuend − subtrahend = difference.
Understanding the equals sign in subtraction
The equals sign (=) in mathematics means "is the same as" or "has the same value as." In subtraction sentences, it shows that the value on the left side of the equation (the subtraction problem) has the same value as the number on the right side (the answer or difference).
- 10 − 6 = 4 means "Ten minus six is the same as four"
- 14 − 5 = 9 means "The difference between fourteen and five has the same value as nine"
- 20 − 11 = 9 means "Twenty take away eleven equals nine"
The equals sign is not a "get the answer" symbol but rather a balance symbol. It tells us that both sides of the equation represent the same quantity, just in different forms.
Strategies for solving subtraction problems up to 20
There are several thinking strategies that first graders can use to solve subtraction problems within 20. These strategies help build number sense and mathematical understanding rather than just memorizing facts.
- Counting Back: For 12 − 3, start at 12 and count back 3 numbers: 11, 10, 9. So 12 − 3 = 9.
- Using Known Facts: If you know 10 − 4 = 6, then 11 − 4 = 7 (one more than 6).
- Making Ten: For 13 − 5, think: 13 − 3 = 10, then 10 − 2 = 8. So 13 − 5 = 8.
- Thinking Addition: For 15 − 7, think "What number plus 7 equals 15?" Since 7 + 8 = 15, then 15 − 7 = 8.
- Using Visual Models: Draw 14 circles, cross out 6, and count how many remain uncrossed (8).
Different strategies work better for different problems and different students. Practice multiple strategies to find which ones make the most sense to you. The goal is to become flexible and efficient with numbers.
Subtraction with number lines
A number line is a straight line with numbers placed at equal intervals along its length. It provides a visual model for understanding subtraction as moving backward or "jumping back" from a starting number.
- To solve 8 − 3 using a number line:
- Start at 8
- Move 3 spaces to the left (backward)
- Land on 5
- So 8 − 3 = 5
- To solve 16 − 7 using a number line:
- Start at 16
- Move 7 spaces to the left
- Land on 9
- So 16 − 7 = 9
When using a number line for subtraction, always start at the minuend (the first number) and move left (backward) the number of spaces equal to the subtrahend (the number being subtracted). The number you land on is the difference.
Subtraction with manipulatives and visual models
Manipulatives are physical objects that help students understand mathematical concepts by allowing them to see and touch the numbers they're working with. Common manipulatives for subtraction include counting blocks, linking cubes, buttons, or even drawings of objects.
- Using counting blocks for 11 − 4:
- Make a group of 11 blocks
- Remove 4 blocks from the group
- Count the blocks that remain: 7 blocks
- So 11 − 4 = 7
- Drawing pictures for 19 − 8:
- Draw 19 circles
- Cross out 8 circles
- Count the uncrossed circles: 11 circles
- So 19 − 8 = 11
Manipulatives and visual models are especially helpful when first learning subtraction concepts. They make abstract numbers concrete and help students understand what subtraction actually means in real-world terms.
Fact Families: The connection between addition and subtraction
A fact family is a group of related addition and subtraction facts that use the same three numbers. Understanding fact families helps students see the inverse relationship between addition and subtraction—that they are opposite operations.
- The numbers 7, 4, and 11 form this fact family:
- 7 + 4 = 11
- 4 + 7 = 11
- 11 − 7 = 4
- 11 − 4 = 7
- The numbers 5, 9, and 14 form this fact family:
- 5 + 9 = 14
- 9 + 5 = 14
- 14 − 5 = 9
- 14 − 9 = 5
If you know one fact in a family, you can figure out the other three. For example, if you know 8 + 6 = 14, you also know 6 + 8 = 14, 14 − 8 = 6, and 14 − 6 = 8. This relationship makes learning math facts more efficient.
Subtraction word problems within 20
Subtraction word problems are real-world situations described in words that require subtraction to solve. To solve these problems, students must identify what is being asked, determine which numbers are important, and decide which operation (subtraction) to use.
- Maria had 15 stickers. She gave 6 stickers to her brother. How many stickers does Maria have now?
- Solution: 15 − 6 = 9 stickers
- There were 18 children on the playground. 9 children went inside. How many children are still on the playground?
- Solution: 18 − 9 = 9 children
- David read 13 pages of his book on Monday. On Tuesday, he read 7 fewer pages than on Monday. How many pages did David read on Tuesday?
- Solution: 13 − 7 = 6 pages
When solving word problems, look for key phrases that indicate subtraction, such as "take away," "gave away," "how many are left," "how many more," "fewer than," or "difference between." Drawing a picture can often help visualize what the problem is asking.
Missing number subtraction problems
A missing number subtraction problem is a subtraction sentence where one of the three parts (minuend, subtrahend, or difference) is unknown. Students must use their understanding of the relationship between these parts to determine the missing value.
- Missing minuend: [] − 5 = 7
- Think: "What number minus 5 equals 7?"
- If 7 is the difference, and 5 is the subtrahend, the minuend must be 7 + 5 = 12
- Check: 12 − 5 = 7 ✓
- Missing subtrahend: 14 − [] = 6
- Think: "14 minus what number equals 6?"
- If 14 is the minuend and 6 is the difference, the subtrahend must be 14 − 6 = 8
- Check: 14 − 8 = 6 ✓
- Missing difference: 17 − 9 = []
- Think: "What is 17 minus 9?"
- This is a standard subtraction problem: 17 − 9 = 8
- Check: 8 + 9 = 17 ✓
When solving missing number problems, you can use the inverse operation (addition) to check your work or find the missing part. For example, if the minuend is missing in "[] − 4 = 9," you can add: 9 + 4 = 13, so the missing minuend is 13.
Subtraction patterns and properties
Subtraction has specific patterns and properties that help us understand how numbers behave when we subtract. Recognizing these patterns makes subtraction easier and helps students develop number sense.
- Subtracting zero: Any number minus 0 equals itself.
- 15 − 0 = 15
- 8 − 0 = 8
- 20 − 0 = 20
- Subtracting a number from itself: Any number minus itself equals 0.
- 12 − 12 = 0
- 7 − 7 = 0
- 19 − 19 = 0
- Subtracting 1: Any number minus 1 equals the number that comes just before it when counting.
- 14 − 1 = 13
- 9 − 1 = 8
- 20 − 1 = 19
- Order matters in subtraction: Unlike addition, subtraction is not commutative. Changing the order changes the result.
- 10 − 3 = 7 but 3 − 10 does not equal 7
- 15 − 6 = 9 but 6 − 15 does not equal 9
Understanding subtraction patterns helps with mental math. For example, knowing that subtracting 1 simply gives you the previous counting number allows you to solve problems like 17 − 1 instantly without needing to count back.
Checking subtraction with addition
Since addition and subtraction are inverse operations, we can use addition to check the accuracy of our subtraction work. This verification method helps catch errors and reinforces the relationship between these two operations.
- To check 13 − 5 = 8:
- Add the difference (8) to the subtrahend (5)
- 8 + 5 = 13
- Since this equals the original minuend (13), the subtraction is correct
- To check 16 − 9 = 7:
- Add the difference (7) to the subtrahend (9)
- 7 + 9 = 16
- This equals the original minuend (16), so the subtraction is correct
The checking process follows this rule: If a − b = c, then c + b should equal a. This relationship always holds true for subtraction problems and provides a reliable way to verify your answers.
Real world applications of subtraction within 20
Subtraction within 20 applies to numerous everyday situations that first graders encounter. Understanding these practical applications helps students see the relevance of subtraction beyond the classroom and strengthens their problem-solving skills.
- Snack time: If you have 17 grapes and eat 8, how many are left? (17 − 8 = 9)
- Classroom supplies: If there are 20 pencils in a box and 6 are being used, how many are still in the box? (20 − 6 = 14)
- Sports: If a basketball team scores 18 points and the other team scores 11 points, what is the difference in their scores? (18 − 11 = 7)
- Saving money: If you want to buy a toy that costs $15 and you have saved $9, how much more money do you need? (15 − 9 = 6)
- Cooking: If a recipe calls for 16 chocolate chips and you already put in 7, how many more do you need to add? (16 − 7 = 9)
- Calendar: If today is the 14th of the month and your birthday is on the 20th, how many days until your birthday? (20 − 14 = 6)
Notice how subtraction answers different types of questions: "how many are left" (take away), "how many more" (comparison), and "how much longer" (measurement difference). Recognizing what type of question is being asked helps you choose the correct operation.
Building fluency with subtraction facts within 20
Subtraction fluency means being able to recall subtraction facts quickly and accurately without having to count or use manipulatives. Developing fluency requires practice with various strategies until the facts become automatic.
- Flashcards: Create flashcards for subtraction facts within 20 and practice them daily.
- Games: Play subtraction games like "Subtraction War" with cards or online math games.
- Timed Practice: Set a timer for one minute and see how many subtraction problems you can solve correctly.
- Sing Songs: Learn subtraction songs or chants that help you remember facts.
- Use Technology: Practice with educational apps or websites that focus on subtraction facts.
- Daily Word Problems: Solve one or two subtraction word problems each day.
Fluency doesn't mean just memorization—it means understanding the concepts so well that you can recall facts quickly. Start with strategies (like counting back or making ten), and with practice, these strategies will become so fast they'll seem like memorization.
Common Core alignment: CCSS.MATH.CONTENT.1.OA.A.1 – Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. CCSS.MATH.CONTENT.1.OA.B.4 – Understand subtraction as an unknown-addend problem. CCSS.MATH.CONTENT.1.OA.C.6 – Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.
Notes for Teachers
This lesson is aligned with CCSS.MATH.CONTENT.1.OA.A.1, CCSS.MATH.CONTENT.1.OA.B.4, and CCSS.MATH.CONTENT.1.OA.C.6. Use it for whole-class instruction, small group work, independent practice, or homework.
The comprehensive content covers conceptual understanding, procedural fluency, and problem-solving applications for subtraction within 20. All material is 100% original, fact-checked for mathematical accuracy, and designed for first-grade learners using age-appropriate American English.
The lesson progresses from concrete models (manipulatives, drawings) to visual representations (number lines) to abstract numerical work, following the CRA (Concrete-Representational-Abstract) instructional sequence recommended for building deep mathematical understanding.