In this lesson plan, your learner will practice subtracting across 10 by focusing on subtracting a single-digit number from a teen number that results in crossing the ten boundary. They will explore multiple strategies using visual aids like ten-frames and number lines and have opportunities to see which method they prefer.
When teaching subtraction across the ten boundary, two effective strategies are often used: "subtracting through ten" and "subtracting from ten."
Subtracting Through Ten:
The "subtracting through ten" strategy involves breaking down the subtraction process into two steps to make it easier to manage.
First, subtract enough from the minuend to bring it down to ten. Then subtract the remainder from ten. For example, to solve 12 - 4: Subtract 2 from 12 to get down to 10. Then, subtract the remaining 2 from 10, resulting in 8.
This can be visualized using tools like tens frames, bead bars, or number lines. On a number line, you would start at 12, move back 2 steps to reach 10, and then move back 2 more steps to reach 8.
Subtracting From Ten:
The "subtracting from ten" strategy is slightly different but also involves two steps. First, subtract the entire subtrahend from ten. Then add back the difference between the original minuend and ten.
For example, to solve 12 - 4: Subtract 4 from 10, which gives you 6. Then add the difference between the 12 and 10 (which is 2) to 6, resulting in 8.
This method can be useful because it aligns with the "counting on" strategy, helping learners see the connection between different subtraction techniques. This strategy is also foundational for understanding subtraction with larger numbers, such as subtracting from 100.
Teaching Plan
The following activities will help your learner explore strategies for solving subtraction problems that cross the ten boundary. Be sure to work at a pace that is comfrotable for your learner.
Examples and visuals to support the lesson:
1. Subtracting Through Ten
To introduce the subtraction through ten strategy, revisit the funfair ride scenario from Adding Across 10, this time starting with more than ten children. For example, "12 children are on the ride, then 4 get off. How many are left?"
Walk your learner though the steps of subtracting through ten. First, subtract down to ten and then subtract the rest from ten: "12 - 4 = 12 - 2 - 2 = 8."
Act out the story or use picture representations as your learner describes the story: "First there were twelve children on the ride. Then four got off. Now there are eight children on the ride."
Skill Check
I can solve subtraction problems in steps by subtracting a part down to ten, and then subtracting the other part.
2. Modeling Subtraction Through Ten
Next, provide an opportunity for your learner to work through the story with counters and tens frames.
Guide them through the process of partitioning and subtracting: "We are going to partition the four into two and two. First, we subtract two from twelve to get to ten. Then we subtract the remaining two from ten. Now we know that ten minus two is equal to eight."
Encourage your learner to describe the process in sentences: "First we took away two counters to make ten. Then we took away another two counters to make eight."
You can also model the process on a bead bar and number line. The bead bar can help link the tens frame representation to the number line. As you use the model, have your learner continue describing the process in full sentences.
Have your learner practice writing equations to express the two-stage process. Make that your learner understands the correct notation for representing each step:
Incorrect: 12 - 2 = 10 - 2 = 8
Correct: 12 - 2 = 10, then 10 - 2 = 8
Correct: 12 - 2 - 2 = 8
Skill Check
I can use different math tools to show the steps for subtracting down to ten and then subtracting the rest.
3. Subtracting from Ten
To introduce the strategy of subtracting from ten, tell the same story but subtract four children from the ten in the first carriage (instead of 2 from the second carriage then 2 from the first carriage).
Emphasize that it’s still four children getting off but partitioned differently: "First, we take away four counters from the ten, leaving six. Then we add on the remaining two: six plus two equals eight."
Next, encourage your learner to compare and constrast both strategies. Show the two methods side by side, asking your learner: "What’s the same? What’s different?"
Explain that sometimes one approach might be more efficient than the other depending on the numbers involved.
Revisit both methods with new equations that bridge ten, such as 15 - 9. Encourage your learner to discuss which method they think might be easier.
Skill Check
I can solve subtraction problems by subtracting from ten and then combining the parts that are left.
4. Additional Practice
Provide regular practice using counters and visual aids like tens frames and bead bars. Provide ample practice with both methods to help your learner progress to solving these calculations without physical counters.
Also, encourage your learner to practice number facts up to ten. The more fluent they are with number facts, the more confident they will be with the subtraction strategies.
Gradually move to just using equations, starting with those that already show the partitioned subtrahend or minuend.
Present problems that involve different approaches, such as: "12 - 3 using subtraction through ten." "17 - 9 using subtraction from ten."
Emphasize that sometimes one method is more efficient based on the specific numbers involved.
Skill Check
I can use and describe two different ways of subtracting across ten.
Summary
By the end of this lesson, your learner will be confident in subtracting across ten using the make-ten strategy. They will be adept at using visual aids like tens frames, bead bars, and number lines to partition numbers and simplify subtraction problems. These foundational skills will not only make subtraction more intuitive and engaging but also prepare them for more complex math challenges ahead. As they gain confidence in their subtraction abilities, they'll find themselves better equipped to tackle a wide range of mathematical problems with ease and enthusiasm.
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Skill Check