This unit plan will provide you with tools and resources to teach your homeschooler strategies for adding and subtracting within 20. Your learner will explore the structure of teen numbers by partitioning them into tens and ones, solve addition and subtraction equations based on this structure, and learn to bridge through ten using the make-ten strategy.
Here is a description of the strategies that are mentioned in this unit plan. As your child develops fluency with adding and subtracting within 20, they will begin to select strategies that work best for them. Encourage them to explore various strategies and practice using them in different contexts. By allowing your child to choose efficient strategies, they will become more confident and proficient in solving basic addition and subtraction problems.
Relating Addition and Subtraction:
One of the key concepts in developing fluency in adding and subtracting within 20 is recognizing the relationship between the two operations. Addition and subtraction are inverse operations, meaning they undo each other.
For example, we can use the addition sentence 2 + 3 = 5 to represent combining 2 apples with 3 apples into a group of 5 apples. The opposite operation would be removing 2 apples from the group of 5 apples and leaving 3 apples. We can represent that scenario with a subtraction sentence: 5 - 2 = 3.
Part-Part-Whole Models for Teen Numbers:
Part-part-whole models are visual tools that help learners understand how numbers can be broken down into parts and combined to form a whole. In the context of teen numbers, these models illustrate the concept of partitioning into "ten and some ones.
Consider the number 14. Using a part-part-whole model, we can show that 14 consists of 10 and 4 by writing 14 as the "whole" and 10 and 4 as the "parts." Explain to your learner that the number 14 can be described as "10 and 4 more."
Equations with the "Ten and Some More" Structure:
Part-part-whole models not only help visualize numbers but also aid in writing and solving addition and subtraction equations based on the tens and ones structure.
Using the example of partitioning 14 into 10 and 4, we can write an addition equation such as 10 + 4 = 14, or a subtraction equation like 14 - 4 = 10.
This structure can help your learner solve missing number problems such as 17 - ? = 7 or 8 + ? = 18.
Applying Single-Digit Strategies to Teen Numbers:
Strategies used for single-digit addition and subtraction within ten can be extended to teen numbers by leveraging the tens and ones structure.
For example: To add 14 + 3, partition 14 into 10 and 4. Combine the 4 with 3 to get 7. Then, add the 7 to 10 to get 17.
To subtract 15 - 6, partition 15 into 10 and 5. Subtract 6 from the 10: 10 - 6 = 4. Add the remaining 4 to the 5, resulting in 9.
Bridging Through Ten:
Calculations that bridge through ten can be recognized visually on a number as calculations that cross over the number ten. For example, to add 8 + 4 on a number line, we would start at 8 and move 4 units to the right, ending at 12. During this process, we had to cross the number ten.
These calculations can also be done by applying the "make ten" strategy. It simplifies the process for learners by breaking numbers down into parts that can make ten.
For example, when adding 9 + 6, your learner can break the smaller number (6) into 5 and 1. The one can be combined with the 9 to make ten (9 + 1 = 10). Then the 10 can be combined with the 5 resulting in a total of 15.
For subtraction, it helps to partition the teen number into 10 and some ones. For example, to subtract 13 - 4, partition 13 into 10 and 3, then subtract 4 from 10 to get 6, then add the 3 to get 9.
Unit Plan for Adding and Subtracting Within 20
Now that we have discussed key concepts and strategies, let’s explore some engaging activities for teaching your learner about adding and subtracting with teen numbers. This unit plan should be taught gradually throughout the school year to allow your learner time to develop fluency and confidence.
Learning Goals
The activities in this unit will help your learner develop the following skills:
Solve addition and subtraction equations based on the tens and ones structure of teen numbers.
Use single-digit addition and subtraction strategies to add and subtract single-digit numbers to and from teen numbers.
Solve addition and subtraction equations that involve doubles of 6, 7, 8, and 9 and halves 12, 14, 16, and 18.
Apply the make-ten strategy to simplify calculations involving numbers close to ten (bridging ten).
Begin by introducing your learner to the tens and ones structure of teen numbers (11-19) by partitioning them into "10 and some more."
Demonstrate that teen numbers are composed of ten and some more. For example, 14 is 10 and 4 more. Use visual aids like ten frames, number lines, or base-ten blocks to show this concept.
Provide your learner with a set of ten frames and 11-19 counters. Have them fill one ten frame completely to represent 10 and put the remaining counters on a second ten frame. For example, for 14, fill one ten frame and place 4 more counters in the second frame. Repeat this for each teen number from 11 to 19.
Then guide your learner in writing equations that represent the ten and some ones structure. For example, 14 = 10 + 4. Practice with different teen numbers to reinforce the concept.
Provide your learner with missing number equations based on the ten and some ones structure. For example: 10 + 5 = ? and 17 - ? = 10.
2. Using Single-Digit Strategies
Next, encourage your learner to apply their knowledge of adding and subtracting single-digit numbers to calculations with teen numbers. Here are a few examples:
Adding and subtracting one: Learners can use the sequence of numbers to add 1 (find the next number) or subtract 1 (find the previous number). For example, to add 15 + 1, they can recognize that 16 is the next number after 15. Similarly, to subtract 15 - 1, they can recognize that 14 is the previous number before 15.
Doubles and halves: If your learner has memorized doubles and halves within 10, they can use this to calculations such as 14 + 4. Realizing that 4 + 4 is 8, your learner can add 8 to the 10 from 14. To write out the steps, first partition 14 into 10 and 4. The expression becomes 10 + 4 + 4, then 10 + 8, which is 18.
Guide your learner in recognizing patterns with adding single-digit numbers and teen numbers. For example, adding 5 to a number that ends in 5 results in a number ending in zero (5 + 5 = 10 and 15 + 5 = 20). Similarly, subtracting 5 from a number that ends in 0 results in a number that ends in five (10 - 5 = 5 and 20 - 5 = 15).
Provide a variety of missing number problems and word problems so that your learner can learn to recognize patterns and develop their own strategies.
3. Doubles and Halves with Teen Numbers
Next, guide your learner in exploring doubles and halves involving teen numbers. Remembering doubles and halves will help them become more fluent with adding and subtracting within 20.
Begin with a review of doubles and halves within ten. Explain that doubles are two of the same number added together. For example, double three is 3 + 3.
Use visual aids like counters or drawing dots to show doubles within teen numbers. For example, show that double 6 is 12 by placing 6 counters in two groups.
Provide your learner with counters or small objects that they can count with. Have them practice doubling numbers like 6, 7, 8, and 9 by creating two equal groups and counting the total.
Next, explain that halves involve dividing a number into two equal parts. Use visual aids like counters or drawing dots to show halves within teen numbers. For example, show that half of 14 is 7 by dividing 14 counters into two equal groups.
Have your learner practice finding halves of numbers like 12, 14, 16, and 18 by dividing the total into two equal groups.
Provide your learner with missing number problems that involve doubles and halves. For example: 6 + ? = 12 and 18 - 9 = ?.
4. Bridging Through Ten
Once your learner can fluently add and subtract with the ten and some ones structure, introduce them to calculations that bridge ten.
Begin by reviewing the pairs of numbers that make ten. Practice with missing number problems that involve making ten such as 8 + ? = 10.
Teach your learner to use the make ten strategy to solve addition problems like 9 + 6. Ask your learner to identify the number that makes ten with nine. Once they recognize that the number is 1, have them take 1 away from the 6 and join it with 9 to make ten. Then add the 5 that is left from six to 10 (10 + 5 = 15).
Use visual aids and equations to show this process. For the example of adding 9 + 6, the equation can be written as 9 + 1 + 5 showing that 6 is partitioned into 1 and 5.
Next, show your learner an example of bridging ten to solve a subtraction problem. For example, to subtract 17 - 8, first partition 17 into 10 and 7. Then subtract the 8 from ten, leaving 2. Add the 2 to the other 7, resulting in 9 as the answer.
Demonstrate this process using visual aids and equations. The equation for 17 - 8 can be written as 10 - 8 + 7 to show that 8 needs to be subtracted from ten.
Teaching your child strategies for adding and subtracting within 20 is an essential part of their mathematical development. By partitioning teen numbers into tens and ones, solving equations, and exploring doubles and halves, your learner has developed a thorough understanding of these concepts. Keep practicing these skills to reinforce and extend your learner's mathematical proficiency, making everyday math tasks easier and more intuitive.
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