In this unit plan, we will explore strategies and activities to help your homeschooler master the art of solving addition and subtraction word problems. They will learn how to represent, solve, and explain solutions to addition and subtraction problems. They will also practice using words, objects, drawings, and numbers to understand and solve the word problems.
Modeling Word Problems
To help your child grasp the concept of representing and solving single-step problems, it's important to provide them with various tools and strategies. Here are a few tools that are mentioned in this unit plan.
Part-Part-Whole Mats: Part-part-whole mats are visual tools that help learners understand the relationship between parts and a whole. These mats often feature a large cherry model or similar graphic. Learners can use physical objects such as counters or toys, to represent the word problem.
First-Then-Now Story Mats: First-then-now story mats are used to represent the sequence of events in addition and subtraction problems. These mats help learners visualize the progression from the initial quantity to the final result. Objects can be moved from one box to the next to represent the steps of the word problem.
Linking Cubes: Linking cubes are versatile tools that can be connected and compared to represent quantities and their relationships. They are especially useful for comparison problems where learners need to visually see the difference between two amounts. As an alternative, your learner can color boxes on grid paper to represent the linking cubes and compare their lengths.
Addition and Subtraction Strategies
It is important that your learner can confidently add and subtract within 10 when solving word problems. That way, the focus is on understanding the word problem rather than getting stuck on the calculations. Here are a few addition and subtraction strategies:
Counting On: Counting on is a simple and effective strategy for solving addition problems. It involves starting with the larger number and counting on from there. For example, if the problem states, "John has 5 apples. He buys 3 more. How many apples does he have in total?" Your child can start with 5 and count on 3 more: 5, 6, 7, 8. The answer is 8.
Counting Back: Counting back is a straightforward strategy for solving subtraction problems. It involves starting with the larger number and counting back to find the difference. For example, if the problem states, "There are 9 balloons. 5 balloons pop. How many balloons are left?" Your child can start with 9 and count back 5 using their fingers: 9, 8, 7, 6, 5, 4. The answer is 4.
Making Tens: Another useful strategy is making tens. This strategy is particularly helpful when the numbers involved are close to the next multiple of 10. For example, if the problem states, "Sara has 8 pencils. She buys 7 more. How many pencils does she have in total?" Your child can recognize that 8 and 2 make 10, and there are 5 left over. So the answer is 10 + 5 = 15.
Using Doubles: Doubles are pairs of numbers that are the same, such as 2 + 2 or 6 + 6. Knowing doubles can be a valuable strategy for solving addition problems. For example, if the problem states, "Mary has 3 stickers. Her friend gives her the same amount. How many stickers does Mary have now?" Your child can recognize that 3 + 3 is the same as double 3, which is 6.
Using Related Facts: Related facts are pairs of addition and subtraction problems that share the same numbers. Knowing that addition and subtraction are inverses can simplify the process of solving subtraction problems. For example, if the problem states, "There are 9 birds on the tree. 7 birds fly away. How many birds are left?" Your child can think of the related addition fact, 7 + ? = 9. By recalling that 7 + 2 = 8, they can determine that 9 - 7 = 2.
Solving Word Problems
Use the following steps as a general guideline to help your child solve word problems. Keep in mind that it is more important to follow a strategy that feels natural and comfortable to your learner rather than adhering to a step-by-step process.
Step 1: Understand the Problem: The first step in solving a word problem is understanding the problem itself. Encourage your child to read the problem carefully, identify the key information, and determine what the problem is asking. They can underline or highlight important details and rephrase the problem in their own words to ensure comprehension.
Step 2: Represent the Problem: Once your child understands the problem, they can represent it using words, objects, drawings, or numbers. This step helps them visualize the problem and make connections between the mathematical operations and the real-world context. They can create a diagram, draw a picture, or use manipulatives to model the problem.
Step 3: Select the Operation: After representing the problem, your child needs to determine which operation (addition or subtraction) is needed to solve the problem. They can consider the relationships between the quantities and the action described in the problem. For example, if the problem mentions adding, combining, or bringing together, addition is the appropriate operation. On the other hand, if the problem involves taking away, separating, or finding the difference, subtraction is the right operation.
Step 4: Solve the Problem: Once your child has selected the operation, they can solve the problem using the appropriate strategy. Encourage them to choose a strategy that they are comfortable with and explain their reasoning behind their solution. If they are unsure, encourage them to try multiple strategies or use trial and error to find the correct answer.
Step 5: Justify the Solution: After solving the problem, it's important for your child to justify their solution. They can explain their reasoning, provide evidence from the problem, or use mathematical language to support their answer. This step helps strengthen their communication skills and ensures a deeper understanding of the problem-solving process.
Unit Plan for Addition and Subtraction Word Problems
Now that we have discussed key concepts and strategies, let’s explore a sample unit plan for addition and subtraction word problems. The activities in this unit plan will help your learner develop their ability to represent, solve, and justify solutions to addition and subtraction word problems. Keep the numbers within 10 until your learner feels confident to move on to numbers within 20 or more.
Learning Goals
The activities in this unit plan, will teach your learner how to:
Explore a variety of addition and subtraction word problems including part-part-whole, joining, separating, and comparison problems.
Represent single-step addition and subtraction word problems using various models.
Solve addition and subtraction word problems using appropriate strategies.
Write addition and subtraction sentences (equations) to represent word problems.
Begin with a review of part-part-whole representations such as cherry models or bar models. Make sure that your learner understands what each number in the models represents.
Once your learner is comfortable with part-part-whole models, present them with a word problem that involves finding the "whole" of a part-part-whole scenario.
For example: "Sara has 5 red apples and 3 green apples. How many apples does she have in total?" In this example, the 5 red apples and 3 green apples represent the parts and the objective is to find the whole.
To help your learner understand the word problem, provide them with a part-part-whole mat that has a large cherry model on it. Use physical objects like toys or counters to represent the red and green apples.
Have your learner place the 5 red counters in one group and the 3 green counters in another group to represent the two parts of the cherry model. Then slide the objects to the "whole" section of the cherry model to demonstrate joining the apples together.
Have your learner count the apples to see how many there are altogether. Make sure that your learner understands the connection between finding the total number of apples and joining the groups together as a "whole."
Next, guide your learner in writing an addition equation to represent the story problem. Write the equation as 5 + 3 = __. Then have your learner fill in the total (8). Ask them what each part of the equation represents in the story problem to check their understanding.
2. Part-Part-Whole Subtraction Problems
Once your learner is comfortable with finding the "whole" of a part-part-whole word problem, present them with a word problem that involves finding a missing "part."
For example: "John has 10 candies. Some are chocolate, and some are strawberry. If 4 of the candies are chocolate, how many are strawberry?" In this example, the 10 candies represent the whole, the 4 chocolate candies represent one part, and the objective is to find the remaining part.
To help your learner understand the word problem, provide them with a part-part-whole mat that includes a cherry model. Use physical objects like candies or counters to represent the candies.
Have your learner place 10 counters in the "whole" section of the cherry model. Then, move 4 counters to one of the "part" sections to represent the chocolate candies, while moving the remaining counters to the other "part."
Next, guide your learner to count the remaining counters to find out how many candies are strawberry. Ensure your learner understands the relationship between the whole and its parts in subtraction problems.
Have your learner write a subtraction equation to represent the story problem. Write the equation as 10 - 4 = __. Then, have your learner fill in the total (6). Ask them to explain what each part of the equation represents in the story problem to ensure comprehension.
3. Joining Problems (First-Then-Now Addition)
Present your learner with a joining problem where something is added to an initial amount, resulting in a new total. Encourage your learner to explain or act out the story in their own words.
For example: "Jake had 4 toy cars. Then, he got 6 more toy cars for his birthday. How many toy cars does he have now?" In this example, 4 toy cars represent the initial amount, 6 more toy cars represent the additional amount, and the objective is to find the new total.
Have your learner place 4 toy cars in the "first" section of the mat. Then, move the 4 cars to the "then" section while joining 6 more toy cars with them. Slide all the toy cars to the "now" section to demonstrate the total amount of toy cars after the addition.
Next, guide your learner to count the total number of toy cars. Make sure they understand the sequence of the events (first, then, now).
Have your learner write an addition equation to represent the story problem. Write the equation as 4 + 6 = __. Then, have them fill in the total (10). Ask your learner what each part of the equation represents in the story problem to confirm their understanding.
Once your learner is comfortable modeling and solving joining problems, show them a separating problem where something is removed or taken away from an initial amount, resulting in a new total. Encourage your learner to explain or act out the story in their own words.
For example: "Sarah had 12 candies. She ate 5 candies. How many candies does she have now?" In this example, 12 candies represent the initial amount, 5 candies eaten represent the amount subtracted, and the objective is to find the remaining total.
Use a first-then-now mat to help your learner visualize the problem. Provide them with toys or counters to represent the candies.
Have your learner place 12 candy counters in the "first" section of the mat. Then, move the candies to the "then" section while removing 5 candy counters to show the candies eaten. Slide the remaining candy counters to the "now" section to demonstrate the total candies left after subtraction.
Next, guide your learner to count the remaining candies. Ensure they understand the sequence of events (first, then, now).
Have your learner write a subtraction equation to represent the story problem. Write the equation as 12 - 5 = __. Then, have them fill in the total (7). Ask your learner to explain what each part of the equation represents in the story problem to ensure understanding.
5. Comparison Problems (Finding the Difference)
Before introducing your learner to comparison problems, it is helpful for them to have an understanding of comparing lengths. This will allow them to represent the quantities in the word problems as lengths of bars or connecting cubes.
Present your learner with an example of a comparison problem. For example: "Tom has 8 marbles. Lily has 3 marbles. How many more marbles does Tom have than Lily?" In this example, 8 marbles represent Tom's quantity, 3 marbles represent Lily's quantity, and the objective is to find the difference.
Provide them with toys, counters, or linking cubes to represent the cars. Have them connect or arrange 8 items side by side to represent the number of Tom's marbles. Then connect or arrange 3 items to represent Lily's marbles. Line up the two rows of objects so that the lengths can be compared easily.
Have your learner compare the lengths of the rows of objects by counting the difference between them. Demonstrate that Tom has 5 extra marbles that do not line up with Lily's marbles. Make sure that your learner understands that the extra marbles represent the difference between 8 and 3.
Have your learner write a subtraction equation to represent the story problem. Write the equation as 8 - 3 = __. Then, have them fill in the total (5). Ask your learner what each part of the equation represents in the story problem to confirm their understanding.
Throughout this unit, your homeschooler has developed their ability to represent, solve, and justify solutions to addition and subtraction word problems. Word problems provide real-life contexts for applying mathematical concepts and skills. By solving word problems, children develop problem-solving strategies, improve their number sense, and strengthen their mathematical communication skills. Your learner will be able to apply these skills to real-world scenarios, making informed decisions and solving everyday problems.
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