In this lesson plan, we will focus on solving first-then-now problems. This lesson builds upon previous experiences where learners have engaged with first-then-now addition and first-then-now subtraction. By integrating both concepts in this session, learners will deepen their understanding and prepare to explore the inverse relationship between addition and subtraction.
Understanding First Then Now Problems
First-Then-Now Addition Problems: First-then-now addition stories involve actions where something is joined to or combined with another. These problems involve combining or bringing together two or more quantities to find the total. For example: There are 5 apples in a basket. Then 3 more apples are added to the basket. How many apples are there in total? (5 + 3 = ?)
First-Then-Now Subtraction Problems: The first-then-now structure can also be used to solve subtraction problems where something is taken away or removed from an initial quantity. These problems typically follow a sequence of events: first, there is an initial situation, then an action is performed (such as taking away or separating), and finally, the result or remaining quantity is described. For example: There are 10 pencils on the desk. If 4 pencils are taken away, how many pencils are left? (10 - 4 = ?)
Parts of Addition Equations
The parts of an addition equation can be described as the augend, addend, and sum.
Addends: Addends are the numbers that are being added together to find the total sum. In most situations, both numbers being added are simply referred to as addends. For example, in the equation 3 + 5 = 8, both 3 and 5 are addends.
Sum: The sum represents the quantity that results from the addition process. It is the total or combined value of the addends. Example: In the addition equation 3 + 5 = 8, the number 8 represents the sum of 3 and 5.
Augend: In contexts where it is helpful to distinguish between the two numbers being added, such as in first-then-now story problems, the first value is called the augend. It is the number to which another number (the addend) is being added. Example: In the addition equation 3 + 5 = 8, the number 3 is the augend and 5 is the addend.
Parts of Subtraction Equations
The three parts of a subtraction equation are the minuend, subtrahend, and difference.
Minuend: The minuend is the total or the whole quantity from which another quantity (the subtrahend) is to be subtracted. It is the starting or initial amount. Example: In the subtraction equation 10 - 4 = 6, the minuend is 10.
Subtrahend: The subtrahend is the quantity that is to be subtracted or taken away from the minuend. It represents the amount that is removed or taken away. Example: In the subtraction equation 10 - 4 = 6, the subtrahend is 4.
Difference: The difference is the result of subtracting the subtrahend from the minuend. It represents the remaining or resulting quantity after the subtraction. Example: In the subtraction equation 10 - 4 = 6, the difference is 6, which is the quantity left after subtracting 4 from 10.
Teaching Plan
The following activities will help your learner become confident in finding missing parts of first-then-now problems.
Examples and visuals to support the lesson:
1. First Then Now Addition
Present your learner with representations of first-then-now addition that show only two parts. Ask your learner to draw the missing part of the story and equation. Have them explain how they found the missing part. Here are a few examples:
"We don't know how many coins Jamal had at first. Then, he got two more coins. Now, he has five coins. How many coins did Jamal have at first?" In this story problem, the first addend is missing. The equation can be written as: ? + 2 = 5.
"First, there were two dogs in the park. We don't know what happened then. Now, there are seven dogs in the park. How many more dogs came to the park?" In this scenario, the second addend is missing. The equation can be written as: 2 + ? = 7.
"First, there were four pencils in the cup. Then, two more pencils were put in the cup. How many pencils are there now?" In this story, the sum is missing. The equation can be written as: 4 + 2 = ?.
Skill Check
I can find missing parts of first-then-now addition stories.
2. First Then Now Subtraction
Next, provide your learner with representations of first-then-now subtraction stories. Just as with the addition problems, provide two out of the three parts of the story. Have your learner identify the missing part and explain how they found their answer.
"We don't know how many cakes were on the plate at first. Then, two cakes were eaten. Now, there are five cakes on the plate. How many cakes were on the plate at first?" In this story problem, the minuend is missing. The equation can be written as: ? - 2 = 5.
"First, there were five bowling pins standing. Then, some of the pins were knocked down. Now, there are two bowling pins standing. How many bowling pins were knocked down?" Here, the subtrahend is missing. The equation can be written as: 5 - ? = 2.
"First, there were three children in the pool. Then two children got out of the pool. How many children are in the pool now?" In this scenario, the difference is missing. The equation can be written as 3 - 1 = ?.
Skill Check
I can find missing parts of first-then-now subtraction stories.
3. Challenge Activity
To provide additional challenge, provide your learner with a problem that has two missing parts. Ask them to find multiple ways to satisfy the missing parts. For example: "Can you write a story that ends with six children on the bus?" Challenge them to write an addition story and a subtraction story.
Skill Check
I can find missing parts of story problems that have two parts missing.
Through the exploration of first-then-now addition and subtraction problems in this lesson, your learner has developed a solid foundation in understanding these operations within the context of sequential actions. Exploring addition and subtraction together will introduce your learner to the inverse relationship between addition and subtraction laying the groundwork for more advanced problem-solving strategies.
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Skill Check