Estimating Sums and Differences
Lindsey Anderson, Ms. Luick, Grade 6
Brief Description: Students will learn the steps needed to estimate sums and differences of fractions. They will learn two different ways to estimate fractions – by using a number line and comparing the numerator and the denominator. Once students can estimate fractions, they will learn how to estimate the sums and differences of fractions. The lesson will begin with an explanation of the rules of estimation and a brief discussion about why it is important. Finally, students will have time to practice by working independently and putting problems on the board.
Rationale: Estimation is a very important skill that it is imperative for a student to learn. Fractions are used frequently throughout our daily lives (a recipe calls for ˝ cup of some ingrediant; a store declares that all items are ˝ off) and because most people do not walk around with calculators, learning how to estimate is a very useful mathematical tool that we can utilize throughout our lives. In addition, estimation is important because it will enable a student to predict answers and check the reasonableness of their answers. Using estimation will help them achieve greater success when adding and subtracting fractions.
Prior knowledge: Most of the students in the class have experience from previous lessons on estimating whole numbers and decimals. In addition, they come to the lesson with the ability to add and subtract fractions with like and unlike denominators.
New Jersey Core Curriculum Standards:
2. Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.
3. Determine the reasonableness of an answer by estimating the result of operations.
Objective: Students will be able to estimate sums and differences of fractions. They will learn that it is helpful to estimate sums and differences in order to check the reasonableness of their answers, predict answers, and when an exact number is not necessary. They will learn to estimate fractions through the use of number lines as well as utilizing the rules. In the next few days, students will learn to add and subtract mixed numbers and will be able to use estimation to check the reasonableness of their answers.
Hook: To introduce the topic of estimation, I will begin by putting this problem on the board: 1/8 + 4/5. I will ask students how this addition problem could be solved without changing the denominators. I will call on volunteers and begin a discussion about estimation. I will ask students why they think it would be useful to estimate fractions (possible answers: (1) to check the reasonableness of answers, (2) when an exact answer isn’t necessary, (3) to predict what an exact answer will be).
Finally, I will put the homework on the board for students to copy. They will be given 6 problems (addition and subtraction of unlike fractions) and be asked to do three things: (1) estimate the sum or difference; (2) solve the problem; (3) determine whether or not their answer was reasonable based on their estimate. I will do one example problem in order to model the correct method. While they are copying the homework, I will help any students that need additional explanations. As a challenge, I will put up a bonus problem. The problem will be an addition problem using mixed numbers. They will be asked to do the same three things they are doing for the other problems. This will get students thinking about the next lesson, which will be the addition and subtraction of mixed numbers.
Materials used in lesson: The only materials I will be using for this lesson are the chalkboard and my own brief outline of the lesson. Students will be using their notebooks only.
Questions and Examples: I will put a fraction addition problem on the board and ask if anyone knows a quicker and easier way to add the problem in our heads. I will then ask why it is helpful to estimate the sums and differences of numbers and fractions? After hearing student responses, I will explain that estimating fractions is useful when we want to check the reasonableness of our answers, when an exact number isn’t necessary, and to predict about what an exact answer will be.
Closure: I will end the lesson by calling on volunteers to tell me the different ways we can estimate fractions and why it is important. I will ask them to each think of a word problem and real life example of when they would need to estimate fractions. They will each think of their own word problem and we will share out tomorrow.
Individualization: Because different children have different learning styles, I will structure my lesson so to meet different needs. First, for the auditory learners, we will discuss as a class the importance of estimation and discuss the steps. For the visual learners, I will write the steps on the board and show them different methods they can use to estimate fractions. Throughout the lesson, we will work as a class, in groups, and independently on problems I will put on the board. During the independent and group work, I will walk around the classroom and give additional assistance to any student who may need it. Extra bonus problems will be put on the board for those who finish early.
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