Lesson 3 of 8
Objective: SWBAT estimate with fractions.
As an introduction to this lesson, I want to know what students already know about estimating. They will answer the following questions in their notebook:
- What does estimating mean to you?
- How is estimating a useful tool in math?
- When can it be used?
After about 10 minutes, I will randomly select students to share their thoughts.
We will discuss and students will write down the definition of benchmark.
A benchmark can be a fraction, decimal, or percent that is common, familiar, easy, and well known!
Based on the definition, students will be asked to give their own example of a benchmark. Students often give examples such as 1/2, 50%, 3/4, 100%, and 0.5.
Why are these fractions, decimals, and percents more familiar to you?
Students may respond with:
- These are the first fractions we learned.
- I think of these percents because of test scores.
- These are used a lot in cooking and baking.
This lesson is an introduction for how and why we estimate fractions. The first steps for students will be to draw a number line marked with the benchmarks 0, 1, and 2. Many students are visual and it helps for them to see the placement of the fractions in relation to the benchmarks.
We will work through a few examples together, with students engaging in discussion.
Ex. 1 - Estimate 9/10.
- Is 9/10 between 0 and 1 or 1 and 2? How do you know?
- Is it closer to 0 or 1? How do you know?
Ex. 2 - Estimate 3/8.
- Is 3/8 between 0 and 1 or 1 and 2? How do you know?
- Is it closer to 0 or 1? How do you know? (If students struggle with these questions, I will pose the next question.)
- Would it be helpful to use another benchmark to estimate 3/8? (Students may suggest plotting 1/2 on the number line.)
Ex. 3 - Estimate 1 1/4.
- Is 1 1/4 between 0 and 1 or 1 and 2? How do you know?
- Is it closer to 1 or 2? How do you know?
The next portion of the lesson focuses on how students can use benchmarks to estimate the sum of 2 fractions. We will work through a few examples together. For each example, it is important to provide fraction bars for the visual learners. Example, Visual Representation of Fraction Sums
Ex. 4 - What is a good estimate of 4/5 + 7/8?
- What is a good strategy for finding the estimate of the sum of fractions? (If students respond with adding the fractions and then rounding the answer, challenge them with the next question.)
- Is there a quick method for estimating the sum without finding the actual sum first?
- Which benchmark is 4/5 nearest? How do you know?
- Which benchmark is 7/8 nearest? How do you know?
- Now that we've found an estimate for the individual fractions, what should we do next?
I will conclude the lesson by posing the question: How can estimating the sum of fractions be useful? Students may respond with various answers. I would like them to observe that it's useful because
- it's easier than doing the actual math
- it's quicker than doing the actual math
- you can check if you did the math correctly
- you can predict the answer
Getting Close Game
Following the lesson, students will play Getting Close Game (from the Connected Mathematics 3 curriculum). This game allows students to practice their estimating skills.
Students will play in groups of four. Each group will receive a set of the playing cards. Each student will receive the cards number 0,1,2, and 3. I will read the directions aloud to students:
Students will hold the numbered cards 0, 1, 2, and 3 in their hand out of view of their opponents. The playing cards should be face down on the table. One student turns two of the cards over. Each student estimates the sum of the two cards and decides whether it is closest to 0, 1, 2, or 3. After each student has determined the answer, place your chosen card on the table at the same time. The student whose card is closest to the actual sum is the winner of that hand and will keep the two playing cards. If there is a tie, then each player receives a playing card. The group will play another round and continue until there aren't any more playing cards. The player with the most cards wins.
As students play, I will circulate throughout the room to answer questions and assess students' ability to estimate fractions correctly.
I will pose the following questions to students to assess their understanding of estimation.
What was a useful strategy in playing the game?
For which pairs was it easy and for which pairs was it hard to estimate the sum? Why?
Is it possible to find the actual sum when you are estimating?