The Do Now is a review of a previous concept of finding and comparing unit rates. Students will have 5 minutes to independently answer the Do Now problem and should refer to their notes for guidance on how to solve the problem.
Mr. Steiner needs to purchase 60 AA batteries. A nearby store sells a 20-pack of AA batteries for $12.49 and a 12-pack of the same batteries for $7.20.
a. Would it be less expensive for Mr. Steiner to purchase the batteries in 20-packs or 12-packs?
b. What is the difference between the costs of one battery?
After 5 minutes, students will have the opportunity to discuss the problem, compare their strategies, and check their answers with their group.
Through discussion and questioning, students will develop the steps for converting between fractions, decimals, and percents.
Decimals to Fractions
Example 1 - Rewrite 2.48 as a fraction
How would we say this decimal?
Students should know that the decimal is two and forty eight hundredths.
Why is this decimal a mixed number?
Students should recognize that it is a mixed number because there are 2 wholes.
What would this decimal be as a fraction?
Students should conclude that it is 2 48/100. They should reduce the fraction completely to 2 12/25.
We will complete another example together.
Example 2 - Rewrite 3.8025 as a fraction.
Fractions to Decimals
Example 3 - Rewrite ¾ as a decimal
Most students will be familiar with this fraction and know that it is 0.75.
How can you prove that ¾ is equivalent to 0.75?
Students may suggest that ¾ is equivalent to 75/100, which is equivalent to 0.75. I will explain that this is one strategy of changing a fraction to decimal.
I will present another problem, where students will find it difficult to use this strategy.
Example 4 - Rewrite 8/9 as a decimal
Can we use the strategy of finding an equivalent fraction with a denominator of 100?
Students should understand that this strategy will be difficult because 9 can not be divided into 100 evenly. I will explain that another strategy will be to divide the numerator by the denominator.
Students will divide the fraction and should notice that they have a remainder.
For our division algorithm, we usually bring down the next number, but in this example the dividend is only 8. How can we continuing our division problem?
Students should understand that if we write 8 as 8.00 we can continue our division.
Example 5 - Rewrite 45/6 as a decimal
What are two methods for converting this mixed number?
Students should realize that they have the option of changing the mixed number to an improper fraction before performing the division. Students may also realize that they can divide the numerator by the denominator and add 4 as the whole number.
Students are heterogeneously seated by math level, with at least one high level and low level math student in each group. I will give groups a list of commonly used fractions and they will determine if they know the decimal equivalent, without performing any calculations.
Students will have 5 minutes to determine the conversions. They may have difficulty with 1/3 and 2/3 since they are non-terminating decimals. After 5 minutes, groups will share out their answers with the class.
To assess students' understanding of converting between fractions and decimals, students will independently complete problems. If students should finish the problems early, I will encourage them to try the challenge problems.
Convert each fraction and decimal.
* A common mistake that students make is they forget to reduce the fractions completely.
After 10 minutes, students will discuss their work and answers with their group. If there is any confusion after the group discussion, we will discuss the problems as a class.
To help students remember the algorithm for converting a fraction to a decimal, I will share with students a song that some may find helpful.
I'm a Little Fraction (sung to I'm a Little Teapot)
I’m a little fraction
Yes I am
Here is my numerator
Here is my denominator
When I become a decimal
Hear me shout
Tip me over and divide me out.
I will play the song "I'm a Little Teapot" so students can hear how the lyrics fit the song.