GrandyGSMS - Unit 2: Fraction, Decimal, Percent

Our next unit in math is our fractions, decimals, and percentages unit.

We started with with reviewing the following concepts (please see some videos or extra practice if you need a refresher):

Here are some videos and practice for all of those concepts:

Converting mixed numbers to improper fractions

- Here is some practice

Topic 1: Converting Fractions to Decimals

We will cover this in two mini lessons, as there are two methods you can use to convert fractions to decimals!

OPTION 1: Create Equivalent Fractions
*Keep in mind this method can ONLY works if we can create an equivalent fraction of 10 or 100 from our original fraction. Meaning, the denominator of the original fraction is a factor of 10 or 100 (1,2,5,10,20,25,50,100)

- Here is a worksheet using ONLY equivalent fractions

OPTION 2: Long Division
*This method always works, but takes a little more time (we will not be using a calculator).

This video explains both methods
- Here is a worksheet where you can use equivalent fractions for some, but need to use long division for others
- This video explains how to convert mixed numbers to decimals

Topic 2: Converting Decimals to Fractions

Our next lesson is on converting decimals to fractions. It is important that students always reduce their fractions to lowest terms! To do this, they can find the GCF of the numerator and denominator and divide by that!

a) Terminating Decimals to Fractions:

Here is a video on converting terminating decimals to fractions & another video!
- Here is a worksheet to practice terminating decimals to fractions & another one

b) Repeating Decimals to Fractions:

Here is a video explaining converting repeating decimals to fractions (watch first four examples ONLY)

Here is a worksheet to practice repeating decimals to fractions
Here is a worksheet that practices converting both terminating and repeating decimals to simplified fractions
Try this practice quizizz after you have watched the video and completed a few practice questions.

Topic 3: Converting with Percentages

Fraction, Decimal, and Percent Conversions - Watch this video for an explanation of all types of conversion before you start practicing. This is another video of a song to help you remember the steps!

We will be writing a quiz on converting between fractions, decimals, and percentages this week. Here is a copy of the practice quiz, and you can find the answer key here.

Decimal operations

The next topic we will be covering is adding, subtracting, multiplying and dividing decimals. Students have covered this on a more basic level in grade 6, so will mostly be familiar of the steps.

Topic 1: Estimating with decimals

The most important skill when it comes to decimal operations is estimating. This is the skill they will most likely use in the real world, so the first thing we will do when encountering an operations with decimals problem is to estimate the answer.

For adding, subtracting, and multiplying, we rely on rounding to the nearest whole number for our estimations. Here's an graphic that shows how we round to the nearest whole number.

Here is a video that shows a few examples

Here is a video that shows how to use rounding to estimate sums and differences

When estimating decimal divisions, it is more helpful to use compatible numbers. These are numbers that work well for division. Knowing your multiplication tables or using a multiplication chart is helpful when looking for compatible numbers.

Here is a video showing a few examples

Topic 2: Adding/Subtracting Decimals

Adding and Subtracting decimals numbers is a concept covered in grade 6, which we quickly review together. It is important that for each problem, they line the numbers up vertically (one on top of the other), making sure to line up the decimal points.

Before calculating any answers, they should first be estimating! This will allow them to hopefully identify if they've made any mistakes when calculating.

Here is a video explaining adding decimals

Here is a video explaining subtracting decimals

Here is a practice sheet with answers

Topic 3: Multiplying Decimals

In grade 6, students learned how to multiply decimals by whole numbers (13.45 x 12), in grade 7, we learn how to multiply decimals by decimals (13.45 x 3.4).

Here is a video showing multiplying a decimal by a decimal <---------------------- this is what we focus on in grade 7

Here is some practice with multiplying decimals by decimals

Topic 4: Dividing Decimals

In grade 6, they covered decimals divided by whole numbers (12.5 divided by 3). In 7th grade, we cover decimal divided by decimals. We have already spent a significant amount of time in class practicing the basic long division steps (both with our number sense review unit, and with our fraction to decimal conversions) so it is expected that students have the long division procedure mastered.

Here is a video explaining this topic

Here are is a practice sheet & another

Here is a worksheet that includes practice for all decimal operations

Topic 5: Percent of a Number

The last topic in our unit is calculating the percent of a number. This is especially applicable in the real world when it comes to calculating tax, sales, tips, etc.

Here is a video that shows how to calculate the percent of a number

Here is some practice with basic percent calculations

Here is a video showing some example of tax, tip, discount

Here is some practice with word problems & answers