Division of Fractions by Whole Numbers and Fractions by Fractions

Before the Christmas break we were learning how to divide fractions by whole numbers (and by extension, divide fractions by fractions). I've always found that is much easier to teach this using models so that the kids understand the concepts before applying any rules or algorithms. Students and even teachers (some anyway) are familiar with using "Keep Change Flip" as a procedural method used to solve division with fractions, but don't truly understand why it works. As follows:

Given the following problem: Mr. E has ½ a bar of hersheys chocolate. He wants to split it equally between his three friends. How much chocolate will each friend get?

Chocolate bar before dividing equally between 3 friends (½)

 

Chocolate bar after dividing it equally between 3 friends (⅙)

Therefore:

From there, students develop the understanding that dividing is the same thing as multiplying by the reciprocal (For example: ½ ÷ 3 = ⅙, and can also be written as ½ × ⅓  which also equals ⅙).

Knowing that division is the same as multiplying by the reciprocal, you can easily divide fractions by fractions.

Example:  ½ ÷ ⅙ can be written as ½ ×  6/1 which = 6/2 which = 3.

Lastly, this also applies to whole numbers. Example:  
12 ÷ 4 = 3 
12 × 1/4 = 12/4 = 3


Wait!
If you have time, watch the video below of a student that has difficulty with the model (mainly due to a lack of conceptual knowledge of division) and my attempt (which I don't think was that great) at helping her solve the problem!

P.S. - Division of fractions by fractions can be modeled using fraction strips. I made a post prior to this where students were using them to solve word problems. It can be found here: Dividing Fractions by Fractions - Fraction Strips

GCF Word Problems

It has been such a while since I've made a post! My nephews were victims of a major car accident days ago and are currently recovering.  I am also sick with the flu and wasn't able to teach yesterday.

We've been going over GCF word problems in class! Today I had students look at the following task from Illustrative Mathematics: Bake Sale Task


The idea is for students to gain the understanding that the cookies can be arranged into different numbers of bags based on the factors of the total number of cookies. Example:

48 Chocolate Chip Cookies can be arranged in the following ways:

 

Later students develop an understanding that if they are to arrange the vanilla wafers and the chocolate chip cookies into bags with the same amount of cookies in each bag and none left over, that the only way to do so would be by using common factors of 48 and 64.

Homework - Tape Diagrams and Equivalent Ratios - 10/5/2016

We've been using tape diagrams to visualize equivalent ratios. The homework for October 5th has us demonstrate how we can use tape diagrams to show that two ratios are equivalent as well as solve ratio word problems.

The video below should help with the problem set for tonight's homework. As usual, if you have any questions leave a comment and I will get back to you as soon as possible!

Homework/Classwork - Equivalent Ratios and Tape Diagrams

Last week we used tape diagrams to learn about equivalent ratios and solve word problems. Tape diagrams are a great way to visualize ratio relationships. Last week's classwork is an example of how we can use a tape diagram to represent and solve a problem.

The videos below should help with what we've been covering in class recently!  If you have any questions please feel free to leave a comment and I'll get back as soon as possible!

Classwork - Tape Diagrams and Equivalent Ratios

Last week we used tape diagrams to learn about equivalent ratios and solve word problems. Tape diagrams are a great way to visualize ratio relationships. Below is an example of how we can use a tape diagram to represent and solve a problem.

Example: The ratio of the number of shoes Mr. E has to the number of sneakers Mr. E has is 5:2

If Mr. E has 25 shoes, how many sneakers does he have?

The five tapes represent the number of shoes Mr. E has. If we divide (25 ÷ 5)  then we know that each tape represents 5 shoes.

Now we can find out the number of sneakers Mr. E has, which is 10. Mr. E has 10 sneakers.

Homework - September 26th - Ratios

Today we learned about ratios in class. Ratios are a comparison between two (or more) quantities. For example, if I wanted to write the ratio of the number of shoes I have to the number of sneakers I have, I would write the ratio 5:2, because I own 5 pairs of shoes and 2 pairs of sneakers. There are two other ways we can represent ratios. We  can also write ratios as a fraction (5/2), or we can just write it out (5 to 2).

We can also represent ratios using a drawing. We call this a Tape Diagram.

The video below will help you with tonight's homework (9/26/2016). If you have any questions please feel free to leave a comment and I'll get back as soon as possible!

Homework - SOLVE - September 21st (Step V/E)

Today we spent some more time with step V and E of solve. Remember that SOLVE is a set of problem solving steps that make it easier for us to solve challenging word problems. If you need to review the first two steps (S and O), click here.

Today we went over Steps V and E in class:

Step V (Verify your plan with action) -
Estimate your answer.
Carry out your plan.



We want to estimate what the answer might be so when we finally solve the problem, our answer should be reasonable (that is, it should be close to the estimate)

Step E (Examine your results) -
Compare your answer to the question
Compare your answer to the estimate
Is your answer accurate? 
Write your answer in a complete sentence

In step E of solve we compare our answer to the estimate to see if our answer is reasonable, and we also check our work (we can use the opposite or inverse operations) to see if our answer is accurate. Lastly, we answer the question in a full complete sentence.

The following videos should help with the homework for September 21st. If you have any questions, please leave a comment and I will reply as soon as possible!

Homework - SOLVE - September 16th

Today we spent a little more time covering the third step of the S.O.L.V.E. method, Step L. Remember that SOLVE is a set of problem solving steps that make it easier for us to solve challenging word problems. If you need to review the first two steps (S and O), click here.

Today we went over Step L in class:

Step L (Line up a Plan) -
Writing a plan in words with no numbers.
Choose an operation or operations.

The reason why we write a plan in words with no numbers is because doing this helps us focus on what the numbers in a word problem represent. In other words, when writing a plan, instead of using numbers, we use what the numbers stand for. 

The following videos should help with the homework for September 16th. If you have any questions, please leave a comment and I will reply as soon as possible!

Homework - Solve Step L

Today we went over the third step of the S.O.L.V.E. Method in class, Step L. Remember that SOLVE is a set of problem solving steps that make it easier for us to solve challenging word problems. If you need to review the first two steps (S and O), click here.

Today we went over Step L in class:

Step L (Line up a Plan) -
Writing a plan in words with no numbers.
Choose an operation or operations.

The reason why we write a plan in words with no numbers is because doing this helps us focus on what the numbers in a word problem represent. In other words, when writing a plan, instead of using numbers, we use what the numbers stand for. 

The following videos should help with the homework for 9/14 ~ 9/15. If you have any questions, please leave a comment and I will reply as soon as possible!

Homework - Solve Step S and Step O

We have been going over the first two steps of the S.O.L.V.E. Method in class. SOLVE is a set of problem solving steps that make it easier for us to solve challenging word problems. We have gone over the following two steps in class:

Step S (Study the Problem) -
- Underlining the question
- Restate what the problem is asking you to find (Do NOT re-write the question, but restate the question in your own words)
              
Step O (Organize the Facts) -
- Identifying the facts (placing a marker after each fact)
- Eliminating the unimportant facts (crossing out facts that do not help us solve the question)
- Listing the important facts (listing facts that are important to solving the question)


The following video should help with the homework for 9/13 ~ 9/14. If you have any questions, please leave a comment and I will reply as soon as possible!

Homework Help #1 - Finding the Unit Rate

Homework Help #1 - Finding the Unit Rate
(note: the top of the sheet should say "unit rate" not "unit price")

Homework Help

The Homework Help page is intended to be a guide for students to complete specific homeworks, and also a resource for students to re-visit prior topics covered in class. It features specific homework monitors that I go through homework with at the end of the day.

There are different homework monitors from each class, so different students will be featured on different homework help posts. Please understand that there is simply not enough time to make videos and update this section daily. Try to check it once a week towards the end of the week or weekend.

Going Back: Negative and Positive Integers I Homework Discussion

Use the tutorial video above to help you complete the homework! Use the comment section below to discuss any challenges, strategies or questions you have for today's homework!

Going Back: Positive and Negative Integers II Homework Discussion

Use the tutorial video above to help you complete the homework! Use the comment section below to discuss any challenges, strategies or questions you have for today's homework!

Stem and Leaf Plots - Homework Discussion

Use the tutorial video above to help you complete the homework! Use the comment section below to discuss any challenges, strategies or questions you have for today's homework!