Mrs. Davis' 4th Grade Math and Science All Stars!!!: January 2015

Throughout this unit, students learned how to multiply fractions by whole numbers as well as multiply whole numbers by mixed numbers. Below you will find strategies that your child learned throughout this unit as well as some sample problems. Students were able to apply many of the same strategies that they already knew from being able to multiply a whole # by a whole #.

Strategies for Multiplying a Whole Number By a Fraction

Sample Problem:

This student solved this problem with a model.

This student used repeated addition.

Strategies for Multiplying a Whole Number by a Mixed Number

Sample Problem:

Example of student using a model:

Example of student using repeated addition:

Example of student using the distributive property:

Another Sample Problem:

Writing Fractions as a Product of a Whole Number and a Unit Fraction

Monday 1/5-

Lesson: When Can You Add and Subtract Fractions?

(The purpose of this lesson was for students to understand that you can only add and subtract fractions if the wholes of those fractions are the same size.)

We began this lesson with the Problem of the Day. Please keep in mind that before this lesson students did not have experience with adding and subtracting fractions.

Since students had not had experience with adding and subtracting fractions, I was expecting some misconceptions. As you can see below, this student knew from the context of the problem that they were adding the fractions, but they added both the numerator and denominator to get the answer 4/ 12.

Since there were other students that had this misconception, we had an interesting class discussion. It is amazing to hear all the student's ideas! As a class, we concluded that although we agree that we are adding the pieces together, those pieces are still called sixths, they did not change to twelfths. We are taking the one sixth from the one tray and combining with the other three sixths, which would be 4/6 total.

Below is a correct response. You can see that this student's model shows them combining the 3/6 with the 1/6 to have 4/6 in all.

We then discussed the following questions and looked in depth at #4. We talked about how you could not still say that we had 4/6 in all because the wholes are different sizes, therefore the pieces (the sixths) would be different sizes. The emphasis was that we can only add fractions if the wholes are the same size!

Below we built on the problem of the day to explore subtracting fractions.

Below you can see this student's model shows were they started with the 4/6 and subtracted 2/6 since she ate 2 pieces and then there were 2/6 left.

We continued this lesson with students using models to add and subtract fractions.

Tuesday 1/6

How Can You Decompose a Fraction?

During this lesson, we were exploring all of the ways that we can break apart fractions. Below is an example of all of the ways to break apart 4/6.

We began the lesson with this problem below.

Below is a student's response showing how they broke up the 6 slices onto 2 dishes.

We then charted this as a class.

Wednesday 1/7

What Generalization or Rule Can You Make About Adding And Subtracting Fractions with the Same Denominators?

I didn't take any pictures of this lesson. However, the purpose of this lesson was for student's to understand that when adding or subtracting fractions with the same denominator, you can just add or subtract the numerators and the denominator stays the same. Example: 2/8 + 3/8 = 5/8. We had a lot of discussion using models about why this works.

Thursday 1/8

How Can You Rename Fractions Greater than 1 and Mixed Numbers?

We began this lesson by reviewing what a mixed number is and what a fraction greater than 1 is. See anchor charts below.

You can see an example of how you could rename the mixed number

(2 5/6) as a fraction greater than 1 (17/6).

Below is an example how you could rename the fraction greater than 1 (16/3) as a mixed number (5 1/3).

Students began the lesson by solving these 2 problems.

Then we did a mix-pair-share activity were each student was given a card with either a fraction model, mixed number, or fraction greater 1 and they had to pair up with their match. See pics below!!