Multiplying fractions by whole numbers is an extension of a 4th grade common core standard. Students worked with models solve problems involving fractions and whole numbers last year. I spend time transitioning students' thinking by working with models at the beginning of this lesson. The purpose for this is three-fold. First, multiplying fractions by whole numbers is an important foundational piece of multiplying fractions. Second, connecting students with their prior learning experience allows for them to connect these pieces. I want to help the students make connections between concepts rather than learn each in isolation. Additionally, by starting the lesson with modeling, students who did not master this in fourth grade will experience additional tangible opportunities to work with manipulatives. All students benefit from deepening their understanding of a concept through hands on experiences.
For the launch, I move all students to the carpet. This way, when they are working with manipulatives I can more easily see how they manipulate the tools and they can also learning from seeing what their classmates do to model a situation.
To prepare for this lesson, I have interlocking cubes arranged in stacks of 10. I ask each student to take 30 cubes. While students model multiplication situations, I demonstrate the mathematical procedures using the white board.
At this time, I create examples to move student thinking from multiplication of whole numbers to multiplication of fractions.
• Show me 2 groups of 4
• Show me 4 groups of 5
• How can I represent groups of using a symbol or sign? (x)
Now, the stick of 10 represents a whole, not a ten...
• Show me 3 groups of 1/2.
• Show 1/2 groups of 3.
(It is important to show the students that there are multiple ways to represent this. You can have 3 groups of 5 cubes (because 5 is 1/2 of the whole that we started with) or you can take the three wholes and cut the whole group in 1/2 which would be 1 whole and a 1/2.)
• Show me 5 groups of 1/5
• Show me 1/5 of 5
Move away from unit fractions:
• Show me 1/5 of 10. This is shown with 2 cubes from each of the wholes (20 cubes) or taking the whole set of 10 rods and breaking that into 5ths.
• How can you model 2/5 of 10? (First, students have to determine 1/5 of 10. Second, students need to identify two fifths. (by putting 2 groups of 1/5 together).
Continue with examples like this 2/3 of 6. 3/4 of 8 and 5/6 of 12
Today, you can come back to using these manipulatives if they will help you. Next, we are going to use drawings to help solve problems involving multiplication of fractions and whole numbers. To do this, we are going to think about fundraising, have you ever had to raise money for something before?
Students move back to their seats for the guided practice part of this lesson. At this time students learn to use drawings to represent the models they were just practicing with. These drawings will help them solve problems when numbers are too large to use manipulatives.
I have selected 8 problems from the text book. The first 4 problems are in sets. First the students find the unit fraction of the whole number, then use that to find a different fraction of the same whole number.
For example: 1/7 of 14 then 3/7 of 14
The next four do not have the unit fraction as a scaffold.
For each problem, students use drawings to solve.
As we move through the process, encourage students to share new strategies they discover (moving away from the drawing to the procedure of dividing the whole by the denominator and then multiplying by the numerator). If students do not discover this on their own, I begin to add it into my modeling.
After these practice problems, I introduce the independent practice.
I post 5 fundraising thermometers on the board. Each is labeled with a goal at the top, and some fraction of the thermometer colored in. (BTW - there is an easy to use fund raising thermometer on line that you can use to enter units and quantities to generate a picture.)
The labels I include are:
• Sports Team Fundraiser ($240)
• Scouting Fundraiser ($48)
• The latest version of a new electronic device. What what you think your kids will be the ost excited about. I chose I Need a New iPad Fundraiser ($720)
• 6th grade Camp Bournedale Trip Fundraiser ($480)
Collectively, we spend a short time discussing these thermometers and interpreting them.
Students choose an area of interest, then move to a predetermined area of the room to work on solving problems related to their fundraising interest.
All students work on answering the same questions (with different numbers based on the group that they choose). At each group, there are five problems for students to work on. Collaboration is encouraged.
Toward the end of the independent practice time, students share their answers with on another, then I provide an answer key to help them settle any math arguments and help one anther find mistakes.
I will have a "challenge" prepared for students who complete work on time. This challenge will extend their thinking in multiple ways. Unlike the other problems, this one will not control for numbers that are an exact fit. Students will have to work with remainders. Also, this question will tell the students how much money has been raised. They will have to determine what fraction this represents. I will make this available for students to work on throughout the rest of the week.
Students answer the question:
Did you know a lion spends about 5/6 of the day sleeping? How many hours in a day does a lion sleep? How many in a week?
I collect the students' work and place them into intervention groups if needed. I will meet with students who need additional help during the morning meeting tomorrow.