How To Multiply Fractions

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How To Multiply Fractions – Building blocks, tiles, playing cards, counters, floorboards, measuring tapes, and thousands of 1-inch plastic tiles. Young and eager, jumping first with balance. My students have used almost every scale under the sun…except pattern blocks.

As a tool for teaching fractions, these modeling blocks will be more useful (and my students will understand fractions better!).

How To Multiply Fractions

Model blocks are now my absolute favorite way to teach all fraction concepts. What makes them powerful is that students rely on their understanding of fractions as relationships

Multiply Fractions Printable Resource Pack

. Also, having different shapes helps students see how some parts actually fit together. Since there are no turning marks on the piece, the possibilities are endless in how you use the design blocks!

While I now use the block system to teach all fraction concepts, my favorite concept to teach with Design Blocks is multiplying fractions. Algorithms for multiplying fractions seem easy, tempting students to “shortcut” and skip concept building. understand

Building Blocks can be a difficult concept to do hands-on, but Building Blocks makes it easy (and a lot of fun!) Let’s walk through some example problems so you can bring this powerful activity into the classroom!

Before we get into how to teach multiple fractions with modeling blocks, make sure you (and your students!) are clear about what each fraction represents. While you can make each area represent the whole, I often use a hexagon for the whole.

Ks3. Number. 10. Multiplying & Dividing Fractions

Another important thing to note about modeling blocks is that you will be limited to the number of halves, thirds, and sixths for the problems you create! They make a fourth and twelfth add-on pattern block if you want more blocks than the six you already have!

Now that you know the value of each modeling block, let’s dive into how students can use modeling blocks to model all kinds of different fractional and numerical development problems.

Considerable progress has been made in how fractional optimization problems should be formulated. The first step in the progression is multiplication or multiplication as equal groups.

Multiplication is easier to understand for students who see multiplication as multiple units because it follows the same line of thinking as whole numbers. It is not a big leap for students to go from understanding 2 groups of 3 (2 x 3) to understanding 2 groups of ⅔ (2 x ⅔).

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Multiplying Fractions Using A Visual/number Line

However, it will take several chances before students discover the algorithm for multiplying a whole number by a fraction. (And they

Stella ate 3 bags of dog food last week. If each bag contains one pound of dog food, how many pounds did Stella’s dog eat?

On the math mat, students will form three groups of ⅔. They can call it 6/3, or rearrange the whole piece to see that the answer is both. Stella the dog ate 2 kilos of dog food last week.

Multigroup problems may also involve mixed numbers as factors, such as 3 groups of 1 ½. As long as the multiplier (the number of units) is a whole number, this last problem will occur exactly as it did. See the diagram below for how to design a 3 x 1 ½ with pattern blocks.

Multiplying Fractions Using A Number Line Or Graphic

The states’ position stops here (of course, check your position to be sure!) For fifth graders, however, they need to understand a different type of problem.

The goal of this stage in the development of multiplication is for students to begin to see the form of multiplication

This is when they learn that improvisation can lead to a small product, which means we have to give students a chance to create that idea, or it can feel confusing and weird!

Stella the dog ate a bag of dog food last week. If each bag contains 3 pounds of dog food, how many pounds did Stella’s dog eat?

How To Teach Multiplying Fractions With Pattern Blocks — Mix And Math

Although the scale of this problem is the same as the previous problem (⅔ x 3 vs. 3 x ⅔), its design feels very different. In this case, students should understand that they are getting ⅔ of a group of 3. Another way of saying this is ⅔ of 3.

For the product ⅔ of 3, students will start with the sum of 3 and then need to figure out how to divide it into thirds (or equal groups of three). They will see that they need to put one whole in each of the three parts. We want to know what 3 of ⅔ is, we know the answer will include two of the three, that is, both because each of the three has one. See the image below for how to do this.

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Let’s take this set of ideas a little further by looking at how fractions are created by fractions.

Another group of problems are partial problems. Again, let’s use our real world context to help understand what this means.

Here’s A Multiplying Fractions Game That’s Perfect For Extra Practice

Stella the dog ate ⅔ of the dog food bag. If each bag contains ½ pound of dog food, how many pounds of dog food did Stella eat?

Instead of finding one part of a group, this situation requires finding the part of another… What is ⅔ of ½ pound of food? In order to model this, they will need to exchange something to help implement it. We know that a trapezoid (1 half) equals 3 triangles (or 3 sixths), which means students can trade a trapezoid for 3 triangles. This will help us when we try to figure out what ⅔ of half is.

To help students understand that two-thirds of a half is two-sixths, look at the diagram below to show students how to place a sixth in each third.

The final step in this development to develop parts is the entertainment part. Now students are challenged to apply what they have learned!

Multiply Fractions Digital & Printable Resource Pack

The final step in the development of the understanding of real fractions is the integration of multiple groups and groups of fractions. This means that the multiplier (the number of groups) is a mixed number, forcing students to think about the exact number of groups.

Stella the dog ate 2⅓ dog treats last month. If each bag contains 4 pounds of dog food, how many pounds did Stella’s dog eat?

In this condition, dog Stella ate 2 bags of food (2 x 4 pounds—multiple groups) and ⅓ bags of food (⅓ x 4 pounds—partial groups). Students must combine their understanding of both types of fractions to successfully solve this problem.

After adding 2 groups of 4 and ⅓ of 4, you will see that Stella’s dog ate a total of 9 ⅓ pounds of dog food.

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Multiply Fractions By Whole Numbers Worksheet

Stella ate 2⅓ bags of dog food. If each bag contains ½ pound of dog food, how many pounds of dog food did Stella eat?

In this case, Stella’s dog won two groups of ½ pound (multiple groups) and ½ of ½ (one portion). In the picture below you can see that when it was all added up, Stella’s dog ate 1 ⅙ pounds of dog food.

In the last problem we’ll look at in this post, students solve a fractional multiplication problem involving a mixed number by a mixed number.

Stella the dog ate 2 and a half dog treats last week. If each bag contains 2 ⅓ pounds of dog food, how many pounds did Stella’s dog eat?

How To Multiply Fractions: Step By Step Guide

In this problem there are 2 ½ groups of 2 ⅓, which are complete groups of 2 ⅓ (multiple groups) and groups of 2 ⅓ (partial groups). Because students are expected to have a lot of experience with multiple groups and interesting groups before this problem, this process is feasible for students (although it may stretch their imaginations!).

I hope you see now that the game changing blocks are for multiplying fractions. While it may seem inefficient for students to spend all that time modeling and developing algorithms, the hard work will pay off in the end when students understand the basic functions and logic of algorithms!

If you’re like me and don’t know what to do with those modeling blocks in fourth and fifth grade, it’s time to dust them off. You’re missing out on one of the most powerful tools for building students’ understanding of fractions! Welcome to this free lesson guide where you will easily learn two steps to multiply fractions by whole numbers and multiply whole numbers by fractions.

This complete guide to multiplying fractions and whole numbers includes lots of examples, a short animated video lesson, and a free worksheet and answer key.

Making Sense Of Invert And Multiply

Before we explore how to multiply fractions, let’s quickly review how to multiply fractions and fractions (understand how to use the rules below.

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