• best teaching practices
• # Multiplying Fractions: Keeping the Skill in Context

I have found my students struggling to grasp the act of multiplying and dividing fractions conceptually. One suggestion would be to always keep it in context – I like to introduce and practice the skill by using word problems.

5th Grade TEKS related to Multiplication of Fractions
[Supporting Standard] 5.3I represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models

## The progression

– #1 Multiplication of fractions
1) Whole Number Multiplied by a Fraction (Combining Equal Groups of a Fractional Amount)
2) Fraction Multiplied by a Whole Number (Taking a Fractional Amount of a Whole Number)
3) Mix the two type of multiplication problems

## The Break Down

Here are some ways I helped my students “break it down” when applying the skills to word problems
– Combining (x)
2) Draw a model or picture representation
– Helps students strengthen conceptual understanding
– Supports the TEKS that deal with REPRESENTING the multiplication and division of fractions using models
– Shows student thinking and helps students justify their thinking
3) Answer the question in a complete sentence
– Forces students to reflect and makes sure they answered the initial question

## Activate Prior Knowledge

What is multiplication? Combining equal groups.

The commutative property makes the answer correct regardless of the type of multiplication problem, right? Yes, but taking the time to teach students the two different types of problems really makes the difference in their conceptual understanding – which then has an impact on their ability to successfully solving word problems.

# Two types of Multiplication problems

## Whole Number Multiplied by a Fraction (Combining Equal Groups of a Fractional Amount)

### Ms. Shim is running 2/3 of a mile every day. If she runs the same amount for 2 days, how many miles will she run in total?

This problem involves combining equal groups // Two equal groups of 2/3

Equation in words: We need to combine two equal groups of 2/3 to find the total number of miles she runs.

At first, I made my students merely write out the equation (example 2/3 x 2). However, I found that this didn’t help my students really dissect the word problem. What I found that helped was if I made my students write out the equation in their own words and identify the action.

Equation: 2 x 2/3
An extra step if deemed needed.

Model:

Area models and labeling is something I emphasize. This helps me see students thinking and students are able to use their models to prove their thinking.

Answer in a complete sentence: She will run a total of 1 and 1/3 of a mile.
This helps the student reflect. They are forced to go back and make sure they answered the initial question.

## Fraction Multiplied by a Whole Number (Taking a Fractional Amount of a Whole Number)

### Ms. Shim baked 12 cookies and is planning to give them to her friends. However, 1/4 of those cookies were burnt. How many cookies were burnt?

This problem involves taking part of a whole number

The whole number is the total number of cookies Ms. Shim made.
The part that is being taken is the 1/4 of the burnt cookies.

Equation in words: There’s a total of 12 cookies and four equal groups. We need to find how many cookies are burnt in one group.

Total of 12 cookies // Split the cookies in 4 groups because the denominator shows us how many equal groups there are // See how many burnt cookies are in 1 of the groups because of the numerator.

Equation: 1/4 x 12
Model:

Answer in a complete sentence: There are 3 cookies that are burnt.

Stay tuned for a blog post that explains how I teach my students the division of fractions!

• best teaching practices
• # Less than, Equal to, or More than ½

Now that students have had plenty of practice with comparing fractions to a half, this part is just building upon that same foundation! Hands On with Fraction Bars Building upon what students know, they are now ready to compare a fraction to a half! In order to help students understand this in a little more depth, […]

• best teaching practices
• # Making Half

Finding Half Using Fraction Bars Before diving into equivalent fractions, I have found that letting students explore by building ½ with fraction bars helps build a foundation for equivalent fractions. FREEBIE ACTIVITY CLICK HERE After this simple hands on activity, students will understand – The denominator needs to be an EVEN number in order to take half – There […]

• building conceptual understanding
• # Comparing Fractions with Common Denominators & Common Numerators

If students understand what a fraction is and have a good understanding of comparing unit fractions, comparing fractions with a common denominator and numerator will be a confidence booster! Check out these previous posts: Fractions Introduction Unit Fractions Like I’ve said in my previous post, first, I get students to practice by using fraction bars […]

• best teaching practices
• # Fractions Introduction

Start off with a quick conversation to activate prior knowledge *tip: have visual pictures available for students to see “Where and where do we use fractions in everyday life?” on the highway, music, shoe size, cooking, pizza, etc “What does ½ mean to you?” there are two total pieces and one is shaded “What does […]

• resources
• # Hedbanz Game

I love the recent hit activity Hedbanz. It is an activity that has been around for a while but it is now finding its way around the classrooms. This activity lends itself for great math conversations and engagement, for whichever concept that is being taught. For the concept of writing and solving equations with an […]

• best teaching practices
• # Decimal Investigation

Building a strong understanding of how our base ten system works is always so important. Taking the time to help students understand this will help with ‘regrouping’ when it comes to adding, subtracting, multiplying, and dividing – it’s worth the time! Ones – Tenths – Hundredths – Thousandths  One whole 1.00 One whole is […]