Research School Network: How to Plan a Think Aloud in Maths: Worked Examples Two examples to support teacher modelling and explanation
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How to Plan a Think Aloud in Maths: Worked Examples
Two examples to support teacher modelling and explanation
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by Bradford Research School
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Jennifer Green
Dixons Academies Trust
Jennifer is a mathematics specialist and Trust Assistant Principal. She is passionate about evidence-based teaching strategies and improving life chances for disadvantaged students.
In my last blog, I shared a framework for planning an effective ‘Think Aloud’:
1. Define Your Learning Objective 2. Select an Appropriate Task 3. Script Your Thinking 4. Integrate Questions and Prompts 5. Engage Students in the Process 6. Reflect and Adapt
In this follow-up, I’ll share some scripted Think Alouds for different maths problems to help bring the framework from my previous post to life. I have provided some questions for reflection at the end
Example 1: Decreasing by a percentage
Question:
A shop is offering a 25% discount on an item originally priced at £80. What is the final price after the discount?
First, I’ll carefully read the entire problem to fully grasp what it’s asking. I notice that the original price is £80 and the discount is 25%. The question is asking me to find the price after the discount. If something has had a discount, it has reduced in price.
Since percentages represent parts of a whole, I need to consider what 25% actually means. A whole can be represented by 100%. So, this means 25% is equivalent to 25 out of 100, or if I simplify this, one-quarter.
A discount of 25% means I am reducing the original price by 25%. If I know that 25% is the same as one-quarter, I can also say that I am reducing the original price by one-quarter. This tells me I will be removing, or I could say subtracting, a quarter of the original price from the total amount.
Finding a quarter is the same as dividing by 4, so I’ll divide £80 by 4, which gives me £20.
Next, I’ll subtract the discount from the original price: £80 – £20 = £60.
To double-check, I could use another method: finding 10% of £80 (which is £8) and then multiplying by 2.5 to get 25% which is £20 again. The answer is consistent, so the final price after the discount is £60. By checking with two different approaches, I ensure my answer is accurate.
Can you now apply this approach to the next question?
Example 2: Comparing Fractions
Let’s walk through an example of a Think Aloud for teaching students how to compare fractions. Imagine you’re comparing 3/4 and 5/8:
Alright, I see two fractions: 3/4 and 5/8.
My goal is to figure out which one is larger.
To start with let’s think of fractions like pieces of a pizza. If one pizza is cut into four slices and another is cut into six slices, the slices are different sizes. You can’t fairly share your pizza between friends unless they are cut the same way.
Fractions are hard to compare if they are not out of the same amounts, if they do not have the same denominator. So to start with, I’ll check if the denominators are the same. They’re not, so I’ll need to find a common denominator. We can do this by finding the lowest common multiple of our denominators.
The lowest common multiple for 4 and 8 is 8. I’ll rewrite 3/4 as an equivalent fraction with a denominator of 8. To change 4 to 8 I multiply by 2 so I will do the same to the numerator to ensure my fraction is equivalent. That gives me 6/8. I know that 5/8 already has a denominator of 8 so I will leave that the same.
Before we continue, could we have used a different approach here to get a common denominator?
Now, I’ll compare: 6/8 is larger than 5/8 as it represents 6 out of 8 parts instead of only 5 parts. So, 3/4 is the bigger fraction.
Does this result make sense?
Let’s double-check by visualising these fractions pictorially.
Questions for reflection:
1. Did I break the problem down clearly so students can follow along easily? 2. Did I use accessible language and explain things in different ways to help everyone understand? 3. Did I give students a chance to get involved, like suggesting other methods or checking the answer? 4. Did my Think Aloud show helpful strategies that students can use on their own next time?
