## Strengthening a Year 6 decimals lesson

This example is from *Maths — No Problem! Textbook 6A, Chapter 4, Lesson 9*, and covers multiplying decimals. The objective of this lesson is ‘learners can multiply one-digit numbers with up to two decimal places by one-digit whole numbers, with regrouping’.

To begin the lesson, I started my class off with the In Focus task (or anchor task).

Most of my learners tackled the problem systematically, for example, starting with ×9, then ×3 and finally ×2.

You can see the final 18 results below. It’s also worth having a quick discussion about whether there are actually 19 answers if you include all the combinations that multiply to zero.

Instead of moving straight to Guided Practice, I gathered the class together and asked: **“Take a look at the set of data, what other questions could you ask?”**

My class came up with a list which ranged from the obvious to the more challenging. After writing the questions on the board, we discussed which questions might be harder so learners could decide, in their pairs or threes, the level of challenge they wanted. My learners then completed the answer in their journals.

Here are the journal entries from the lesson:

### Question #1: What is the total?

This seemingly straightforward question lets learners review adding decimals. The first example shows a confident learner who added up the three groups with clear working. They then combined the three totals to work out the final, overall total.

The next example shows a learner working carefully, but it’s clear they’re not as confident in their adding. They’ve added one decimal at a time to gather a running total. When two of their totals didn’t match other groups, they checked back through to find that they had made a mistake on the first sum.

### Question #2: What is the highest and lowest product? What is the range?

Finding the range is a straightforward calculation that can be done mentally or by using a written method. Here the learner found the biggest and smallest number and found the difference using a written method.

### Question #3: Write the decimals in ascending and descending order

Reading decimals and their place value should be within reach of most learners. By writing an ascending or descending list, children soon spotted they could copy it out in reverse! The class discussed whether writing the decimals in ascending order might be slightly easier because we generally learn to count up with numbers.

### Question #4: Investigate how rounding affects the total

This question is an excellent example of an advanced learner going one step further. Having found the totals of the decimals, they rounded each decimal to the nearest whole number and added them up.

The learner then asked, “did the sum of the whole numbers match the total if you added all the decimals and then rounded the answer?” Then they reasoned why the answers were (slightly) different.

*The reason that this answer is different from what the other answer would be rounded is because more numbers were rounded up here than in the other answers.*

### Question #5: Find the mean

Finding the mean meant remembering how to do this from Year 5 work. With a ‘no calculator’ rule, this involved quite a hard division sum. Learners worked it out and explained how in the example below.

*I found this by adding all of the products up and then dividing it by the amount of products there is, in this case the sum is 226.44 ÷ 18 = 12.58*

### Question #6: What if the question involved tenths instead of hundredths?

What would happen if you moved the decimal point, so you are looking for tenths rather than hundredths? There are still 18 combinations, but there’s a greater range to investigate once you’ve got all the totals.

### Question #7: What if you were adding instead of multiplying?

The learners chose whether to add the number to the whole or the hundredth. They soon found that the difficulty level was low as there’s no renaming.

### Question #8: Can you convert the products to fractions?

This question gave learners that chance to revisit concepts from the previous fractions chapter, including simplifying to the lowest form.

### Question #9: Find the median

This is one of the more challenging problems as there are two middle numbers with a gap between 0.90. This learner worked through the problem and wrote an explanation for others to follow.

*The middle number is 8.25, because the number of numbers is 18, and 18 doesn’t have a middle number. You have to find the 8th and 9th [correction to 9th and 10th], find the difference, half it and add it on to the 8th [correction to 9th] number.*