I’ve said it before, and I’ll say it again … one of the things I love about my freelance business is the variety. As well as editing, I particularly enjoy teaching primary school pupils. Maths is one of the subjects I boost in tutoring. Don’t worry, nothing as complicated as BitmoAnnie is doing in the image!

This blog post follows on from my general blog post About Tutoring. In this post, I continue to share tips from the 30 years I spent in the classroom teaching 5 – 11 year olds.

### Who is this blog post for?

Proofreaders are asked to proofread not only educational reading and writing texts for publishers, but also materials in Maths and Science, the other core subjects. With the latter subjects, the ability to fact-check that answer books are correct, and marking schemes match, is a definite advantage and sought after skill.

This post is also for ex-teacher freelancers who are considering adding tutoring to their portfolio of jobs. Many of the newbie editing freelancers I have come across are already offering tuition. Indeed, it’s a no-brainer to apply our finely-honed skills to running a freelance tuition business, over which we have sole control.

### Maths lesson

Now here I describe how I tutor an hour’s Maths lesson. I enjoy using particular resources, described below, to encourage engagement and learning.

This Maths lesson is aimed at an average 8-year old in Year 4. It is divided into three parts: mental warm-up, written practice and reinforcement, finishing with a fun game to wind up the hour.

### Pre-requisites for this lesson:

- Mental number bonds to 20.
- Times tables knowledge of x2, x5, x10, x3, x4, x6, x8 (according to the National Curriculum 2014, children should know all times tables by Year 5). Notice I have listed them in the order they are taught from Year 1.
- Some division tables knowledge of ÷2, ÷5, ÷10, ÷3, ÷4.

### Resources for games:

- Wrap-ups (I’ll come to these in a moment)
- dice
- playing cards
- iPad or Android tablet device

### Mental starter (10 minutes)

Use mental maths strategies to add quickly and efficiently. The purpose of this is to settle into a focused frame of mind, and warm up the little grey cells. So, a speedy game of Snap with playing cards for hand/eye agility and coordination is a thrill.

Or throw two dice and add, or multiply, with speed. Extending this, throw three dice and add by finding the largest number first; or find two numbers which make ten; or near doubles.

My favourite starter is the Wrap-up.

Wrap-ups are available as all four operations (+ – x ÷) as well as fractions. The photo shows the times tables version of a Wrap-up.

Each key has a separate times table, with answers mixed up on the back, for self-checking. A string is wound matching the question to the answer, while saying the question out loud. For example, 4 x 3. The child winds the string around, matching the question to the answer.

I vary the vocabulary used to ask the question: 4 lots of 3; 4 sets of 3, 4 groups of 3, 4 times 3, 4 multiplied by 3.

Rotating the string round and round, at the same time as vocalising the question, is known as the VAK approach – visual, auditory, kinaesthetic. The child uses the strategy they feel best suits their learning. It is especially appropriate for children who can’t keep still as they learn. (One of my tutee clients has ADHD.) Wrap-ups are available from this website.

### Main session (30 minutes)

Written short multiplication method**: **carry out multiplication calculations using the following as an example, 854 x 4.

### Vocabulary

It is vital to use the correct vocabulary when describing a strategy. Children tend to use the word ‘sum’ to describe any operation involving numbers! ‘Sum’ describes addition only – it means ‘total’. The answer to a multiplication question is the ‘product’. So, we could re-write the above question as: “What is the product of 854 and 4?” (This extends the question level to Year 5, as the word ‘and’ confuses the concept; a common error is for children to read the question as addition.)

### Method

On squared paper, set out the 3-digit number, 854, (with one digit in one square) in the column values HTU, drawing two horizontal lines underneath as the place to write the answer. It astonishes children that the = sign means the same as those longer lines in a written strategy.

It’s hard to describe the method here, but I’ll have a go. Set out x4 underneath with the 4 in the Units or Ones column. Multiply 4 by the 4 Ones, making 16. Write 6 Ones in the space for the Ones answer, and ‘carry’ the 1 Ten into the Tens column. Multiply 4 by the 5 Tens. This equals 20, then add on the carried Ten to make 21 Tens. One Ten stays in the Tens column, and ‘carry’ the 20 Tens into the next column as 2 Hundreds. Multiply 4 by the 8 Hundreds to make 32 Hundreds, then add the carried 2 to make 34 Hundreds. The completed answer is 3,416.

Linking the calculation to a real-life problem gives the answer more context: “If four people each made £854 in one month, how much was earned altogether?”

### Mastery

If children can explain how they got their answer using the correct terminology, then it shows they have a secure concept of the method.

A common error is to forget to add on the carried digits, so I reinforce this aspect repeatedly. More able mathematicians can check the answer by using the inverse operation, division. Skills can be extended by multiplying ThHTU by a single digit.

One of the most common parental comments is that methods have changed since they were at school. So they feel it’s hard for them to help their children. Ask your child’s teacher for clarification. Some schools produce a handy leaflet for parents with how the Maths methods are taught.

### Lesson plenary (10 minutes)

My pupils love using a Maths app on my Android tablet to round up the session and relax. These include *Card Match*, *Solitaire* (which I knew as *Patience* when I was young), and *Countdown*. They often beat me, too.

### Why I tutor … part 2

Having been a classroom teacher, with many conflicting demands on time, you find that, simply, there are not enough hours in the day to spend quality 1-1 time with each child. Improving reading skills is probably the highest priority.

I find doing private tuition much more rewarding: I can choose the resources I want to use; planning for one child takes so much less time than for a class; children feel more relaxed to ask questions when there are just two of you. If you’re thinking about tutoring … what are you waiting for?

### Feedback

Finally … positive feedback … makes it all worthwhile. Here is a comment from the parents of a 6 year old boy: *“Annie is a fun, calm, creative and experienced tutor who immediately put my son at ease. He looks forward to her lessons and loves her ideas and games. We would definitely recommend her.”* Really chuffed!

Read on to the end to find links to Primary Maths websites I have found useful for resources. Let me know if you are a tutor and share resources you find useful.

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** **Kindly proofread by Lisa de Caux, SfEP Intermediate Level Member, https://www.ldceditorial.co.uk

### Useful Primary Maths website resources:

- https://www.ncetm.org.uk/ – This is an excellent resource from the National Centre for Excellence in the Teaching of Maths (NCETM) which supports Maths across all school and college phases.
- https://whiterosemaths.com/ – White Rose Maths

### Teacher bloggers

- www.mrspteach.com/ – primary teacher and Deputy Head, Jo Payne. Pearson Teaching Awards winner for use of IT.
- www.teachertoolkit.co.uk/blog – known as Ross Morrison McGill, the most followed secondary teacher on social media and top UK blogger of 2018.