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 tutoring Primary School pupils. Maths is one of the subjects I am asked to boost. Don’t worry, nothing as complicated as BitmoAnnie is doing above!
This blog post follows on from the introductory #TallTartanTells About Tutoring. I am continuing to share tips from my 30 years in the classroom teaching 5 – 11 year olds.
Who is this blog for?
As a proofreader and retired teacher, I aim my services at educational publishers. Proofreaders are asked to proofread not only English reading and writing texts for publishers, but also materials in Maths and Science, the other core subjects. In the latter cases, the ability to check that answer books are correct and marking schemes match is a definite advantage.
It is also for other ex-teacher freelancers who are considering supplementing their editing/proofreading income by adding tutoring to their portfolio of jobs. Many of the newbie editing freelancers I have come across are already doing 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.
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)
- 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. Furthermore, 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: 4 lots of 3; 4 sets of 3, 4 groups of 3, 4 times 3, 4 multiplied by 3.
Moving 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.) They 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.
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’, funnily enough. 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.)
So, on squared paper, set out the 3-digit number, 854, in the column values HTU, with two horizontal lines underneath as the place for 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?”
If children can explain how they got their answer using the correct terminology, then they have a secure concept of the method.
A common error is to forget to add on the carried digits, so I often 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 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 the Maths methods 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 (I knew it 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 doing tutoring … what are you waiting for?
Finally … positive feedback … makes it all worth it. 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.” 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.
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/resources/51240 – this podcast is one of a number of excellent resources from the National Centre for Excellence in the Teaching of Maths (NCETM) which supports Maths across all school and college phases.
- https://whiterosemaths.com/ – This month White Rose Maths are running #Barvember. This to encourage everyone to use the bar model. They believe that the Bar Model is a useful tool for helping children visualise and then solve maths problems. Even some of the most complex problems can be seen much easier when represented visually.