Nicola’s mathematics
Let me introduce you to a family member, Nicola. Nicola is 8 years old and has not been to her local school since the lockdown started in March 2020.
From the 4th July, UK families have been able to create a bubble with another family bubble and this has allowed me to work with her on a near daily basis.
I thought it might be useful for others to see our journey, what works and what doesn’t. If you find this content helpful, you will also be able to use any printed materials on this page for you to download and use.
My first day with Nicola was going to be a factfinding mission. I needed to know, what she already knew, what was iffy and what she hadn’t covered due to not being in school. I knew that Nicola’s confidence in mathematics was quite low. A typical little girl who loves reading and writing.
Here are my factfinding steps

Track back to the previous year group, in Nicola’s case, Year 2.Print out the NC for number which includes place value, addition, subtraction, multiplication and division.

What equipment was Nicola comfortable with?Which bits could she use comfortably, and which bits were completely new (but useful)?

Would she enjoy some sort of problem solving?Where should I start? Problem solving is tricky stuff, if mathematics isn’t your favourite subject.
Week 1
I knew that Nicola would have been using numbers up to 1000 but thought I’d go in on the first day and use twodigit numbers.
I wanted to know whether Nicola could build a number? Did she know what I meant by this? Would she be comfortable using different numbers and different quantities of 1s and 10s?
I thought I’d give her simple activities such as counting on and back in 1s or 10s from any given twodigit number and if I felt she could, we would move into the early hundreds.
I’d then looked into assessing her addition and subtraction strategies.
Activities from the first week
I took along a kit of resources.

place value dice

place value arrow cards

digit cards

Numicon and a Numicon 10s number line

base 10 equipment

bundles of straws in groups of 10

place value counters

place value abacus (which only holds 9 beads per spike)

multipositional cubes, such as snap cubes and multilink

and an A4 workbook from a wellknown online retailer, with squared paper inside to work on.
My favourite resource is a set of place value dice.
Place value: Build a number
I found that Nicola already had a good understanding of proportionality, however, I still made her build numbers using the base 10 equipment, Numicon and straws. She was very confident using the base 10 equipment as her school had this resource in her class. She knew what Numicon was, as I would use this with her from time to time in the past but this was the first time we had used it in a more structured learning time. The straws were yet another representation, but I quickly found out that had a preference for the other proportional resources, so I removed them from my kit (for now). Being Year 3, I was wary of using place value counters with her in the first instance, but since she understood proportionality, and it was now her preferred resource, we used them most of the week. Here is a snap of three resources in play.
Nicola was asked to….

Roll the dice

Say what number had been rolled

Build it using arrow cards

Build it using resources, in this case place value counters
After the first lesson, I extended this work to.

Roll the dice

Say what number has been rolled

Add 1 to the number

Add 10 to the number

Build it using arrow cards

Build it using resources
I quickly found out that adding 10 to any number was difficult and she wasn’t able to instantly recall this, so we did the following activities.

count on 10 more fingers from the number rolled

using the tens number line and Numicon, add 10 more

used a Cuisenaire number line and rods to see what happened when 10 was added.
We then extended all the above to adding 10, 10 more and 10 again. Could she see a pattern? What was the same and what was different? For example, which digit changed? Which digit didn’t change?
Some things you just can’t hurry, and this step for Nicola took a little while to embed.
Now she is confident, lessons start with rolling three place value dice and asking…

What number have you rolled?

Add 1 to it, what number do you have now?

Add 10 to it, what number do you have now?

Add 100 to it, what number do you have now?

Subtract 1 from it, what number do you have now?

Subtract 10 from it, what number do you have now?

Subtract 100 from it, what number do you have now?
During this time, we also looked at

using a number track and semistructured number line

placing numbers correctly on a number line

comparing numbers but building both with mathematical resources and using < or > correctly.

comparing numbers using number cards and < or > correctly
Problem solving
So where do you start with someone who hasn’t had any formal teaching for many months with problem solving? I love problem solving and reasoning, it’s the best bit of mathematics for me. Learning to add is just a skill but using your skills to solve problems, that’s mathematics!
I decided to give Nicola some problems that I would pitch to good Year 1 children.
This first problem is called birthday presents. Nicola read the problem, then read it again, put her pencil down and looked at me. It was obvious that she did not know where to start. So, I pulled out some coloured cubes and we built a picture of the problem until she could solve it.
The following day, I went back with a similar problem.
This poses a similar question but this time we know the number of presents but not the age. This gave us the opportunity to explore patterns, add numbers together quickly and predict the number of presents or the age of Lucy.
Here are two more problems I used with Nicola.
When solving Bucket and beanbags, we looked at how we could find every possible combination. I showed her how to be systematic and I was delighted when she used a systematic approach without being prompted with the digit card problem Between 30 and 40.
Planning
I had my suspicions Nicola’s skills in addition would be relatively good and her subtraction much weaker. This was the case. So, my plan was to continue with building her confidence with number, increasing the size of numbers up to 1000. In every lesson there was some problem solving, still aimed below her year group, again building her confidence and providing her with a much needed problem solving toolkit. A focus on addition would be more appropriate the following week.
Resources used this week
Birthday presents click here
Bucket and beanbags click here
Arrow cards: published by AutopressEducation.co.uk
Maths link cubes: Learning Resources
Place value counters 2.5 cm diameter: Inspirational Classrooms 3108403 Amazon shop