Two Step Number Bonds Problems {Living Maths}

When the girls reached a solid understanding of their number bonds, I found myself asking an important question: what comes next? Knowing number bonds is foundational, but understanding how to apply them is where real mathematical confidence is built. Could they apply this knowledge to two step number bonds problems?

To explore this, I pulled a handful of problems from a Year 6 curriculum to see whether the girls could transfer what they’d learned into work expected for their age. This wasn’t about pushing them ahead for the sake of it. It was about checking whether our approach to homeschool maths — one rooted in understanding rather than repetition — was actually working.

Why Curriculum Still Matters (Even When You Don’t Follow One)

Before moving away from a curriculum-based maths approach, Gary and I thought long and hard about it. We talked it through not only with each other, but with the girls themselves. One of the biggest advantages of homeschooling is the freedom to teach children where they are, not where a scheme of work says they should be.

If my only aim was “life maths”, then memorising timetables or racing through worksheets wouldn’t matter. It honestly wouldn’t bother me whether they took GCSE maths at 14 or at 24. But I do care deeply about choice.

I never want a lack of qualifications to become a stumbling block later in life, for example, discovering that a maths GCSE is required for a course they’re excited about. So while we no longer teach from a curriculum, I still refer to one occasionally as a sense check, making sure what we’re learning will translate into exam success if and when it’s needed.

What I don’t believe in anymore is sitting children down to complete 30+ sums a day. These days, I’ll give one or two carefully chosen problems, just enough to check understanding. Maths is cumulative; practice in old areas happens naturally as new concepts are layered on.

This is the heart of living maths: meaningful learning, not endless repetition.

Applying Number Bonds Through Two-Step Problems

After skimming the Year 6 papers, I set the girls the basic one-step problems first. There were only a few, and they handled them easily. So I moved on to slightly trickier questions, those that were worded differently or involved two step number bond questions.

C10 flew through these independently, so I gave her an occasional extra problem to keep her occupied while her sister worked more slowly. I set just one problem per day, always alongside number bond games and hands on maths activities.

Some examples included:

• Multi-step “make a whole and split into parts” problems
  One question asked how many apples would be left after two days. C10 solved it confidently, clearly visualising the whole and its parts.
• Difference problemsA 120cm stick is cut into two pieces so that one piece is 30cm longer than the other. How long is each piece?
• Bank balance problemsClaire has £2.50. Claire’s and Mike’s balances add up to £31. How much does Mike have?

These posed no difficulty at all.

When Confidence Wobbles (and Why That Matters)

One problem changed the tone entirely:

A 240cm length of wire is cut into three pieces. The shortest and longest pieces are each 20cm shorter or longer than the third piece. What is the length of the third piece?

Both girls froze. L10’s tears arrived before she’d even begun, that familiar look of instant defeat. Sitting beside her made all the difference. We returned to the only tools she’d been given so far:

1. Do what you can
2. Use a number bond diagram

Once she was nudged in the right direction, she could do it, but it felt long and exhausting for her.

Later came the most emotionally challenging question of all:

The difference between two numbers is 19…

Unknowns, labels, letters, this was overwhelming. But by reframing x and y as labels (rather than scary letters) and repeatedly returning to visual number bond diagrams, something clicked.

She didn’t just solve the problem. She understood it.

That moment, when she realised she could replace y with what it equalled in terms of x, was electric. Inside, my heart was singing. This is why we choose hands on maths and visual tools. This is why we slow down.

Over the following week, similar problems became easier. There was still prompting, but less panic. The real test will come after a break, can they still apply the ideas later? For now, a quick-fire verbal quiz on number bonds to 10 showed me we were ready to move on.

Next step: number bonds to 20.

Hands-On Activities to Support Two Step Number Bonds Lesson

Here are some practical ways to reinforce two-step number bond understanding at home:

• Number Bond Diagrams with Counters
  Use coins, beads, or LEGO to physically build wholes and parts.
• Story Problems with Toys
  Act out difference and sum problems using figures, animals, or food items.
• Balance Scales
  Show equality and difference visually by balancing objects.
• Verbal “What If?” Games
  “If the whole is 40 and one part is 19 more than the other, what could that look like?”
• Chalk or Whiteboard Maths
  Big writing reduces fear and encourages experimentation.

These activities keep maths grounded, visual, and accessible, especially for children who find abstract thinking intimidating.

Reflection Questions for Parents

• Does my child struggle more with wording than with the maths itself?
• How often do I prioritise understanding over speed?
• What tools does my child return to when they feel stuck?
• Am I allowing space for emotions to surface during learning?
• How might slowing down now build confidence later?

For all of my living hands-on maths posts, click here