Explore number bonds – numbers that add up to another number – with Julie Mountain and Felicity Robinson
number bonds explained
A number bond describes the ways that a whole number can be made up of (or ‘partitioned’ into) smaller parts. Understanding the relationship between parts-of and whole numbers is an essential skill for our emerging mathematicians. It’s also known as composition, and this can be applied to creating, combining and arranging other maths concepts such as patterns, fractions and shapes. Abundant loose parts are great at helping children ‘see’ whole numbers and constituent parts, through physical manipulation of resources, reinforcing addition and subtraction as inverse maths operations – don’t forget that splitting a big number into smaller sets is as important as bonding them to make the bigger number.
everyday number bond play
Many of the simple resources you have outdoors already can be repurposed for exploring number bonds and combinations. Simple activities like collecting ‘one’ pile of leaves or cones and counting how many leaves or cones make up ‘one’ pile are a good way to introduce the idea before moving onto simple number bonds to five or ten.
- Use daily routines to reinforce how smaller numbers contribute to one bigger number: at snack time: how many forks do we need and how many plates – how many together?
- As an alternative to a ten frame, use air bricks that have holes through the centre and small sticks or other objects that will drop into the holes; ask children to show you how many combinations of sticks will fill all the holes. You could also use other array resources such as egg boxes with pebbles.
- Mark numbers onto large log slices, lay them out on the ground and ask children to jump onto the slices to make bonds as you call the numbers out.
- Involve children in making DIY cuisenaire rods: go on a hunt for lots of sticks that are at least one metre long; trim them to size so they are exactly one metre in length, then divide one stick into two 50cm lengths, one into three 33cm lengths, one into four 25cm lengths and one into ten 10cm lengths. Colour code the ‘fractions’ so that children can easily match them back up into one-metre lengths.
- Collect pots and pans from the Mud Lab and spoons or sticks for beaters. Divide the children into two groups to play musical number bonds: one group chooses a number and another number less than that to beat out on the pans (e.g., choose number six then make two beats). The other half of the group listens and counts along, then beats out the remaining numbers up to the total (e.g., four more).
outdoors and active
proves that movement is crucial to cognition; being active outdoors is a great way to introduce and reinforce complicated concepts such as those found in maths and other STEM subjects.
- Number bond bodies: Chalk a large circle on the ground, plus a series of smaller circles (or use large hoops or rope) and join the smaller circles to the largest one with a chalk line. Start with as many children as you can fit into the large circle, and together, count the total. Then ask children to choose a nearby circle to bounce or leap into. Once in a circle, each group of children should count themselves and call out how many they are, then hop, skip or jump back to the main circle and count themselves again. Repeat to show children that many different sets of numbers can make up the total.
- Skittles: Make ten Bottle Babies* and mark a number from one to ten onto each one, to use as skittles. Line up the skittles in a row and give children a number to aim for: ‘knock down two skittles to make five’, remembering to chalk the number sentences onto the ground. *(Fill plastic bottles with water and add food colouring, glitter or small-world objects; superglue the caps back on).
- Giant abacus: create this using two or three parallel ropes or thick string pulled tightly and secured in place across a fence or between two posts – before securing the ends, thread ten large beads or quoits along each rope. Abacuses are usually small and great for fine motor skills – this one requires whole body effort to use, as well as maths skills.
maths in the garden: growing broad beans
Our beans are growing like crazy – how do yours look? Make sure yours are located somewhere cool and light so they don’t overheat or dry out. There are lots of observations and measurements to make now – you could do them daily or on the same day each week:
- Place a tall, straight stick into each bean’s compost and use a marker pen to mark the height of the bean. As the bean grows taller, you’ll need this stick to support the stem – source some plant twist ties in readiness.
- Use a 30cm ruler to measure the height accurately and plot it onto a simple bar graph – eventually you’ll need a longer ruler. Judging by the pace of growth, how long do children think it will be before the bean is taller than the ruler?
- Decide which is the largest leaf and measure it. Mark it with a tiny dot; when you revisit it the following week, is it still the largest leaf?
DIY outdoor maths kit
It isn’t necessary to spend big money with educational suppliers to enrich maths outdoors. Many of the resources you already have will lend themselves to double duty, with creativity and maths high on the list of loose parts affordances.
The contents of our DIY ‘instant’ outdoor maths kits vary as things wear out or we spot something exciting to add to it, but as a general rule, the kit is used to inspire adults to add a mathematical element to play children are already engaged in.
Here are some suggestions for getting your kit going – keep it in a small tub or tin, or in a drawstring bag:
- For measuring: a tape measure; lengths of tape measure ribbon (find online or in sewing shops); a 30cm ruler; 1m and 50cm lengths of string; and a roll of string.
- For counting: laminated or loose numbers; a hundred square; cloth ten frames; large playing cards; a few multi-link cubes.
- For maths vocabulary: our ‘sparky words’ – https://tinyurl.com/SparkyMathsPLL
- For weighing: a luggage scale (you suspend objects to it to weigh them).
- Plus: a small pair of sharp scissors; ten curtain rings; a chunky chalk and a marker pen; dice and inflatable dice; small 3D-shaped card boxes (from, e.g., Hobbycraft); ten coasters; paint colour sample strips; a magnifying glass; ten plastic bottle tops.