Adding numbers

Activities to try

1. 1

   Snap the pairs that make a tidy number

   Why it works: Because addition can be done in any order and grouping, reordering to make pairs that total a multiple of ten turns a fearsome four-number sum into an easy sum of round numbers. The properties of operations are a lever, not an abstraction.

   1. Take four addends to add, e.g. 15, 8, 25, and 12, arranged as cards that can be physically moved (paper cards, counters on a tray, or draggable on-screen tiles).
   2. Before adding anything, scan the four numbers and decide which two, placed together, would make a multiple of ten.
   3. Pair 15 with 25 to make 40, and 8 with 12 to make 20, then add the two round numbers: 40 + 20 = 60.
   4. Repeat with 24, 17, 6, 13 (24+6=30 and 17+13=30, giving 60) and say aloud which pair you spotted first and why.
   5. Try one example by adding strictly left-to-right, then again by pairing first, and compare how much easier the paired route felt.
2. 2

   Partition into tens and ones, and compose the tens carefully

   Why it works: When many ones are combined they can compose more than one ten. Pooling all the ones and exchanging every full ten before recombining is a reliable way to make sure no composed ten is lost. If a composed ten is dropped, the answer comes out ten too small, or more than ten too small if several tens are dropped.

   1. Take all four addends and split each into its tens and its ones: for 15, 8, 25, 12 the tens are 10, 0, 20, 10 (the single-digit 8 has no tens) and the ones are 5, 8, 5, 2.
   2. Add all the tens together (10 + 0 + 20 + 10 = 40), then pool ALL the ones together before exchanging.
   3. From the pooled ones, exchange every full ten you can: here 5 + 8 + 5 + 2 = 20, which makes two tens and no leftover ones; if the ones had totalled 23 you would make two tens (not one) and keep 3 ones.
   4. Recombine the composed tens with the tens you already had (40 + 20 = 60) and check it matches the paired-up method.
   5. Use base-ten blocks or ten-frames so that making more than one ten from the ones is something you can see, not just carry in your head.
3. 3

   Explain and defend the smartest grouping

   Why it works: Explaining the chosen grouping makes the properties a conscious, reusable strategy and shows that reordering never changes the total.

   1. After solving a four-addend sum, say which two numbers you added first and why that order made the work easier.
   2. Answer 'you added them in a different order than they're written — does that change the answer, and how do you know?'
   3. Given 19 + 4 + 1 + 6, decide which you would add first and justify it (19 + 1 makes 20, then + 4 + 6 reaches 30).
   4. Pick a sum where no neat pair exists and explain what you do then (partition into tens and ones).