Math Learning Steps

Number meaning

Seeing a two-digit number as some number of tens and ones is central to understanding and working with those numbers. Doing two-digit addition and subtraction requires fluency with the concepts of place value. Develop that understanding through lots of experiences with physical objects and written numbers.

Bundles of tens

Take something you have lots of, make a large pile of it, and put some of them in a few bundles of ten. For example, out of that large pile ask your child to gather 23 of them. Then ask your child to group them in groups of ten. They will form two groups of ten and 3 singles. See what happens with the groups of ten in these 23 things as you put in some additional items or take some away, always making sure that there are no more than 9 single items at any time.

Expanded form

The expanded form of a number is writing it as a sum of its place value parts. For example, 23 would be written as 20 + 3, and 256 would be written as 200 + 50 + 6. Practice with your child converting in both directions between a number’s usual form and its expanded form. Point out that the expanded form of a number is the same as taking that many things and bundling them into groups of ten and have ones left over.

Counting with tick marks

Counting using groups of five tick marks is a natural thing people like to do and is strongly related to place value. If you are counting 23 things with tick marks, you will end up with 4 bundles of 5 and 3 tick marks left over. Those 4 bundles of 5 can be reorganized as 2 bundles of 2 groups of 5, which is our expanded form view of 23.

Skip counting

Skip counting by various numbers is a way to build mental practice with adding or subtracting single-digit and double-digit numbers. Although it is a great way to practice, this does require some mental steps that not every child will be ready for at this point – there is no hurry. Here are two examples. With lots of practice, these thinking steps will become automatic.

Skip count upward by 8 starting at 23. Think of 23 as 20 plus 3 more. Using the number bonds for 10, 3 will need 7 more to make a group of 10. Use 7 out of the 8 being added so that 3 plus 7 forms another group of 10. So, 23 + 8 becomes 20 + 10 + 1, which is 31.

Skip count downward by 5 starting at 23. Break up 5 into 3 and 2. To subtract 5, we will first take away 3 and then take away 2. 23 subtract 3 brings us to 20, which we will think of as 10 + 10. Subtracting the remaining 2 from one of those 10’s leaves 8, so our answer is 10 + 8, which is 18.