Adding two-digit numbers without renaming
The purpose of this activity is to support students learning to apply their knowledge of basic facts and place value to solve addition problems with two-digit numbers, without renaming ten ones as a ten.
About this resource
New Zealand Curriculum: Level 2 to early Level 3
Learning Progression Frameworks: Additive thinking, Signpost 5 to Signpost 6
These activities are intended for students who understand place value with two-, and possibly three-digit numbers but are not yet able to use this knowledge to solve two-digit addition and subtraction problems. For some students, revision of addition and subtraction basic facts (number bonds to 20), may be needed prior to, and alongside the use of these activities.
Adding two-digit numbers without renaming
Achievement objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Required materials
- Place value materials composed of individual items grouped into tens, such as BeaNZ in film canisters, ice block sticks bundled with rubber bands (hundreds with hair ties), or a paper form of Place value people 1. Bundled materials are important as they allow partitioning and combining without the need for “trading” tens blocks for ones, or vice versa.
- Place value with 2 digits 1 allows for the organisation of materials into columns and, in turn, supports calculation strategies.
- Place value to 4 digits 2 three-column and four-column place value boards.
See Materials that come with this resource to download:
- Place value people 1 (.pdf)
- Place value with 2 digits 1 (.pdf)
- Place value to 4 digits 2 (.pdf)
The examples below use images of BeaNZ and canisters used to physically model the numbers. You may prefer to use ice block sticks in bundles of 10, or Place value people 1. We recommend that you focus on just one of these within any given lesson.
1.
Pose addition problems, initially, with two-digit numbers that do not require renaming (i.e., the digits in each column add up to no more than 9). Set up a physical model, model the calculation using the materials, and record the calculation vertically.
- You have 24 beans and I am going to give you 33 more beans.
- How many beans do you have now?
- I am going to write the equation vertically. I am making sure to line up the tens and ones columns. This helps me to see how many tens and ones I am adding.
2.
Let students solve the problem with materials. Encourage them to verbalise their thinking with a partner, as they work, and provide time for them to share their ideas with the wider classroom. You might model this by “thinking aloud” and asking questions.
- What do you notice about 24?
- How many tens are in 24?
- How many extra ones are there?
- How many tens make 33?
- How many extra ones are there?
- If you add 2 tens and 3 tens, how many tens do you have?
- If you add 4 ones and 3 ones how many ones do you have?
- What is the number for 5 tens and 7 ones?
3.
Emphasise the connection between tens and ones, as different units, that can be combined separately in the process of adding a whole two-digit number.
For example,
- 24 and 33 are made up of tens and ones. I can make the numbers with materials (refer to the place value board) and see the different tens and ones in each number.
- I can add all of the tens to make 50 (demonstrate using materials) and I can add all of the ones to make seven (demonstrate using materials).
- Now I have added all of the tens and ones, I can see the total answer to 24 + 33. It is 50 + 7, 57.
4.
Pose similar addition problems to develop fluency with adding two-digit numbers without renaming. As students progress, refine the written algorithm to not include the partial addends.
1.
Pose further addition problems with two-digit numbers, that do not involve renaming ten ones as a ten, set in real-world contexts. Choose realistic contexts appropriate to your students, and encourage students to relate the problem back to the equipment if necessary.
For example:
- There were 23 boys and 42 girls at the kapa kaka competition. How many children were there altogether?
2.
Increase the level of abstraction by covering the materials, asking anticipatory questions, and increasing the use of the vertical algorithm, whilst decreasing the use of materials.
3.
Extend the problems to include addition with three-digit numbers where renaming is not needed. Use more structured materials like place value blocks to work with three-digit numbers. A suggested sequence for extending the difficulty of the additions is:
- Adding two-digit numbers without renaming (e.g., 45 + 32)
- Adding three-digit multiples of ten without renaming (e.g., 420 + 150)
- Adding three-digit numbers without renaming (e.g., 324 + 501).
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