Build understandings of 2 digit number inside the hundred grid. Then stretch the grid to a number line.
All the components of number sense are covered and learners develop the foundation for automaticity with adding and subtracting 2 digit numbers.
Learners must trust 10. That is why I begin with 2 colour fives. Once students are using the grids to think I move to solid colour and eventually no colour. Thinking with 100 is my goal.
Here you see 53 blocks built into the grid. First we looked at the pattern when you add tens. See the list of numbers? We went back to 53 and now we are removing 10 to see how to count backwards by tens. 53 minus ten equals 43 but right now the focus is internalizing the pattern, not writing the equations. WRITING EQUATIONS IS A DIFFERENT PATHWAY IN THE BRAIN and must be taught with deliberation and patience.
Match, Sort, ORDER & COMPARE ways to express numbers to build mental fluency and RECALL skills.
Keep your brain working, that is how you build lasting recall.
You can see that students do not want to give up the equal sign. However, expressing a number does not require an equal sign. We know these are all about 64 because that is the number we are studying. This task was to show ways to “express” 64. Instead some students are writing equations for addition statements. Number Sense is not grounded in number facts. It is grounded in number relationships. The relationship we are working on in this image involves using tens and ones to express 64.
Three tens, 34 ones is also 3(10) + 34(1) or 30 + 34
3(10) + 3(10) + 4 (1) or 30 + 30 + 4
They all equal 6(10) + 4 (1) or 60 + 4
Fluency with expressing number multiple ways needs to then be connected to equalities.
Pull the number you made in the 100 grid, out into a number line formation. Can you still see the parts? The 2 colours help you make sense. Find referents on the number line. Consider how far from questions to develop magnitude. Fill in the rest to 100. This number line ends at 54, how many would you add efficiently to get to 100?
Inverses are not “just fact families”. Inverse relationships makes clear that addition and subtraction are the same operation. If you can add, you can subtract. Once you are clear on ways to express the entire number, you are able to flexibly manipulate the relationship. IF 37 + 48 = 85 then 85 – 37 = 48. This is much more than a “fact family”. Teach inverse right from the beginning of your work with number.
CONTINUE TO BUILD THE FOUNDATIONS FOR NUMBER SENSE AS STUDENTS MOVE INTO WORKING WITH THE THOUSAND. BUILD, EXPLAIN, REPRESENT, COMPARE.
BERCS CARDS for Two, Three, Four Digit Number:
When you purchase the Two, Three or Four Digit Number Book, you get access to the Members Only area which offers support for working with the concepts & the cards. It includes a range of practice tasks and masters.
When you purchase 3 or more of the Two, Three or Four Digit Card Decks you get access to the Members Only area as well.
Card Decks are $12 each. Each Two, Three or Four Digit Book is $39 and sent to you as a pdf.
And now there are Booklets of Tasks to support student practice:
Two Digit Number Book: $39.99 (pdf to download)
Three Digit Number Book: $30 (pdf to download)
Four Digit Number Book: $30 (pdf to download)
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