Number Sense for 2 digit numbers: automatic recognition when embedded within a familiar referent. Express multiple ways that acknowledge the base ten system. Magnitude & Density: Position and explain “closeness” within a set of numbers when embedded within a familiar referent Equalities: all expressions can be used to create equalities which eventually can or may become additions. Inverses: How many more to familiar referents becomes addition and subtraction.

Number Sense for 2 digit numbers: automatic recognition when embedded within a familiar referent. Express multiple ways that acknowledge the base ten system. Two digit numbers are related to 100 in an area model and in a linear model. How far to related to one fourth, one third, one half , two thirds, three fourths of one hundred or to 25, 50, 75 and 100.

We want automatic recognition when embedded within a familiar referent We want automatic recognition when embedded within a familiar referent. I see 54. Express multiple ways that acknowledge the base ten system. I can express as 4 (10) + 14 (1) or 30 + 24 Area models are compact and therefore more likely to be held, stored and remembered.

Number Sense for 2 digit numbers: Magnitude & Density: Student can position and explain “closeness” within a set of numbers. When do orientation and direction matter? Only when reading & writing the symbols, or fitting the conventions of the number line. If you understand magnitude then you know that on a number line the growth moves to the right. 54 is ten times more than 5. It is twice as much as 25 If you understand density then you know that 54 is between 53 and 55.

Rotations, translations and reflections do not affect the quantity. Change the position within the 100 it is still 39. In an area model students can see the actual size comparison for more and less. 39 is less than 50 but more than 25.

A number line is about “seeing” the sequences and considering how the symbols give clues to the growth and shrinkage or the change in count if you will. There is no visual clue to interpret the actual change in “size”. You need to understand the magnitudes as you read the symbols now. 0 50 100

First you place your number and explain why. It is closer to 50 than 0. It is more than 25. I thought about the 20, 30, 40 39 is almost 40. What will your students say? 0 50 100

As you build your number sense you can begin to use the number line and the area models to explain differences between quantities. It is a way to keep track in place of writing equations. The goal is not to practice the “counting by ones sequence.” 0 50 100

I stretched the number line longer to have room to show. I know it is 11 to 50. I think one more then 10 more. I know it is 61 to 100 so 39 + 61 = 100 and 100 – 39 . 39 40 50 100 +1 +10 +50

Once I am comfortable with two digit numbers I can “open” the number line and think about things like 39 + 53 or 92 – 39 because I can see how they are related in my mind. Eventually I can just do the mental calculations. . 39 92

In my world of math you do not count by ones on number lines In my world of math you do not count by ones on number lines. You show thinking. Once we get to high school counting by ones will not be an option for solving problems. 0 50 100

Number Sense for 2 digit numbers: Students who do not have ten must build tens by snapping together blocks or piecing together ChunkitZ till they trust ten and do not need to count.

Number Sense for 2 digit numbers: Once they trust blocks as fives, snap 2 into a ten and build the tens into a hundred grid. We express the number flexibly.

Number Sense for 2 digit numbers: Students build their trust for the decades by building them into the hundred grid with you. See ppt “Introducing the 100.

Number Sense for 2 digit numbers: We stretch the build to model the number line. We replace life size with smaller versions to manage on the page. Proportional reasoning allows us to trust the smaller version.

Number Sense for 2 digit numbers: Express multiple ways Build 54 50 4 5

As an area model…. 50 4 5

Number Sense for 2 digit numbers: You can separate to see ways to describe 50 4 5 3 tens, 24 ones or 30 + 24 4 tens, 14 ones or 40 + 14

Number Sense for 2 digit numbers: Magnitude & Density: You can stretch to a number line 50 4 5

Number Sense for 2 digit numbers: Express multiple ways using “place value” These all use “place value” Can you see them in 54? 50 + 4 4 + 50 5 tens, 4 ones 5(10)+4(1) 40 + 14 14 + 40 4 tens, 14 ones 4(10)+14(1) 30 + 24 24 + 30 3 tens, 24 ones 3(10)+24(1) 20 + 34 20 + 34 2 tens, 34 ones 2(10)+34(1) 10 + 44 44 + 10 1 ten, 44 ones 1(10)+44(1)

Number Sense for 2 digit numbers: automatic recognition when embedded within a familiar referent. Express multiple ways Magnitude & Density Equalities: all expressions can be used to create equalities which eventually can or may become additions.

These can all be linked with the equal sign. 40 + 14 = 30 + 24 2 (10) + 34 (1) = 20 + 34 50 + 4 4 + 50 5 tens, 4 ones 5(10)+4(1) 40 + 14 14 + 40 4 tens, 14 ones 4(10)+14(1) 30 + 24 24 + 30 3 tens, 24 ones 3(10)+24(1) 20 + 34 20 + 34 2 tens, 34 ones 2(10)+34(1) 10 + 44 44 + 10 1 ten, 44 ones 1(10)+44(1)

Number Sense for 2 digit numbers. Express multiple ways Magnitude & Density: Place on number lines Equalities: 30 + 47 = 7 (10) + 7 (1) 40 + 37 = 50 + 27 Inverses: How many more to familiar referents(50, 100) becomes addition and subtraction.

Inverses: How many more to familiar referents becomes addition and subtraction. I can use the white to determine how many to 100. That allows me to create an addition or subtraction about 100. I see 6 + 40 or 46 to get to 100 54 + 46 = 100 100 – 54 = 46 100 – 46 = 54

Can you explain an addition for 100? Ready? There will be 2 colours. Can you explain an addition for 100? Can you turn it into a subtraction? Can you see it on a number line?

Can you see it on a number line?

Purple is 34 Yellow is 66 34 + 66 = 100 66 + 34 = 100 100 – 34 = 66 100 – 66= 34