### Place Value

## Place Value Cards

I have become a huge fan of place value cards! I first saw this handy teaching tools last summer while I was at a teaching conference in Vegas. I thought they could be helpful for more visual learners, while being lower maintenance than the classic Base 10 blocks. But now that I’ve used it with the students, I can’t imagine learning without them! The place value cards have solved so many mistakes second graders often make, such as not lining up digits correctly when adding or subtracting, forgetting the place of each digit, or not understanding the true value of digits in numbers (such as, the 5 in 59 actually represents 50, not 5). We have used these handy cards for place value, multi-digit addition and subtraction and composing and decomposing numbers. but the biggest help has been teaching the students to write numbers in expanded form. Year after year, second graders have struggled (and been clueless) with this concept. But with place value cards the kids easily understand how a number can be decomposed. Here’s an example we did in class this week.

This is how we show the number 485 using place value cards. Notice that each place value is color-coded. This is vital for kids to realize that each digit in a number has a different value. When they realize this, they no longer line up digits incorrectly because they understand that the ones have to be added to each other, the tens have to be added to each other, etc.

Then, to write in expanded form, the kids simply pull the cards apart, or “expand” the number. So this:

is written as 400+80+5. Expanded form is suddenly a piece of cake!

I f you would like to make your own place value cards to use at home, I found this great set here. If you are going to make your own, please remember that color-coding is vital! Ones should be white, tens should be red, hundreds should be orange and thousands should be yellow. Otherwise, enjoy!

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## Number Branching

Number branching is a technique that was taught at the parent Math Night. Here’s how it works: The student writes the two (or three) digit number. Below it, they break the number up by ones and tens. So 49 would be 40 and 9. 63 would be 60 and 3. 215 would be 200 and 10 and 5. This is what it looks like:

The next step would be using this technique to add numbers. This gives kids a process to follow to be able to add numbers quickly in their head. When kids breakdown numbers in this way, they can quickly and easily add the ones and tens. It also builds a sense of the way numbers are composed and decomposed. This strategy builds a strong foundation for algebra in later years. Here’s an example of how that this would look.

35 + 42 would turn into

35 + 42

/ \ / \

30 5 40 2

That would turn into:

35 + 42

/ \ / \

30 5 40 2

(30+40) and (5+2)

which the kids can add easily in their head. That would be:

35 + 42

/ \ / \

30 5 40 2

(30+40) and (5+2)

OR

70 and 7 = 77

Seem complicated? Too many steps? That’s because you do this naturally, nearly every time you add. Teaching kids the step-by-step process, and having them write out each step, gives them the thinking process you want them to acquire. The goal is to make this a non-thinking process. That way, they’ll be able have the innate step-by-step process when they get to higher skills, like adding algebraic equations or combining 10-digit numbers. Just remember that this is all in preparation, and creating a base for, later on!

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