Category: Resources

May 18th, 2017 by megan

Second grade students are using expanded form to add and subtract multi-digit numbers.

Common Core State Standard

Use place value understanding and properties of operations to add and subtract.

CCSS.MATH.CONTENT.2.NBT.B.7
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Students have really enjoyed working with larger numbers!

Addition Example

347 + 218 = _____

Solution:

300 + 200 = 500

40 + 10 = 50

7 + 8 = 15

500 + 50 + 15 = 565

Instruction was moving along swimmingly until the subtraction examples required regrouping.  As often happens, some students caught on to the concept of regrouping right away. Others continued to struggle, writing number sentences like this: 20 – 30 = 10. Traditionally, students would be taught to cross out and “borrow”, but what student is actually making sense of that process?  One of my former students once noted, “I don’t know why we call this borrowing.  It’s kind of stealing.  We’re not giving anything back here.”
I love the flexibility that the expanded form brings to the subtraction algorithm; it’s regrouping at it’s best!  Here are two different strategies from the same class:

Strategy 1 Strategy 2
347 – 218 = _____

Solution:

300 – 200 = 100

30 – 10 = 20

17 – 8 = 9

100 + 20 + 9 = 129

 347 – 218 = _____

Solution:

300 – 200 = 100

10 – 10 = 0

37 – 8 = 29

100 + 029 = 129

Because the class was split between students that definitely needed more practice and those who didn’t, I pulled a group of 8 students in need of enrichment.  That freed up time for the other 14 to work closely with their teacher.

We played a game inspired by Marilyn Burns (I’m pretty sure).  I’m not certain what she calls this game or if it is even she that created the idea, but someone deserves credit for it.  I created the pages, not the activity. We played two rounds with a standard die numbered 1-6.  After that, I let students play with a 10-sided die labeled 0-9.  It was a blast!

Here are the game boards:  

Addition and Subtraction Challenge

I had this problem, from Open Middle, in my back pocket.  I didn’t need it, so I’ll save it for another day!

Close to 1000

 

 

Posted in Resources

May 18th, 2017 by megan

First grade is working on making sense of equations with missing values.

 

Common Core State Standard

Work with addition and subtraction equations.

CCSS.MATH.CONTENT.1.OA.D.8
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ – 3, 6 + 6 = _.

As I watched students work through their problem set, I noticed quite a few friends filling in the blanks like so: 5 = – 3.  Although I understood the mistake, I hoped that students could learn to read these statements with understanding.  In response, I created a card game that I thought could help.  

With all of the cards out on the table, I asked, which representation matches the number sentence? Good discussion ensued as students went to work pairing up the cards.

Here is an example of two cards that match:

The activity was originally done with the number line cards, but I liked it so much I created a version with tens-frame representations:

Enjoy!  

Posted in Resources