Week 5: Addition & Subtraction with Different Bases

This week we only had class on Tuesday the 5th and our first homework assignment was due. We started off Tuesday working on some addition and subtraction practice problems using multiple techniques to solve them.

Our first practice problem was 64 + 77. Here are two examples on how to solve this equation using two different techniques, Partial Sums and Give and Take.


Partial Sums Visual:

Give and Take Visual:












For our second practice problem we had the subtraction problem 145 - 66. The two examples to solve this problems is using the techniques of Compensating and Holy Shift.

Compensating Visual:

Holy Shift Visual:

 

 



We also looked at a time problem to interlude into to our main topic of adding and subtraction with different bases.

 

 

Time Addition Visual:

 

Time Addition Graphed:

 

 

 

The last portion of the class we looked at addition and subtraction with different bases. In elementary school we learned to add in base 10 with stacking and borrowing. This exercise uses simple addition but with different bases. This activity's main goal was for us as future teachers to understand the frustration and confusion elementary students feel when learning stacking and borrowing and to apply that to our teaching methods.

Addition in Different Bases Visuals:

 

Example 1:

Example 2:

 

 

Subtraction in Different Bases Visuals:

 

Example 1:

 

Example 2:

 

 

 This will be my last blog post thanks for all the comments and go Cougs!

Week 4: Subtraction and Addition

On Tuesday the 29th we worked out of our classroom activities booklet on pages 51-55 (handwritten) using 100s, 10s, and 1s number blocks, index cards, dice, and manipulatives.

Since the number blocks and the index cards were already created we worked on activities 2 through 5.

In activity 2 we used dice to determine the amount of base ten blocks we would use to make two three-digit numbers. After rolling the dice we would create the number by using the correct amount number of blocks. If it was possible your group could exchange the amount of 1s, 10s, or 100s to make an easier total of blocks (similar to exchanging money). Once the numbers were established in their simplest form we wrote a number sentence to compare the two words. An example would be 445 < 569.

In activity 3 we used the same base 10 blocks to do addition. First we picked out two different three-digit numbers and represented them in the blocks. After forming the numbers in blocks we combined the numbers by combining the blocks and exchanging them to create a simple answer. All the steps and diagrams were recorded on a piece of paper we would later turn in.

In activity 4 we did a more abstract activity by using single manipulative pieces to represent numbers instead of a more concrete form with the base 10 blocks. Using the index cards to create the two three-digit numbers we expressed them by placing the correct number on of manipulatives onto a place value mat. Once placing the correct amount we exchanged the manipulatives to create the sum.

 

 

 

In activity 5 we did the same process of creating two three-digit numbers and adding them together but this didn't involve any form of manipulatives by using two different addition techniques; Addition without Regrouping and addition with regrouping (also known as stacking and borrowing).

Addition without Regrouping:

Addition with regrouping:

 

On Thursday the 31st we looked at solving an addition and a subtraction problem using multiple techniques to solve each.

 

 

Our first problem was an addition problem, 34 + 28 = 62. Here are five examples to solve this problem.

 

 

Traditional:

Give & Take:

 

 



 

Partial Sums / Instructional Algorithm:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Compensating:



 

Decomposing:

 

Our second problem was a subtraction problem 52 - 37 = 15. There are six examples to solve this problem.

 

Traditional:



 

Partial Differences:

 

Compensating:

 

 

Distance:

 

Decomposing:

 

Holy Shift:

 These techniques are important to remember for set 3 in our homework which is due soon. Stay tuned for next week's blog and go Cougs!