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**MATH JOURNALS WEEKS 1-9**

**EDUC 4032 YDJ**

**ELIZABETH ZADO**

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**Week 2**

**Array**

12 Dot Circles in Rectangle 4 x 3=12 or 4+4+4= 12

**Share your thinking or questions.**

**Before i began i instantly looked at how many circles there were. Looking from a mathematical approach i noticed two shapes the rectangle has 12 dots and the L shaped has 3.**

**What math do you notice?**

**The math I noticed was adding the columns (diagonal or horizontal to get the sum of the dots. When you break it down into two shapes (4+5+6) =15 or (3+3+3+3+2+1)= 15. Also multiplication (4x3) =12+3 =15.**

**What math might students think about?**

**Students can think about how many circles there are in total by using geometry for example the rectangle has an area calculation 3 length x 4 width =12. By observing the patterns it is also possible to make connections between patterns and shapes.**

**How does this activity support the development of number sense? How would you extend it?**

**This exercise allows students to explore different ways to use shapes, patterns to understand addition and multiplication.In addition to extend it educators can add more dots to the equation by adding or removing a line. Moving forward allow students to create they own grouping building their confidence.**

BIG IDEAS FOR NUMBER SENSE

Counting

Operational Sense

Quantity

Relationships

Representation

Operational Sense

Quantity

Relationships

Representation

**Week 3**

Place Value in Addition and Subtraction

Commutative Property also known as the "old switcheroo"

3 + 124 = ?

124 + 3 = ?

124 + 3 = ?

**Week 3**

HUNDREDS, TENS, ONES ,

TRADING MOVING TO THE NEXT COLUMN.

MANIPULATIVE UNDERSTANDING REPRESENTED BY TRADING OR EXCHANGING.

TRADING MOVING TO THE NEXT COLUMN.

MANIPULATIVE UNDERSTANDING REPRESENTED BY TRADING OR EXCHANGING.

Compensation is a mental math strategy for multi-digit addition that involves adjusting one of the addends to make the equation easier to solve.

**Week 4**

Pre Task Cookies

**What was your initial estimation?**When I first looked at this math problem the first way I thought of solving it was counting down (12) and across (15) to multiple to total amount of cookies= 180. Rather than starting it this way it is helpful to break down the arrays depending on the age group we are working with.

**What math might students think about?**Students may think about grouping the array so it is more helpful to count. Once they break down the cookies one way of figuring out the amount is using addition. For example I highlighted a group of 6+6+6+6+6= 30 or another way is have them count vertically 5+5+5+5+5+5= 30.

**How does this activity support the development of number sense?**This activity supports the development of number sense as it allows students to break down the visual of what they see, and they can make comparison to other math strategies students used to solve the problem. This was done by making connections to number comparisons and understanding how much quantities of cookies there are. Explaining how breaking down into smaller groups such as subsiding.

Developing Mathematical Models

**Common Multiplication Strategies**

Doubling: 2 x 3 x 6 = 6 x 6.

Halving and Doubling: 4 x 3 = 2 x 6.

Using the distributive property: 7x 8 = (5x8)+ (2x8). 7x8= (8x8)-8.

Using the distributive property with tens: 9 x 8= (10 x 8)-8.

Using the commutative property: 5 x 8 = 8 x 5

**Unitizing-**The ability to be able to count not only objects but also groups understanding that six objects can simultaneously be thought of as one group.