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
Place Value in Addition and Subtraction
Commutative Property also known as the "old switcheroo"
3 + 124 = ?
124 + 3 = ?
HUNDREDS, TENS, ONES , 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.
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.
Week 4 Continued
Have you read any of the math curriculum? Have you looked at the Effective Guides? Have you discovered any picture books, math learning activities, math music, math art that you would like to share with the class?
Egyptian Multiplication- Pre Task
18 X54=972 1 54 2 108 4 216 8 432 16 864
1 108 864 =972
This method relates to the distributive property of multiplication as it broke down the mathematical equation into smaller more manageable equation. For example, in my equation I took 18 X 54 and broke it down into five smaller number 1, 2, 4, 8, 16 (1+1= 2 2+2= 4 4+4= 8 8+8= 16). In this step I doubled until they did not go over 18. Then I did the same thing on the right side until (54+54= 108 …...864). I know that 16+2 will give me 18 so I know what I did to the left I need to do to the right side so I took 108 + 864 = 972. To confirm 18 x 54= 972. This was very different method of teaching as I can remember when I was in secondary school, I learned to multiple by stacking numbers. By using the distributive property method, it helped break down the numbers provided and convert into smaller numbers to work out the equation. As educators giving children the opportunity to take home math equations to mimic the lesson plan allows for the children to share their rich learning opportunities the next day.