EDUC 4032 YDJ 

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.

Egyptian Multiplication- Pre Task

&nbsp; &nbsp;&nbsp;18&nbsp;X54=972&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;54&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;108 4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;216 8&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 432 16&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;864&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 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&nbsp;&nbsp;2+2= 4&nbsp;4+4= 8&nbsp;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.&nbsp;

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?&nbsp;

Pattern Guesser Name: Elizabeth Zado Rule: Position number x 2 +4&nbsp; The rule is that the number of red tiles stays consistent meanwhile the number of blue tiles increase by adding four.&nbsp; How many tiles would there be at the 75th position? How do you know? Add the number of tiles = position X 2 +1&nbsp; = 75 x 2 +1 position&nbsp; =&nbsp;151 What position of this pattern could you build if you had 68 tiles that would use up most of the tiles? Would there be any tiles left over? If I had 68 tiles, I could make 5 positions of this pattern with four remaining tiles left over.&nbsp;

&nbsp;5 people share 4 submarine sandwiches so that they each get the same amount. How much of a submarine sandwich does each person get?

8 people share 7 submarine sandwiches so that they each get the same amount. How much of a submarine sandwich does each person get?

Window Problem: How would you solve this problem? When i first looked at the problem as a multiplication chart, and therefore I muliply 12 x 15= 180, that now gives a total number of array. I will multiply the length of window with the height of windows in this image 12x15. I used the egyptian model How many windows are in this array? Show your thinking.&nbsp; 15 x12 1---&gt;12 2---&gt;24&nbsp;&nbsp;&nbsp;-------&gt;&nbsp; 4---&gt;48 8---&gt;96

What math thinking does this model support? The math thinking model this supports is a problem solving approach which allows students to explore different ways to solve the problem. I did not know to use the number provide so I created&nbsp;new&nbsp;sets of numbers to explore with. I like this model because it allows students to use mental math concepts to help children calculate the answers. Students are encouraged to use sums of numbers they are familiar with 10’s, 5,s. The number line is a visual representation which also helps strengthen those more comfortable with addition rather than subtraction. Applying these “family” numbers sentences can promote future multiplication/ division understanding.

How did you make your design? What processes did you go through to ensure you had the correct number of each colour of tile? To begin I knew I would need at least 12 tiles per section by looking at the ratio 3:2:6:1 therefore I added them together 3+2+6+1= 12. I know I need to fill 60 tiles, so I took 12 X 5 = 60. I then took every number and multiplied it by 5. 3 x 5: Blue = 15&nbsp;&nbsp;&nbsp;2 x 5 = 10 Red 6 x 5= 30 Green 1 x 5= 5&nbsp;yellow&nbsp; How many of each colour would you have if you used 696 tiles? How do you know? First, I already know that 3+2+6+1= 12 so I took 696 and divided it by 12 which gave me 58. To check my answer, I took 12x 58= 696. This tells me how many colours we can have in each row therefore we must multiply the quantity per colour in each row by 12. Blue= 174&nbsp;&nbsp;&nbsp;Red = 116&nbsp;&nbsp;&nbsp;Green = 348&nbsp;Yellow = 58 How many red tiles would you have if your design used 258 green tiles? How many tiles would there be in total? How do you know? There would be a total of 43 red tiles. 43 x 6= 258. With every 2 red tiles there would be 6 green tiles. Making the ratio 2:6&nbsp; What is the fewest number of tiles you could use in your design if you wanted to maintain the ratio? The fewest number of tiles you can use is 12. To determine this, I added the ratios together. This is the lowest amount of each colored tile.

Share your thinking or questions.&nbsp; I have only used one other coding software called Sketch which I find more easier to navigate. This webpage took some time to work. Overall, what helped me was a YouTube video I found the original video was not much help.&nbsp; &nbsp; What math do you notice? There are different mathematical concepts within this app and with coding. In this app students would be required to know what a square looks like (4 sides, all sides are equal recognising angles in geometric shapes. Surface area and volume could also be involved. &nbsp; &nbsp; What math might students think about? Depending on the grade and age of the child there could be many different math concepts to take into consideration. For instance, students could consider geometric, algebra, area, perimeter, measurement Students might recognize geometry as they are creating their different shapes and angles depending what they decide on.&nbsp; &nbsp;&nbsp; How does this activity support the development of proportional, spatial, algebraic reasoning, and multiplicative thinking? This activity supports many mathematical skills, it supports spatial reasons as students need to visualize their thoughts of what is going to happen once complete and what the next steps are going to be. They need to be familiar with the direction they want the turtle to go and the object/ shape. The activity supports the development proportional, spatial, and the understanding of patterns angles, positions of shapes and understanding how the numbers repeat to create the shape/pattern.

Commutative Property also known as the "old switcheroo"

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

Share your thinking or questions.&nbsp; Before i began i instantly looked at how many circles there were. Looking from a mathematical approach i noticed two shapes the rectangle&nbsp;has 12 dots&nbsp;and the&nbsp;L shaped has 3. What math do you notice? The math I noticed was adding the columns (diagonal or horizontal&nbsp;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.&nbsp;Also multiplication (4x3) =12+3 =15.&nbsp; 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&nbsp;it is also possible to make connections between patterns and shapes.&nbsp; 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.

Counting Operational Sense Quantity Relationships Representation

MATH JOURNALS WEEKS 1-9 EDUC 4032 YDJ ELIZABETH ZADO

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.&nbsp; 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.&nbsp;&nbsp; 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.&nbsp;

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.

Chapter 1 Week 1:

In the reading Lessons from the TIMSS Videotape Study, Geist (2000) 

Week 1 Strategies for advancing childrens mathematical thinking.pdf

References Nagel, &amp; Swingen, C. C. (1998). Students’ Explanations of Place Value in Addition and Subtraction.&nbsp;Teaching Children Mathematics,&nbsp;5(3), 164–170. Postlewait, Adams, M. R., &amp; Shih, J. C. (2003). Promoting Meaningful Mastery of Addition and Subtraction. Teaching Children Mathematics, 9(6), 354–357.&nbsp;