Elk Interaction Picture In our continued look into 'How Does Human Interaction Change and Identity,' the kids were given a photograph of a group of people standing near an elk. They were asked to consider all of our previous learning including the wildlife interaction rules that they had created. We decided to assume that all of the characters in the picture, including the baby and the elk, new the rules. The thought bubbles that the kids created show what each character might be thinking about when being so close to a wild animal. NumeracyWe continue to develop numeracy strategies through exploring different ways to add by developing reasoning skills through strategy games, and working towards clear explanations of our mathematical thinking. Front end addition is a useful strategy that can be used to add 3-digit numbers. In this strategy, and these examples, numbers are partitioned into hundreds, tens, and ones and added. This is called front end addition, because you start with the front end of the numbers or the hundreds. Students find most success with this strategy when they carefully line up their addition into columns as would be found on the place value chart, either by physically drawing lines, or by carefully lining up their numbers as they record them. Closest to 100 or Closest to 1000 Students have working with a partner, using two decks of playing cards to develop estimation and mathematical reasoning skills. If playing to 100, students draw 6 cards and choose 4; if playing to 1000, students draw 8 cards and choose 6. With the cards they have chosen, students combine their cards to make 2 two-digit numbers (Close to 100) or 2 three-digit numbers (Close to 1000). So What Are the Best Numbers To Make? When mathematicians prove their thinking, they often use a similar problem with smaller numbers to explain their thinking. After playing this game over a few days, we wanted to get a sense of our students strategies and reasoning. We provided the students with a situation in which they had flipped over these 6 cards when playing Closest to 100 6, 3, 1, 4, 8, 7 They were asked to make the best number possible, just like they would do if they were playing the game. Some of their thinking and strategies are listed below. Trial and Error: Clive's notebook demonstrating his process of testing possibilities. Trial and Error and Thinking About Other Possibilities: The best number you could make would be 13 + 87. I looked at a few and they weren't far from 100 so I knew that I could find a better answer. I looked over the numbers and saw that some were closer. I found 87 and 14 and saw that was 101 so it was pretty close. Then I found 87 and 13 and that was 100 so I knew it was the best number. There might be others that make 100 also. ~ Finn~ Trial and Error, with evidence of thinking: "61 and 48 because when you add them up they make 109 and its only 9 away from 100. It's an Ok answer but not the best. I was too big, so next time I would choose 47 and 63 ... oops, that's too much. 63 and 37... I looked at 47 and decided that I needed smaller numbers. This time I got 100." ~Adam~ Comparing sizes: I think 13 + 87 because 13 is way lower than all of the other numbers and also 87 is really close to 100. If you add them up then you get 100. If you split them into expanded form then you would have 80 + 7 and 10 + 3. Then you add 3 + 7 = 10, then 80 + 1- = 90 then add 90 + 10 = 100. Expanded form is a great strategy that helps me a lot. ~ Chloe~ Considering Probability: 87 and 13 would be the best numbers because 87 + 13 + 100 and we are going for Closest to 100 and my answer is exactly 100 and if I was playing against someone I have a high likelihood of winning. ~ Mayan~ 86 and 14 = 100 I decided to keep this number because it is either equal to the others or better than the others. ~Georgia~ Developing a Strategy (although not all of the following responses resulted in the best solution at this time, these strategies demonstrate examples of strong student reasoning throughout our investigation): I would put 8 and 1 in the tens because it make at 90 and I would be close. ~Saviero~ I thought 80 + 10 = 90 so I knew it was close. If I had 2 large numbers I knew it would be waaay too high so I chose 18 ... a small number. ~ Lachlan~ 14 and 86 ... These are the best numbers because we're trying to get to 100 and all the other cards are too high or too low. ~ Payton~ I chose 13 and 78 because I knew that if I added 80 with 10 I would be getting close. If I added 10 more from the ones I'd be there.... I wanted to get close to 100 but not over. ~Sofie~ 13 and 87 because the rest of the numbers are not as close to 100 like 63 + 18 = 99 but you can get 100 a different way 83 + 17 = 100. ~Jamie~ Addition Strategies - Revisited The following example demonstrates a sound strategy for the game - finding ways to combine two cards that equal 90 and then finding two additional cards that total to 10, so that the sum will be 100. On the surface, this student appears to understand addition using the traditional algorithm, the strategy most of us as adults were taught in school. By observing the student's explanation, we notice misconceptions about number that may be fostered using this strategy. The student does not articulate that they are, in fact, adding 80 and 10 together to get 90. This becomes problematic for some students, who when taught this strategy, do not fully understand the place value inherent in addition. I looked for what equals 9. 8 + 1 equals nine. Now I need something that equals 10. I could do 6 + 4 = 10. (This student is really looking for what equals 90) Both expanded form addition (see examples on our last blog post) and front end addition (examples above) are addition strategies that support students with developing a strong understanding of the place value of addition. Students who are fluent with using either of these strategies may not use the traditional algorithm and are often quicker at solving these addition situations mentally.
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AuthorsMrs. Montanaro, Mr. Messer and Mrs. Austman teach grades 3/4 at Elbow Park School in Calgary AB. Archives
April 2017
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