Today, we warmed up with some mental math in multiplication of rounding and multiplying basic facts. I started with asking them why 24 would round to 20? I told them I wanted them to explain by factoring out any tens first.
One student simple stated that the 2 tens were in the tens place and that we could pull out the ones making it 20 + 4. I asked if that if we had to round, what would happen to the 4 ones? One student said that the 4 ones is just 'taken" away from the rounded number.
I clarified that "taken away" would mean we subtracted it out. I told them that subtracting the 4 ones was not what happens when we round. I was surprised how this misconception rose to the surface so quickly. To correct it, I gave the example of the number line we used when we learned to round and estimate in addition and subtraction. I quickly drew the number line on the SB and explained to correct any misunderstanding. I think it was important to review the meaning of rounding so they would be prepared for the next part of their lesson! The Educreations Sample demonstrates how I taught them through the misconception.
I opened the SB file of Estimation Classroom Copy and asked my students, “Why is estimation an important step in multiplication?” Several students offered up ideas about having to find "quick" answers to multiplication problems, just like in addition and subtraction. One student said that if she were trying to find out a total really fast and the numbers could be grouped, she would use estimation. We discussed the meaning of reasonable answers and that we use estimation for comparing exact answers. A
I gave an example of throwing a party and that each paper cup was 39 cents. If I had 9 people at my party, about how much would the cups cost in all? One student suggested to round it to 40 cents and multiply that by 9. I let them use their calculators on their iPads. We arrived at $3.60. Through this example, they could apply real life understanding. I asked them if $3.60 was a believable answer? I told them I wanted them to think about the word "reasonable" as the word "believable." I told them I wanted to always step back and question: "Does my answer make sense? Is it believable?"
As I worked through the Smart Board, we started to practice rounding and estimating. We tried several examples in our math notebook, discussing each step. I roved and checked their understanding as they wrote examples and solved on their own.We discussed important strategies in solving word problems.Students took notes in their math notebook as we discussed important points. Students could start to understand why an area model would not be the most practical method of solving and that they needed to use their basic facts as a strategy. They wrote down each word problem vocabulary word that meant to estimate; "approximately","around" and "about" were three of the words. I instructed them to under line the vocabulary words in their word problems that told them it was an estimation problem. This under lining would remind them that we were not looking for exact answers. We reviewed the difference between "exact" and "approximate." As I gave explicit examples, they quickly caught on to the process and concept, and I decided it was time to hand out the assignment to work on for awhile in class so I could monitor progress.
I passed out Assignment # 6 Estimation and we read the directions together aloud. I wrote a sample problem for #1 on the whiteboard so that students understood exactly what I wanted to understand from them. I told them that I wanted them to compare their estimated answer with their exact answer as they had in the past during the addition and subtraction unit. I told them that they needed to explain how they did the problem, and then I demonstrated what I wanted by writing a short sentence about 45 x 6 and 50 x 6.
There was a rich, but brief conversation started by one of my students about how the estimation was larger because I had rounded up. CCSS help us with getting kids to think more deeply and make connections. I am starting to see this as we transition. As they worked, I roved the classroom, reminding them to use their classroom notes. I left th SB file up on the SB so it was an easy reference.