Sorry Folks, this is a long one! I usually send this information out in sections as we work through it, but I dropped the ball on that one this year. My apologies. Right now we are working on two digit subtraction and will be working with three digits soon.
Here is a quick overview of what we have been practicing so far in our Addition and Subtraction unit. The best way for you to see how your child is doing with these concepts is to have a conversation about them and do a few practice examples together
1. Doubles and Near-Doubles Addition Facts: We spent quite a bit of time practicing our doubles facts as a class and individually. We focus on doubles because they are often easy to learn and can be a helpful mental math strategy for solving other addition facts that are close to the double. Students practiced solving “near doubles” equations and explaining the strategy as clearly as they can.
Example: (students are asked to show that they can use both of the possible doubles to solve each problem)
I know 6+6=12
6+8 is 2 more.
I know 8+8=16
6+8 is 2 less.
2. Making 10:
Example: To solve 6+8 we may think: Take 2 from the 6, leaving 4. Add 2 to the 8 to make 10, then add the 4 to get 14.
Or, use an adding a 10 fact like the example below.
We know 10+6=16.
8+6 is 2 less.
We have also been practicing our addition facts that make 10.
3. Related Addition and Subtraction Facts (Fact Families):
Example: If we know 7+6=13 we also know 6+7=13, 13-6=7, 13-7=6. Using “fact family” knowledge is often most useful for students to solve subtraction equations by thinking of the related addition fact.
4. Estimating Sums: We use the following three strategies to help us build mental math skills.
1. Add only the digits in the tens place.
So, 59+23 is estimated to be 70.
2. Take one number to the closest 10.
So, 59+23 is estimated to be 73.
3. Take both numbers to the closest 10.
So, 59+23 is estimated to be 80.
We focus on learning the strategies and practice deciding which strategies gives the best estimate based on the numbers presented in the problem.
5. Three Digit Addition:
We continue to work hard at maximizing our learning about numeracy while exploring addition and subtraction of three digit numbers. The students have many strategies for working with three digit number equations. The samples below are examples of some of the strategies we have been working with. Please keep in mind that these are just basic examples and individual students will often take apart and re-construct the numerals in unique ways that match their understanding of numbers. When this happens it is often a very good sign that they are good mathematical thinkers. There is a big difference between blindly following steps to get the correct sum and being able to make efficient adjustments to strategies based on the problem that is presented.
300 + 200 = 500 (add the hundreds)
60 + 50 = 110 (add the tens)
8+7 = 15 (add the ones)
500 + 110 = 610
610 + 15 = 625
500 (add the hundreds)
110 (add the tens)
15 (add the ones)
For both addition and subtraction some students need to build/draw base 10 materials to help them visualize what is happening to solve three digit problems.
Subtraction is always one of our biggest challenges in grade three mathematics. If a student’s understanding of place value is somewhat shaky, the mental calculations required for three digit subtraction can be difficult. In these instances it is often tempting to teach the more traditional vertical procedure of borrowing/trading that many of us learned in school. This is without question a very valuable strategy for completing quick calculations, but that is not always our goal at school. Providing students with opportunities to work with numbers in a manner that will hopefully help them fill in their number sense ‘gaps’ is one of my greatest goals. I find that if I teach the students to use the more traditional strategy right away, they are able to memorize the procedure and get the correct answers without necessarily understanding place value. Using other strategies offers me a lot more insight into their thinking. They can show me how wonderful it is or, where the breakdown in their understanding may be. Most of the strategies I focus on come from the mental math strategies used by the students in our class. I help them refine these strategies and find ways to record their thinking, but it is a team effort.
402-100= 302 (subtract the hundreds)
302-20= 282 (subtract the tens)
282-8= 274 (subtract the ones)
I hope this was helpful.