This week in math my class was focusing on learning various mental math strategies that will help us to learn how to solve addition questions in our head without the need for the a calculator or a pencil and paper. I feel that it is important to teach these strategies prior to teaching the student the standard algorithm. By doing this students can learn flexible thinking in relation to numbers and learn how to make math easier for their brain to to handle large numbers in their heads. I feel that the standard algorithm is very important for students to learn as it is a quick strategy for pen and paper math problems later. However teaching students to be flexible thinkers when it comes to numbers is essential to them having a comfort with numbers.
Throughout this unit I keep repeating to my students to train their brain to work smarter not harder. That is a key idea when using mental math strategies. I tell students that some numbers are friendly and some are not. Friendly numbers end in 0 and 5. These are nice numbers that are easy to add in their head. I tell them that zeros are really friendly they are your best friend and fives are a close friend. I am honest with them that sometimes when I look at an addition question I get overwhelmed because I cannot see the answer. However, by using friendly numbers and flexible thinking I can turn unfriendly numbers into friendly ones. I find that this is a helpful strategy for students to learn.
Prior Learning Needed
Before I begin teaching this unit it is important that students have an understanding of the following math principals.
1) Understanding place value system of the numbers they are required to add
2) Understanding that there is more than one way to represent a number
3) How to write numbers in expanded form
4) Automatically know most of their addition facts to 20 (teaching grades 3-5 most of my students have these strategies when they arrive in my classroom. If they don't then I always teach the more primary strategies of adding single digits such as doubling, doubling plus one, count up, tens frames etc.)
5) Counting up and counting back by 10s starting at any number
The first strategy that I teach is building on my first math unit of the year, place value. I begin the addition strategies unit by having students draw out the place value pictures for each of the numbers in the questions. Then I have them count up the totals in each column. Using this strategy students can see the action of carrying groups of ten over the the left. This is the same process that happens in the standard algorithm used later. Additionally students can visually see the number split up in to its place value columns. My students and I developed a code for drawing out the place value system with a set of symbols for each column.
Open Number LineThis is a strategy that allows students to draw out their math. This is especially helpful with students that are visual students. It allows them to break apart numbers and focus on simple easy jumps. It also is a great strategy for differentiation. It allows students with gaps in their math learning to make jumps that make sense to them. If they can count by 10s but not 20s. Count by 2s instead of 3's they can. The focus of this strategy is to have them counting by number larger than ones. I start with jumps of tens, fives, twos, and the left overs. My video here explains how this strategy works. I used Educreations app to create this video.
Front End Strategy
This strategy allows students to break apart numbers and add the tens and the ones separately Students should know how to write numbers into expanded form and understand that the number 43 is the same as writing 40 and 3.
For the final strategy I teach the front end strategy. Students look at the question and borrow from one number and add it to the other number to change the question to an easier question with friendly numbers. Students learn with this strategy that there are many ways to write the same question. 59+43= is the same as 60+42= . This flexible thinking about questions is an important strategy to use in math. I always tell my students that they should make their brain work smarter not harder.
How to Practice
I teach math every morning and students start their day with a Daily Math Sheet. This is a daily page that can be used every day. I start the day with a new number of the day which students use to answer the questions on the morning math page. Follow the link to download it free from my TPT store.
I have included it here as a freebie for a limited time.
First 250 downloads are free!!!
I will also included a link to my smart notebook file that I use to teach these strategies along with a few others. Just trying to work a few kinks out.
Hope you enjoyed by first Monday Math Mania!!!