Hello blog followers,
Today, I am not working with AnnaMarie. From now on, we will meet once per week to plan together for our action research project and to coteach.
Today, I was working with a grade 3 and 4 teacher to plan a mental math lesson. She is concerned that her students (like many students) lack mental math skills. In addition, they don't have knowledge of basic single digit addition facts. We had a great discussion about how to tackle this problem. Our conclusion was that we need to do two things.
First, we need to provide opportunities for students to think about numbers in new ways so that they can solve problems mentally. We want them to realize that numbers can be manipulated to make a problem easier to solve, as long as you "undo" the changes at the end. For example, 100  59 could be thought of as 99  59 = 40 + 1. The answer is 41; no regrouping required!
Secondly we need to motivate the students to learn their single digit addition facts. This can be done through drill games, incentives for learning them, assigning practice for homework etc... (Suggestions would be much appreciated!)
Since it is not yet possible to attach file to this blog, I am including the lesson that we planned right in the blog post. It may change before we actually teach it together later this week, but this will give you the gist of it. Sorry it's so lengthy!
Math at ya!
Melanie
Numeracy Lesson Planning Template
Grade: 3/4

Strand: Number Sense and Numeration 
Big Ideas/Key Concepts For The Lesson
BIGWNO5: there are a variety of appropriate ways to estimate sums depending on the numbers involved and the context. Estimates are useful for checking and sometimes all that is needed. (Big Ideas from Dr. Small, Grades K  3)
BIGWNO2: There are many situations to which an operation applied and there are many procedures, or algorithms, for each operation. (Big Ideas from Dr. Small, Grades K  3)
If you aren't already using this book, you have to get it!!!

Curriculum Expectations
3.1 add twodigit numbers, using a variety of mental strategies
3.10 use estimation when solving problems involving the addition of whole numbers

Description of the Problem/Task
Students will be required to use mental math skills to facilitate the adding of numbers that would require regrouping when using the traditional algorithm.

Manipulatives/Materials/Resources Required
Counters, base ten blocks, paper, marker

Before
Getting Started (510 min)
Students will be asked to raise their hand as soon as they know the answer to 9 + 5. They will be told to make sure that they have the answer before raising their hand, since they may be called on to give the answer. Some students will be asked how they figured out the sum so quickly. We will record the various mental math strategies on the board.

During
Working on It (2530 min)
Question 1: What mental strategies can you use to add 59 and 31. Show your work and explain your thinking.
Question 2: What mental strategies can you use to add 19 and 11. Show your work and explain your thinking.
Students will work in groups of two to solve the problem. They will be instructed to show on chart paper, the mental steps that they took to solve the problem. Students will be given the option of solving question 1 or 2, depending on their comfort level with numbers. Students who solve one question and still have time will be encouraged to solve the second question.

After
Consolidation and Practice (1520 min)
The BANSHO will be organized to bring out the following highlights. An anchor chart of mental math strategies will be created.
Highlights
If students come up with other strategies for mental addition, they will be added to the highlights.
 You can use benchmarks numbers for convenience (multiples of 10)
 Mental computation is considering which representation of a number is most useful
 To add two numbers, you can take away from one number and add what you took away to the other number without changing the sum
 You can add or subtract in parts
 To subtract two numbers, you can add or subtract the same amount to or from both numbers without changing the difference
 You can change numbers to make a problem easier to solve, as long as you “undo” the change. (e.g. 10059 could be 9959, and then add the 1 back at the end. This eliminates regrouping.)
many of these ideas are also from the Dr. Small book
Practice Questions:
78 + 21 67 + 32 89 + 41
