Using a Ratio Table

The students will be using a variety of mental math strategies in completing this set of questions.  These problems can help assess students’ mental computation abilities.  The problems should be done as a class and read aloud so that students solve them mentally and can discuss their strategies.   When observing student strategies, you should expect to see them devising shortcuts to help them add/subtract numbers mentally.  As an extension, the students can explain their strategy for each problem.  (SMP 2 and 6)

The students will be identifying two ways to solve a problem.  Strategies may include skip counting, multiplying or dividing.  The object here is to get students to understand that there are multiple ways to solve one problem. (SMP 1 and 3)  

In this section, students will be looking at ratio tables to decide what steps were taken to get to the answer.  The students will be using adding, times 10, doubling, halving, subtracting and multiplying as some of their strategies.  Each slide shows the intermediate steps that were used.  Then, allow the students time to look at 2 problems to discover the steps used to solve it. (SMP 4)

The students will be working in groups and using ratio tables to solve problems using a Showdown.  Each student will work on the problem independently and then show their tablemates their strategies.  Students should be allowed to explain their strategy while others in the group listen and then critique as needed.(SMP #3) When all students have been given the opportunity to  explain their strategy, call a random student from each group to show their answer and explain.

Students may struggle with coming up with the initial ratio.  If this happens, have the students tell you what they know about the problem.  For example, if roses are sold in boxes of 15, what does that tell us about our ratio?  How many numbers do we need to begin with? If I have 1 box, how many roses to do I have? (SMP1 and 2)

I want to know if students really understand how to use a ratio table.  I’m going to have them create their own examples for each of the following approaches:

Adding

Doubling

Subtracting

Times 10

Halving

Multiplying

If time permits, I’m going to have them come up with other approaches to use when filling in a new column.  (x3,x4,x5 etc).  I would like them to say that the approach you use will depend on what you are trying to find.  If you know your multiplication facts then it would be good to use multiplication.  If you are not so good at them, then easier multiplication or addition would be best.