Turn Fractions Into Visuals

Growing up I was taught math in the traditional way.  The teacher gave me some symbolic notation such as 1/2 * 1/4 and then gave me a step-by-step process to follow to the solve the problem, and then we moved on to the next thing with more notation and procedure.  At ANI they present how that should be just one of three approaches.  We need to add in visual models and real world situations and experiment with starting in one of those modes instead.

Attached is a worksheet "Operations with Fractions" that asks the student to make pictures out of fraction problems.  Take a look, give it a try and reflect on how it goes.

Match up Fractions on the Number Line

This week I'm spending two days in Des Moines for the Adult Numeracy Institute.  The focus is on number sense (fractions, decimals and percents) and Data, Statistics, and graphs.  I enjoyed the first warm-up activity that was a match up.  This activity could be tailored to any level of math learner.   The directions are as follows:

Beforehand, the facilitator creates pairs of cards with equivalent values (for example 1/4 and .25 would be paired cards or 1/8 on one card and a picture of 8 connected bars with one bar shaded in on its match).  You can make the task more difficult by using pairs of more complicated numbers or concepts such as having the golden ratio on one card and 1.61803398875 on another.

1. When you get to class, hand out one card to each student
2. Students then find the person in the room that has the equivalent card
3. Once they find their partner, they go to the board and place their cards on a number line
4. Facilitate a discussion about how they know the cards are equal
5. Since this activity has an anonymous factor it's safe to discuss whether cards are placed correctly and then move them if needed

Doing this activity gets students out of their seats and thinking.  They have to talk to each other to problem-solve what constitutes a match, and then they have to conceptually understand where the numbers belong on a number line, which prepares them for more advanced math down the road.  Any errors in mathematical thinking are quickly corrected in a safe environment.