Algebraic Thinking for 6 and 7 year olds? ABSOLUTELY!

This week in math, we’ve been talking about “growing patterns”. Part of having a good number sense is to see patterns, and to be able to extend them. It is also good practice for algebra. Today, we did an algebraic exercise called Tables and Chairs.

We started on the rug, as we often do. I showed the children little squares and said that these represented tables in a restaurant. Using beans for chairs (or people, however they wanted to think about it). I asked how many could fit around a table. The answer was 4. I added a table to our “restaurant”, and children told me that now 8 chairs would be needed. I added a third table, and some children said, “16” and some said “12”. Some children immediately thought that since we doubled the number the first time, then we would keep doubling. Others knew that we were just adding 4 each time. We talked about this as either a repeated addition problem or a multiplication problem. A restaurant with 24 chairs could fit 96 people, and we would know this by simply knowing to multiply by 4.

Then I posed this trickier problem. I told the children that restaurants often have different sized tables to accommodate different sized groups of people - but the restaurant I was thinking of only had these small square tables.  Immediately, the children knew that restaurants "squish the tables together". So, the question - If two square tables were squished together how many chairs could you have? "Eight!" came one response. "No, Seven!" “No, Six!”

Using the squares and beans, children went to their desks to explore this growing pattern. Each time they squished a new table to the line of tables, they found they could add two more chairs. I drew a chart to collect our data, and we noticed a pattern in the chairs column - each time a table was added, 2 more chairs could be added. Children copied this chart down and then extended it, some making it to 20 tables and beyond. Some children relied completely on making the tables and chairs, and some figured out that they didn’t really need the manipulatives; rather they could just use paper. We didn’t QUITE get to the point where we could just figure the problem by a formula – like, C = (T X 2) + 2, but some came pretty close to articulating this.

We will keep working on this type of activity, and continue to talk it through.