## Monday, June 17, 2013

### Bar Model Session at The Bolles School (K-2 Session)

In this class we discussed four problems and what if versions to challenge advanced learners.

See the problems here.

Solution to Problem 1 - this is grade three problem and a grade two version can be crafted from this. Ali had 17 more coins in the end.

Without drawing, some students ended up with 13 more coins. Model drawing allows students to capture complexities of situations (in this case that Billy's number of coins is reduced by 4 in the process).

A Grade 2 version - At first, Ali had 9 more coins than Billy. Billy had 7 coins and he then gave Ali 4 coins.

Problem 2 is a typical two-step word problem in Grade 2. A what if version for advanced learners - What if together Cindy and David has 15 candies (instead of Cindy has 15 candies.). The class decided that it was probably not possible because candies do no come in fractional parts but the problem is okay if it was about Hersey bars or cupcakes.

 Problem 2 Extension: What if .. total number is 15? Is it possible?
 Problem 3

 What if she ended up with five times as much money as him?

 Problem 5 Solution

In Problem 3, which requires advanced techniques of cutting and moving the bars, we did a problem extension. What if .... After Feliz gave Ginny \$12, Ginny had 5 times as much money as Feliz (instead of the same amount)?

A Grade 2 version that is accessible even by average and struggling learners: Feliz had three times as much money as Ginny. After Feliz gave Ginny \$12, they both had the same amount of money.

In Problem 4, we talked about what by Saturday meant. The class could not decide, so we tried both scenario of the fact that by Saturday meant she had folded 50 paper cranes on Monday to Friday as well as she had folded 50 cranes on Monday to Friday (but 50 is not a possible total given that cranes do not come in fractions).

The class continues on Day 2. These classes is a two-hour course on advanced skills in bar model drawing for K-2 teachers. Typically, bar models are used in Grade 2 onwards. Younger students model with pictures or unit diagrams.