Reply To: Lesson 4-1: The Stages of Mastery Action

[Amy Rensko]

Concept: Solve problems using equivalent ratios.

Problem: There are 5 apples and 4 oranges in each fruit basket. The fruit baskets contain a total of 100 apples. What is the total number of oranges in the fruit baskets?

Unconsciously Incompetent: Students may draw out (or skip count) groups of 5 apples and 4 oranges until they have a total of 100 apples and 80 oranges. This is an additive strategy.

Consciously Incompetent: Students continue with a additive strategy like in stage 1. Perhaps they organize their skip counted numbers of fruits in a table.

Consciously Competent: Students begin to use a multiplicative strategy but not the most efficient one. Maybe they multiple 5 apples by 10 to get 50 apples then multiply by 2 to get 100 apples. Then, do the same multiplication steps with the number of oranges to arrive at 80 oranges.

Unconsciously Competent: Students move to a more efficient multiplicative strategy. Such as: 5 apples x 20 = 100 apples so there must be 20 fruit baskets. So, 4 oranges x 20 = 80 oranges.

<b style=”font-family: inherit; font-size: inherit; color: inherit;”>Consciously Masterful: Students continue a multiplicative strategy but use equivalent ratios to find the answer. 5 apples/4 oranges = 100 apples/80 oranges.

[Amy Rensko]

Concept: Solve problems using equivalent ratios.

Problem: There are 5 apples and 4 oranges in each fruit basket. The fruit baskets contain a total of 100 apples. What is the total number of oranges in the fruit baskets?

Unconsciously Incompetent: Students may draw out (or skip count) groups of 5 apples and 4 oranges until they have a total of 100 apples and 80 oranges. This is an additive strategy.

Consciously Incompetent: Students continue with a additive strategy like in stage 1. Perhaps they organize their skip counted numbers of fruits in a table.

Consciously Competent: Students begin to use a multiplicative strategy but not the most efficient one. Maybe they multiple 5 apples by 10 to get 50 apples then multiply by 2 to get 100 apples. Then, do the same multiplication steps with the number of oranges to arrive at 80 oranges.

Unconsciously Competent: Students move to a more efficient multiplicative strategy. Such as: 5 apples x 20 = 100 apples so there must be 20 fruit baskets. So, 4 oranges x 20 = 80 oranges.

<b style=”font-family: inherit; font-size: inherit; color: inherit;”>Consciously Masterful: Students continue a multiplicative strategy but use equivalent ratios to find the answer. 5 apples/4 oranges = 100 apples/80 oranges.