Procedural Plan with Student Thinking and Pitfalls Comparison

**1) Grade Level:** 4^{th} Grade

**2) Performance Expectations:**

4.2.B Read, write, compare, and order decimals through hundredths.

4.2.D Convert a decimal to a fraction and vice versa, and visually represent the number.

4.2.I Solve single- and multi-step word problems involving comparison of decimals and fractions (including mixed numbers), and verify the solutions.

3) Objective: The students will translate word problems to fractions, and convert fractions to decimals

**4) Math Words:**

Fraction: A number that compares part of an object or a set with the whole.

Numerator, denominator, part-whole: A number written with the bottom part (the denominator) telling you how many parts the whole is divided into, and the top part (the numerator) telling how many you have.

Operator: A function, especially one from a set to itself, such as differentiation of a differentiable function or rotation of a vector.

Decimal (also known as decimal fraction): A representation of a real number using the base ten and decimal notation

Point: A geometric object having no dimensions and no property other than its location.

Numeral and Digit: A numeral is a sequence of digits, which may be of arbitrary length. Each position in the sequence has a place value, and each digit has a value.

**5) Starter Problem:**

There are ten tables in the class. Students sitting at tables 2, 3, 4, 5, 6, 7, & 8 are reading while the students from table 1 are in the library, and the students from tables 9 & 10 are making up a science project. What is the ratio of tables reading? Show your answer in a fraction and a decimal. Please show and explain your work.

**6) Student Thinking:**

**OK** – Mary: I used Base Ten Blocks to count 7 out of 10 tables reading, so that is 7/10. This could also be written as 0.7.

**Pitfall**– Johnny: There were 10 tables and 3 weren’t doing reading, so I counted down three times (10, 9, 8) this means that there were 8 out of 10 tables reading, which is 8/10 and that is the same as 0.8.

**7) Our Turn: **

During small group discussion have Mary work with Johnny to count out the Base 10 blocks to get 7 out of 10. Then have them line up 10 blocks, and take away 3 to see where Johnny made his mistake. Have them work on double checking their math by using different strategies.

**8) Your Turn:**

Have the students work on using different manipulatives to solve similar problems, and provide more friendly fractions to build confidence and knowledge base.

Sample question:

As a whole there are ten computers in the class, but six are broken. What is the number of the computers that are working? What is the fraction for the working computers? Convert the fraction to a decimal, and show and explain your work.