Middle School Tasks for Reasoning and Reflection

Part of

The MATH R.U.L.E.S of Engagement

September 29, 2015

Gwendolyn Best

DIRECTIONS: For each incorrect answer, explain why a student might select it as the correct answer. For the correct answer, prove it using words and/or symbols.

Virginia DOE - Grade 6 -2014 RT Item -- Clipart Added

A bag contains red apples and yellow apples. The ratio of red apples to yellow apples in the bag is 9 to 4. Which of these statements could be true?

A. There are exactly 6 red apples and 1 yellow apple in the bag.B. There are exactly 18 red apples and 8 yellow apples in the bag.C. There are exactly 4 red apples and 9 yellow apples in the bag.D. There are exactly 9 red apples and 13 yellow apples in the bag.

Can the use of error analysis as a teaching tool promote reflection, inquiry, critical thinking, diverse reasoning strategies?

Error Analysis

A C

B D

Virginia DOE - Grade 6 -2008 RT Items 2 and 6

DIRECTIONS: For each incorrect answer given in these two items, explain why a student might select it as an answer choice.

AGrade 6

Virginia DOE - Grade 6 -2010 RT Items 23 and 45

DIRECTIONS: For each incorrect answer given in these two items, explain why a student might select it as an answer choice.

BGrade 6

Virginia DOE - Grade 7 -2010 RT Item 2

In the space provided, show the mathematics for the correct answer. Give an explanation of a mistake a student makes or misconception a student has that would lead to selection of each incorrect answer choice.

F G

H J

C

Grade 7

Virginia DOE - Grade 7 -2010 RT Items 9 and 19

DIRECTIONS: Select the correct answer for Item 9. On the back of this sheet, use sentences or labels for the numbers and variable to prove the proportion is set up correctly. Next, for both items, explain why a student might select each incorrect answer instead of the correct one. Finally, work out Item 19 on the back of this sheet.

DGrade 7

Virginia DOE - Grade 87 -2010 RT Items 11, 27, and 46

DIRECTIONS: For each incorrect answer given in these two items, explain why a student might select it as an answer choice.

EGrade 8

FDIRECTIONS: For each incorrect answer given in this item, explain why a student might select it as an answer choice.

Grade 8