example-based math assignments for 4th and 5th graders

COMING SOON

Getting Started

1. Familiarize yourself with the materials.

  • Assignments are grouped by topic, but individual assignments can be used in any order that you find appropriate.
  • Teachers usually determine in advance how MathByExample assignments align with their district math curriculum for Grades 4 and 5.

2. Plan how to orient your students to the materials.

  • Your students may not immediately understand how to complete the exercises. Make sure they know that they will be looking at both correct and incorrect examples of work done by "other students" and answering questions about that work.

3. Consider how to allot time.

  • Assignments are generally designed to take approximately 15-20 minutes. But you may decide to use an assignment over two days or to use two assignments in one day. There may be weeks where none of the assignments align to what you're teaching but other weeks when many of the assignments will fit well. MathByExample is designed to fit flexibly into your classroom without changes in the content you teach.

Various Uses

Teachers use MathByExample assignments in various ways throughout the year.

  • Warm-up / do now
  • Exit ticket
  • Homework
  • During centers
  • Formative assessment
  • Review before a unit test (or standardized testing)

You may decide to have students work on the assignments:

  • Independently With partners
  • In groups

We also encourage you to review the assignments with your class after the students have finished to provide further opportunities for students to process and discuss the targeted misconceptions.

Addressing Frequent Student Errors
(and how MathByExample can help!)

Number:

Confusing factors and multiples

see gr X, p XX

Considering all odd numbers to be prime

see gr X, p XX

Difficulty conceiving of decimals and fractions as quantities less than one

see gr X, p XX

Difficulty with navigating decimal place values

see gr X, p XX

Not relating fractions and decimals to one another

see gr X, p XX

Trouble understanding that there are infinite numbers between each number of the number line

see gr X, p XX

Mishandling empty decimal place values, for example using 3.05 in place of 3.5, or thinking that 1.459 is greater than 1.5

see gr X, p XX

Errors representing whole numbers in fraction form

see gr X, p XX

Confusion with comparing fractions such as 5/6 and 2/3 by thinking that they are just "one away" from the whole

see gr X, p XX

 

Operations with Whole Numbers:

Subtracting the "wrong" direction - for example 2 – 6 = 4

see gr X, p XX

Difficulty reconciling subtraction conventions with negative numbers - for example, think you "can't" subtract larger from smaller

see gr X, p XX

Inaccurately subtracting from numbers with zeros

see gr X, p XX

Reversing dividend and divisor when dividing

see gr X, p XX

Selecting incorrect operation to use in word problems

see gr X, p XX

Forgetting procedures within the long division algorithm

see gr X, p XX

 

Operations with Fractions and Decimals:

Trouble predicting that multiplying a whole number and a fraction would produce a smaller number

see gr X, p XX

Overusing factors for "canceling"

see gr X, p XX

Not using reciprocals of fractions correctly

see gr X, p XX

Not using "remainder" withing division word problems sensibly

see gr X, p XX

Trouble adjusting mixed numbers when subtracting - for example 21/4 – 12/4

see gr X, p XX

Misplacing decimal point when multiplying decimals

see gr X, p XX

Challenges depicting division of fractions (or fraction by whole number) with models

see gr X, p XX

Adding the denominators of two fractions when finding sums

see gr X, p XX

Needlessly applying the process of finding a common denominator for multiplication or fractions

see gr X, p XX

Incorrectly representing remainders as decimals - for example thinking that 14 R3 and 14.3 are the same

see gr X, p XX

 

Geometry & Measurement:

Using linear, area, and volume units incorrectly - for example inch, square inch or cubic inch (in, in2, in3)

see gr X, p XX

Difficulty with properties of kites and other quadrilaterals

see gr X, p XX

Trouble converting basic metric measurements - such as meters and centimeters

see gr X, p XX

Incorrectly adjusting quantities of time from decimal to hours/minutes - for example 5.5 hours = 5 hours, 30 minutes (not 5 hours, 5 min or 50 min)

see gr X, p XX

Unable to solve for unknown angles by considering inherent properties

see gr X, p XX

Development of MathByExample was led by Julie Booth (Temple University) through a SERP collaboration with several school districts. The collaboration has been supported to conduct this work by the Institute of Education Sciences, U.S. Department of Education, through Grant R305A150456 to Strategic Education Research Partnership Institute. The information provided does not represent views of the funders

 

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