Problem:  Suppose Peter wants to order 45 pounds of soil.  He can order the soil in 10-pound bags or 1-pound bags.  How many ways could he order the soil?

Math Topic/Concept:  Place value, patterning.

Materials:  paper and pencil/place value blocks

Classroom Use: (Introductory/Developmental/Evaluation)

Classroom use comments*: Students may need help developing a table to solve this problem.

Grade:  3

Grade Cluster: (EarlyElem/LateElem/MS-Jr.High/EarlyHS/LateHS)

Illinois Goal:  8

Standard:  8.A.1a

Applied? (1-4):  3

Source:  Scotts Foresman-Addison Wesley, grade 3

Answer:  Five ways.  4 ten pound bags and 5 one pound bags,  3 ten pound bags and 15 one pound bags, 2 ten pound bags and 25 one pound bags, 1 ten pound bag and 35 one pound bags, 0 ten pound bags and 45 one pound bags.

Strategies Listed:  make a table, look for a pattern

Solution: See answer.
 

10-lb bags	4	3	2	1	0
1-lb bags	5	15	25	35	45
Total # of bags.	9	18	27	36	45

Extensions or related problems*:  Change the order to 50 pounds of soil.  He can order in 10 pound or 5 pound bags.

Intended rubric or assessment method: ISAT rubric

Write-up submitted by:  Diana Kent

Problem:  Mary, Jacob, Paul, and Terry come to school in different ways.  One rides a bicycle, one comes by bus, one rides on a ferryboat, and one walks.
> Terry crosses a river to get to school.
> Jacob doesn't ride to school.
> Mary sits next to her sister on the way to school.
In what way does each child come to school?

Math Topic/Concept:  Logic, reasoning.

Materials:  Paper and pencil.

Classroom Use: (Introductory/Developmental)

Grade:  3

Grade Cluster: (EarlyElem)

Illinois Goal:  8

Standard: 8.A.1

Applied? (1-4): 1

Source: The Problem Solver 3, Creative Publications, 1987.

Answer:
> Mary - bus
> Jacob - walks
> Paul - bicycle
> Terry - ferryboat

Strategies Listed:  Make a table. Draw a picture.  Use logic.

Solution:
 

	bicycle	bus	ferryboat	walk
Mary	no	yes	no	no
Jacob	no	no	no	yes
Paul	yes	no	no	no
Terry	no	no	yes

Intended rubric or assessment method: Informal assessment.

Write-up submitted by:  Diana Kent

Problem:  Look for a pattern in the shapes.  Can you draw the shapes that belong in the empty boxes?
 
 

Math Topic/Concept:  Patterning

Materials:  work sheet, shape blocks

Classroom Use: (Developmental/Evaluation)

Classroom use comments*:  There is a pattern in the rows, the columns, and diagonally.
This is a challenging pattern problem for third grade.

Grade:  3

Grade Cluster: (EarlyElem)

Illinois Goal:  8

Standard:  8.A.1a

Applied? (1-4):  1

Source:  The Problem Solver 3, Creative Publications, 1987.

Answer:  Line one –  circle, triangle, square, circle, triangle
     Line two – triangle, square, circle, triangle, square
     Line three- square, circle, triangle, square, circle
     Line four – circle, triangle, square, circle, triangle
     Line five_ triangle, square, circle, triangle, square

Strategies Listed:  Look for a pattern.

Solution:  See answer.

Write-up submitted by:  Diana Kent
 

James R. Olsen, Western Illinois University
E-mail: jr-olsen@wiu.edu
updated June 27, 2001