Problem: If a He + He + Ha is 10 and a Ha + Ha + He is
11,
How much is a He + He + He?
Math Topic/Concept: Algebra
Classroom Use: (Introductory)
Classroom use comments: Algebra unit after they have been introduced to symbolic representations and variables.
Grade: 6-8
Grade Cluster: (MS-Jr.High)
Illinois Goal: 6 and 8
Standard: 6.C.3a and 8.D.3a
Source: Awesome Math Problems for Creative Thinking
(Creative Publications)
Grade 6-8 ISBN 0-7622-1285-3
Answer: 9
Strategies Listed: Guess and check or Logical Reasoning
Solution: Since He + He + Ha is 10 and Ha + Ha + He is 11, then the sum of He + He + Ha and Ha + Ha + He is 21. That means 3 He=s and 3 Ha=s are 21, so He + Ha must be 21 divided by 3, or 7. If He + Ha is 7, and He + He + Ha is 10 then the extra He must be a 3. That means He + He + He is 3 x 3, or 9.
Extensions or related problems: Have the student make up their own similar problem and share with a partner.
Write-up submitted by: Jenni Robinson and Denise Mann
Problem: When a stone is thrown into a calm body of water,
it produces a ripple effect of larger and larger concentric circles.
In this activity, you will investigate a similar kind of ripple effect
using pattern block shapes. What patterns can be discovered in a
sequence of ripples?
· Work with a partner. Use a pattern block rhombus shape
as the “stone”, and completely surround your stone with blocks of the same
shape as the first “ripple.” Record your design. Color it using
one color for the original stone, and another color for the first ripple.
· Surround your first ripple with more blocks of the same shape
to form the second ripple. Make sure the entire perimeter of the
ripple is surrounded with new blocks. Record your new design and
color the new ripple a different color.
· Predict how many stones it will take to form the third ripple,
and record your prediction.
· With each new ripple, record the number of blocks in the new
ripple, the total number of blocks used in the design, and the perimeter
of the ripple design.
· Continue these steps up to the sixth ripple.
· Look for patterns in your results. Write an algebraic
expression to generalize your findings.
Math Topic/Concept: growth patterns, sequences, algebraic expressions
Materials: pattern blocks, pencil, paper, crayons or markers
Classroom Use: (Developmental)
Grade: 7-8
Grade Cluster: (MS-Jr.High)
Illinois Goal: 8: algebra
Standard: 8A3b, 8D3a
Applied? (1-4): 2
Source: Super Source: 7-8, Patterns/Functions; Cuisenaire,
1998. ISBN: 1-57452-173-X
Answer: rhombus:
Ripples: blocks added: total blocks: perimeter
1
4
5
12
2
8
13
20
3
12
25
28
4
16
41
36
5
20
61
44
6
24
85
52
n
4n 4[n(n + 1)/2]
+ 1 8n + 4
Strategies Listed:
Solution: The total number of blocks, number of blocks added,
and perimeter are all functions of the number of sides of the polygon as
well as the number of ripples.
Other solution methods (if any)*:
Extensions or related problems*: Continue the investigation with triangle and hexagon pieces, noting patterns and relationships.
Intended rubric or assessment method: ISAT “student friendly” rubric
Write-up submitted by: M.K. Robbins
Problem: Kelly wanted to send a letter to her best friend after she moved. Her friend emailed back the following clues for her zip code. (she loves math J). Find her ZIP, Please. Explain why you think your zip code is correct. Further justify your answer by substituting values into clues 4-7.
___ ___ ___ ___ ___ - ___ ___
___ ___
a b
c d e
f g h
i
1. Each of the digits is used only once.
2. b, c, e, and f are powers of 2.
3. f, g, and h are powers of 3
4. b * c = e
5. h^b = g
6. d > i
7. i – h = g – d + a
Math Topic/Concept: Algebra
Classroom Use: (Developmental)
Classroom use comments*: Use after introduction to Algebra
(review powers)
Have you ever solved a problem like
this before? Which clue helped you get started?
Grade: 7
Grade Cluster: (MS-Jr.High)
Illinois Goal: 8
Standard: 8.D.3a.
Applied? (1-4): 2
Source: Awesome Math Problems for Creative Thinking (Creative
Publications)
Grade 8 ISBN
0-7622-1287-X
Answer: 02478-1935
Strategies Listed: Logical Reasoning, Algebraic Thinking Processes, Computation
Solution: Using the clues you can start finding possibilities.
(b,c, e, and f must be either
1,2,4, and 8) You continue with the clues to determine the answer.
In order for f to be a power of 2 and 3 it must be 1. Since b
times c equals e the only possibilities are 2 times 4 equals 8.
Other solution methods (if any)*: i – h = g
– d + a
5 – 3 = 9 – 7 + 0
2
= 2
Extensions or related problems*: Lower level: use
a five-digit zip code.
Write a new problem that is new is some ways but the same in others.
Intended rubric or assessment method: Teacher discretion for answer and explanation.
Write-up submitted by: Denise Mann and Jenni Robinson
James R. Olsen, Western Illinois University
E-mail: jr-olsen@wiu.edu
updated June 27, 2001