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TM    Solve It  2nd  Problem-Solving Strategies is a collection of activities designed to introduce young children to nine...
nd I t   e 2 v l   So  Developed and Published by  AIMS Education Foundation  SOLVE IT  2nd  i     2008 AIMS Education Fou...
TM  This book contains materials developed by the AIMS Education Foundation. AIMS  Activities Integrating Mathematics and ...
I Hear and I Forget, I See and I Remember, I Do and I Understand. -Chinese Proverb  SOLVE IT  2nd  iii     2008 AIMS Educa...
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nd I t e   v 2 l So    Introduction ............................................ vii Problem-Solving Strategies .............
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Solve It  2nd  Problem-Solving Strategies is a collection of activities designed to introduce young children to nine probl...
SOLVE IT  2nd  viii     2008 AIMS Education Foundation
Suitcase Solutions Adding Up Arrays Shaping Up Symmetry Domino Designs Puzzling Patterns Pondering Patterns  x x x  x x x ...
The guess and check strategy is helpful when a problem is complicated, has large numbers or a lot of data, or when the pro...
Topic Geometry  composing shapes  Background Information This activity makes use of the popular tangram puzzle in a new wa...
3. In order for students to record their solutions, cut out a large supply of tangram pieces from colored paper using the ...
Copy this page onto card stock and laminate for durability. Each student will need two sets of tangram puzzles.  SOLVE IT ...
Fill in the suitcases with tangram pieces. Find as many ways as you can.  SOLVE IT  2nd  5     2008 AIMS Education Foundat...
SOLVE IT  2nd  6     2008 AIMS Education Foundation
Name  Name  Name  Name  SOLVE IT  2nd            7     2008 AIMS Education Foundation
Name       Name  SOLVE IT  2nd  8     2008 AIMS Education Foundation
Name       Name       Name  SOLVE IT  2nd  9     2008 AIMS Education Foundation
Name       Name  SOLVE IT  2nd  10     2008 AIMS Education Foundation
Topic Problem solving, addition  Background Information Mathematical microworlds are problems that are governed by simple ...
6. Assign a second target sum for the array. Have students find as many solutions as they can for this new sum. 7. Continu...
Target Sum SOLVE IT  2nd  13     2008 AIMS Education Foundation
SOLVE IT  2nd  Sum  Sum  Sum  Sum  Sum  Sum 14     2008 AIMS Education Foundation
Target Sum SOLVE IT  2nd  15     2008 AIMS Education Foundation
SOLVE IT  2nd  Sum  Sum  Sum  Sum  Sum  Sum 16     2008 AIMS Education Foundation
Target Sum SOLVE IT  2nd  17     2008 AIMS Education Foundation
SOLVE IT  2nd  Sum  Sum  Sum  Sum  Sum  Sum 18     2008 AIMS Education Foundation
Target Sum  SOLVE IT  2nd  19     2008 AIMS Education Foundation
SOLVE IT  2nd  Sum  Sum  Sum  Sum  Sum  Sum 20     2008 AIMS Education Foundation
Topic Geometry  symmetry  Background Information Pattern blocks are a common manipulative in the primary classroom, and ca...
3. Ask them to identify the lines of symmetry that exist in this shape. Tell them that they need to look at the colors and...
Challenge Two  3 trapezoids, 3 blue rhombuses, 1 triangle Challenge Three  1 hexagon, 1 trapezoid, 2 blue rhombuses, 3 tri...
                 Fill the frame with pattern blocks. Record each solution you find. Count the lines of symmetry in your so...
SOLVE IT  2nd  25     2008 AIMS Education Foundation  ___________ Lines of Symmetry  ___________ Lines of Symmetry  Record...
                 Fill the frame with pattern blocks. Record each solution you find. Count the lines of symmetry in your so...
Record your solutions. Count the lines of symmetry. Challenge  __________________  ___________ Lines of Symmetry  ________...
                 Fill the frame with pattern blocks. Record each solution you find. Count the lines of symmetry in your so...
Record your solutions. Count the lines of symmetry.  Challenge  __________________  ___________ Lines of Symmetry  _______...
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Patterns are pervasive in our world. At an early age, children begin to recognize and identify patterns all around them. L...
DOMINO DESIGNS repeating patterns can easily be created, and students will benefit from seeing the wide variety of possibi...
5. Encourage students to create as many different patterns as they can using the dominoes and not to be limited to pattern...
SAMPLE DOMINO PATTERNS Following are a few examples of the many, many patterns your students may create using their domino...
DOMINO DESIGNS DOMINO TILES  SOLVE IT  2nd  35     2008 AIMS Education Foundation
DOMINO DESIGNS Choose any six dominoes from your set. Make a pattern. Record your pattern.  My Domino Pattern  Make some n...
DOMINO DESIGNS Study the pattern below.  What is missing from this pattern  Find the missing domino in your set. Complete ...
This activity provides an opportunity for students to explore and identify the patterns contained in a hundreds chart and ...
be found on the chart,  top left side, bottom right part, etc.  When the class can recognize that it is a part of the whol...
15 25  51 37  17  62  19  27  1 30  66  11  13  67 48  86  50 59  35 47 SOLVE IT  2nd  40     2008 AIMS Education Foundati...
62  23 35  37 84  74  64 76  47 81 64 SOLVE IT  2nd  92 41     2008 AIMS Education Foundation
1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33 ...
Topic Patterns  Materials Mr. Noisy   s Book of Patterns  see Curriculum Correlation  Pattern task cards  see Management 3...
5. Using sentence strips, create several patterns for the students to identify and extend. Below is a suggested set of pat...
What would this pattern look like in letters  __________________________________________    in colors  ___________________...
What patterns can you make with only  s   What comes next   SOLVE IT  2nd  46     2008 AIMS Education Foundation
SOLVE IT  2nd  47     2008 AIMS Education Foundation  How many rug patterns can you make with 2 kinds of bugs   Draw the m...
1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16  Centimeters  1  2  3  4  5  6  Inches  SOLVE IT  2nd  48     2008 AIMS Edu...
It is often helpful for young children to manipulate objects or act out a problem to arrive at a solution. Using concrete ...
understand a group or set fraction model, it is important for them to act out a problem or to move objects around while th...
    Place five fish in the bowl. One-fifth of them should be green and the rest should be yellow. How many fish are yellow...
SOLVE IT  2nd  52     2008 AIMS Education Foundation
SOLVE IT  2nd  53     2008 AIMS Education Foundation
Color these fish red, orange, yellow, green, and purple.  SOLVE IT  2nd  54     2008 AIMS Education Foundation
students have a good understanding of the numbers 0-9 and the sets that they represent prior to participating in this less...
    Make the numbers 189 and 234. Which one is greater  Use a greater than, less than, or equal to sign to show the relati...
5 6 7 8 9  0 1 2 3 4 SOLVE IT  2nd  57     2008 AIMS Education Foundation
Topic Measurement  Problem-Solving Strategy Use manipulatives  Key Question How can we use square, fruit-flavored candy to...
4. Ask students to choose two birthday cards and determine the heights and widths of their cards in candy units. Have the ...
Part One   Height and Width  Card One Height  _____ Width  _____ Card Two Height  _____ Width  _____ Write about the measu...
Part Two   Area  Trace the cards you chose on the back of the paper.  The area of my first card is ______ square candy uni...
Part Three   Perimeter  The perimeter of ____________   describe what you measured   is ________candy units.  We measured ...
SOLVE IT  2nd  63     2008 AIMS Education Foundation
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Drawing a picture is an effective problem-solving tool for young children. This strategy allows them to    see    the prob...
Management 1. Copy one set of the counting cards onto transparencies to be used on the overhead. 2. The counting clue card...
SOLVE IT  2nd  67     2008 AIMS Education Foundation  How many fingers do two boys and a little girl with blond hair have ...
SOLVE IT  2nd  68     2008 AIMS Education Foundation  Six nests. The first three nests have three eggs. The other three ne...
SOLVE IT  2nd  69     2008 AIMS Education Foundation  Three blind mice. How many tails   Four bears. How many noses   How ...
SOLVE IT  2nd  70     2008 AIMS Education Foundation  Two ducks and three dogs. How many legs   How many hands on four clo...
Topic Problem solving  Management 1. Because of the abstract nature of the riddles, students will likely want to draw out ...
The red apple has fewer than 10 seeds and more than 8 seeds. How many seeds does the apple have   The number of apples on ...
The number of trees in the orchard is more than 20, but less than 30. Both of the digits in the number of trees are the sa...
Topic Problem solving  Procedure 1. Read a problem to the class. You may also wish to write it on the board so that studen...
When dealing with word problems or similar challenges, it is often beneficial to simply write down the numbers and operati...
Topic Problem solving  Background Information Sometimes one of the most useful problem-solving strategies is to simply wri...
4. Ask the class how many shoelaces are in the picture. Invite a student to come to the board and write the number sentenc...
SOLVE IT  2nd  78     2008 AIMS Education Foundation
SOLVE IT  2nd  79     2008 AIMS Education Foundation  3. What other number sentences describe this picture   2. How many m...
SOLVE IT  2nd  80     2008 AIMS Education Foundation
SOLVE IT  2nd  81     2008 AIMS Education Foundation  3. What other number sentences describe this picture   2. How many p...
SOLVE IT  2nd  82     2008 AIMS Education Foundation
SOLVE IT  2nd  83     2008 AIMS Education Foundation  3. What other number sentences describe this picture   2. If Snow Wh...
SOLVE IT  2nd  84     2008 AIMS Education Foundation
SOLVE IT  2nd  85     2008 AIMS Education Foundation  3. What other number sentences describe this picture   2. How many b...
Topic Whole number operations Key Question How can we use a storyboard to act out mathematical problems  Learning Goals St...
Procedure 1.  Give each child a set of 15 frogs and a storyboard, or invite the students to come to the front of the class...
Exploring Operations Through Storyboards Creation Recognition of a Set Given a number the child will build a set to repres...
SOLVE IT  2nd 89      2008 AIMS Education Foundation
SOLVE IT  2nd 90      2008 AIMS Education Foundation
Problem-Solving Strategies Write a number sentence Use manipulatives Work backwards Look for patterns  Topic Whole number ...
Procedure Part One 1. Before having students play the game in pairs, play a few sample rounds as a class. Write _____   __...
My Equations  SOLVE IT  2nd  My Partner   s Equations  93     2008 AIMS Education Foundation
My Equations  SOLVE IT  2nd  My Partner   s Equations                                                                     ...
1  2  3  4  5  6  7  8  9  0  1  2  3  4  5  6  7  8  9  0             SOLVE IT  2nd  95     2008 AIMS Education Foundatio...
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Using logical thinking as a problem-solving strategy involves combining information and using deductive and inductive reas...
Some students find it helpful to use an X and checkmark system to keep track of the information gathered from each clue wh...
Turkey Tracks Pedro is the one with the fishing pole. Tom must be the turkey tanning because Pedro likes to fish and Bob d...
Monique, Sadie, and Juan come to school different ways. 1. Sadie does not ride the bus to school. 2. Juan likes to walk bu...
Monique, Sadie, and Juan come to school different ways. 1. Juan rides to school, but not in a car. 2. Sadie   s best frien...
One October morning a farmer discovered four colorful pumpkins growing in his garden. The yellow, orange, green, and white...
Tom, Bob, and Pedro live on a turkey farm. 1. Bob never wears sunglasses. 2. Pedro likes to fish. Which turkey is which   ...
Three families live beside each other. They each celebrate different winter holidays   Christmas, Chanukah, and Kwanzaa. 1...
One winter morning Mia looked out of her window and saw four beautiful snowflakes lined up from left to right on the windo...
Four children sorted their candy hearts. Each had more of one kind than everyone else. 1. 2. 3. 4.  Abby did not have many...
There are four eggs lined up in the basket from left to right. 1. The solid chocolate egg is between the striped egg and t...
Cho, Ali, Jose, and Sue each own a kite. 1. Ali loves butterflies but does not have a butterfly kite. 2. Jose   s kite rem...
clues to order a set of either three or four astronauts. The clues will also give them practice identifying the ordinal nu...
in spaces in the shuttle and move them around, or they can use the logic grid to eliminate options. If students are unfami...
Clues for three astronauts   Clues for four astronauts    blue, yellow, and red      The yellow astronaut is between the r...
SOLVE IT  2nd  112     2008 AIMS Education Foundation
SOLVE IT  2nd  113     2008 AIMS Education Foundation
Record your solutions.  SOLVE IT  2nd  114     2008 AIMS Education Foundation
Record your solutions.  SOLVE IT  2nd  115     2008 AIMS Education Foundation
SOLVE IT  2nd  116     2008 AIMS Education Foundation
Topic Sequence logic  Materials For each pair of students  4 Teddy Bear Counters  see Management 1  crayons, markers, or c...
Management 1. Each group will need Teddy Bear Counters in four colors  red, green, yellow, and blue. Other markers in thes...
Four teddy bears are having a wonderful time riding a toboggan down the hill together. Can you use these clues to find out...
On the third ride, the bears sat in a totally different order, with no bear sitting where it had sat before. 1. The green ...
Graphs, tables, lists, and Venn diagrams are all organizational tools that are appropriate for young children. However, fo...
the number of fish by the number that will fit in each bowl, they need to have a way to organize the information so that t...
5. Instruct them to use the bowls and goldfish to organize the information. Once they have determined the total number of ...
We have _______ fish. SOLVE IT  2nd  We need _______ bowls. 124     2008 AIMS Education Foundation
We have _______ fish. SOLVE IT  2nd  We need _______ bowls. 125     2008 AIMS Education Foundation
We have _______ fish. SOLVE IT  2nd  We need _______ bowls. 126     2008 AIMS Education Foundation
Background Information The concept of probability is one that students are expected to begin learning at a very early age....
3. 4.  5. 6.  7.  8.  9.  10. Do you think this is likely to happen, or unlikely   very unlikely  Why   You would have to ...
SOLVE IT  2nd  129     2008 AIMS Education Foundation
SOLVE IT  2nd  130     2008 AIMS Education Foundation
Organize your information to answer these questions   1. How many rolls does it    usually    take to win   2. How does th...
Topic Data analysis  Materials For each group  chart paper markers 3-ring binder or spiral notebook for sign in questions ...
7. Make a transparency of one of the sign-in sheets generated by the students and the page of sample data organizers. 8. M...
Sample Data Organizers Number of leaves collected Maple  3  Birch  5  lors s  o c t e Wha ur leav yo are  Green Oak  Orang...
Tell the story of the data. SOLVE IT  2nd  135     2008 AIMS Education Foundation
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The problem-solving strategy of working backwards is simply taking a regular problem and doing it in reverse. This strateg...
Topic Problem solving  Background Information The problem-solving strategy of working backwards is simply taking a regular...
6. Ask the person representing you to stand at the front of the room with the basket and position the    principal    and ...
For each student  student watches  see Management 2  two cotter pins  see Management 6   Topic Problem solving Key Questio...
T.V. scenario   Your favorite television show comes on at 5 00. You have half an hour   s worth of chores to do, half an h...
5. Repeat procedures 3 and 4 starting at 12 30. Continue this process until all students are confident that they can go ba...
SOLVE IT  2nd  143     2008 AIMS Education Foundation
SOLVE IT  2nd  144     2008 AIMS Education Foundation
SOLVE IT  2nd  145     2008 AIMS Education Foundation
3  4  6  12 11  5  1  2  7  9  4  10  6  12 11  5  1  3  8  2  7  9  4  10  6  12 11  5  1  3  8  2  7  9  4  10  6  12 11...
Topic Problem solving  Background Information The strategy of working backwards is one that we are often called on to use ...
2. Explain that they are going to be pretending to be customers in an ice cream shop where the clerk is a little careless....
 .70 one scoop   .40 cookie  1.65 banana split   1.40 two scoops   .60 cupcake   1.55 milkshake  SOLVE IT  2nd  149     20...
A  A  A  A  A  A  A  A  SOLVE IT  2nd  150     2008 AIMS Education Foundation
B  B  B  B  B  B  B  B  SOLVE IT  2nd  151     2008 AIMS Education Foundation
C  C  C  C  C  C  C  C  SOLVE IT  2nd  152     2008 AIMS Education Foundation
D  D  D  D  D  D  D  D  SOLVE IT  2nd  153     2008 AIMS Education Foundation
E  E  E  E  E  E  E  E  SOLVE IT  2nd  154     2008 AIMS Education Foundation
F  F  F  F  F  F  F  F  SOLVE IT  2nd  155     2008 AIMS Education Foundation
G  G  G  G  G  G  G  G  SOLVE IT  2nd  156     2008 AIMS Education Foundation
H  H  H  H  H  H  H  H  SOLVE IT  2nd  157     2008 AIMS Education Foundation
Students are given scenarios describing paths that people take from one location to another. They use the map to work back...
Map One Problems 1. Mandy walks to the library on Saturday mornings. She does not walk by the playground. What is the shor...
SOLVE IT  2nd  160     2008 AIMS Education Foundation
SOLVE IT  2nd  161     2008 AIMS Education Foundation
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Sometimes a problem has so much data that it can be overwhelming. When this is the case, students can    wish for an easie...
For adults and children alike, looking at a random arrangement of objects for five seconds and trying to count how many th...
7. After all groups have completed their arrangements, pair the groups up. Have the students from one group gather around ...
letters. This task is difficult until the letters are made into words, allowing them to be easily remembered when viewed f...
7.  8.  9. 10.  11.  12.  Once they are satisfied that they have an arrangement that will be easy to remember, they should...
SOLVE IT  2nd  168     2008 AIMS Education Foundation
For a primary student, the question of how many different two-color trains you can make with five Unifix cubes is a diffic...
11. Tell students that they are now ready to try the original problem. Encourage students to revise their initial predicti...
How many 5-cube trains can you make with two colors of Unifix cubes  I think there will be ______ different 5-cube trains....
How many 3-cube trains can you make   I think I can make ______ 3-cube trains.  I made ______ 3-cube trains. My 3-cube tra...
How many 4-cube trains can you make   I think I can make ______ 4-cube trains.  I made ______ 4-cube trains.  My 4-cube tr...
Now you are ready to solve our first question. How many 5-cube trains can you make  Now I think I can make ______ 5-cube t...
Extension  How many 10-cube trains can you make  I think I can make ______ 10-cube trains. I made ______ 10-cube trains.  ...
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The problems on the following pages are provided for additional practice with the problem-solving strategies covered in th...
Tameka is 7 years old. Amy is 2 years older than Tameka. Nick is 3 years older than Amy. How old are Amy and Nick   Diego ...
What comes next  A, D, G, J, _____  I gave 3 marbles to a friend. I lost 5 on the way home. I have 6 marbles left. How man...
Mai bought a candy bar. She paid with a dollar. She got  .45 in change. How much was the candy bar   How many capital lett...
I have to take my pets to the vet. I have 2 pet carriers. Each carrier can only hold 15 pounds. My pets weigh 8, 7, 6, 4, ...
Jerome has some balloons. There are 7 pink balloons. There are 3 fewer blue balloons than pink balloons. There are 2 more ...
There were 15 cookies on 2 plates. When 3 cookies were taken away from the first plate, there were 7 cookies left on it. H...
The AIMS Program AIMS is the acronym for    Activities Integrating Mathematics and Science.    Such integration enriches l...
Get the Most From Your Hands-on Teaching   When you host an AIMS workshop for elementary and middle school educators, you ...
AIMS Program Publications Actions With Fractions, 4-9 The Amazing Circle, 4-9 Awesome Addition and Super Subtraction, 2-3 ...
Duplication Rights No part of any AIMS publication   digital or otherwise   may be reproduced or transmitted in any form o...
TM    Solve It  2nd  Problem-Solving Strategies is a collection of activities designed to introduce young children to nine...