South Kingstown School Department
Elementary Math


                                                        
     

Problem Solving Sample Activities and Strategies

Kindergarten
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Exemplar Rubric used to assess problem solving tasks






Problem Solving in Kindergarten

Kindergarten students will be using the following problem solving strategies to answer problems throughout the school year: diagram and key, model, and tally charts.

 Have you ever wondered why you were teaching your child This Old Man, Five Little Monkeys, Hokey Pokey, or B-I-N-G-O, besides the fact that your parents taught them to you when you were growing up?  These songs and poems are just one way teachers are striving to meet the needs of all learners in the classroom.  Children who are exposed to these songs and poems are hearing the message, saying the message, providing gestures to the message, all while learning math skills.  This Old Man and Five Little Monkeys provide practice with counting, the Hokey Pokey is the opportunity for the children to explore spatial relationships, and B-I-N-G-O is a way to introduce children to patterns. 

Throughout the school year kindergartners work on mastering many lifelong skills.  This learning is an essential part to building a good educational foundation.  Many of the skills they are practicing can be worked into a mathematics lesson in some fashion.  For example; Joey has been out enjoying the snow.  On Sunday he made one snowball, on Monday he made two snowballs.  Tuesday he made one snowball, and Wednesday he made two snowballs.  If he continues making snowballs, how many snowballs will Joey make on Saturday?  This problem has the student practicing the days of the week, working with a pattern (1-2 pattern or AB pattern), making a diagram and a key or a tally chart to show the problem, along with number recognition.  A possible extension we could make to this problem would be asking the students to "count up" or find the "total number" of snowballs that Joey can make in one week or even for two weeks.

By teaching math skills through problem solving the students are trying out the concrete concepts they have been learning in class in a more abstract way of thinking.  Some students are able to make connections within a problem to something they know or about something they have noticed while doing the problem, while others need support throughout the process. 
 

A few problems to try with your children:

1.     Half of the children in our Kindergarten class have blue eyes.  How many children have blue eyes?  (Let's say there are 22 students.)

2.    Five little pumpkins sitting on a gate.  They each have 2 triangles for eyes and 1 triangle for a nose.  How many in all?

3.    On Friday, some kids rode their bicycles to school.  There were 3 red bicycles and 3 blue bicycles.  What are some ways they could line up the bicycles to form a pattern?

Answers:
1.     Half of the children in our Kindergarten class have blue eyes.  How many children have blue eyes?  (Let's say there are 22 students.)
Half of 22 is 11.

2.   Five little pumpkins sitting on a gate.  They each have 2 triangles for eyes and 1 triangle for a nose.  How many triangles in all?
One pumpkin has 3 triangles, so five pumpkins have 15 triangles in total.

3.    On Friday, some kids rode their bicycles to school.  There were 1 red bicycle and 3 blue bicycles.  What are the ways they could line up the bicycles to form a pattern?

RBBB                    BRBB
BBRB                    BBBR            

 The above problems in some form will be solved by Kindergartners this year.  This is the stepping stone, that we as teachers build from. as they enter in to the higher grades. 




 Problem Solving in Grade One

First grade students will be using the following problem solving strategies to answer problems throughout the school year: diagram and key, model, tally chart, and number lines.

First grade brings many new skills, and some of the main topics are: correctly writing numbers, counting up to 100 in many different ways (1s, 2s, 5s, 10s, 20s, using tallies, money, objects, etc.), working in great detail with adding and subtracting, measuring 2-D objects, telling time, working with money, and problem solving.  It is very important for students to start putting their thoughts on paper to the best of their ability or at the very least dictate their thinking to an adult that is in the classroom so that they may transcribe the information for them.  Starting early with this process will demonstrate the importance of thinking through a problem, showing how they arrived at a solution, and stating the solution in the form of a sentence.

A common problem solving activity that is completed in first grade classrooms is: Sarah has bunnies.  When she feeds them in the morning she sees 20 ears.  How many bunnies does she have in total?  When solving this problem with the students in class we would first read and re-read the problem a few times with the children so that they become familiar with reading the problem a few times before beginning to work.  After the problem has been read a few times the teachers would then ask the students to tell them what the problem is asking them to figure out, what they know from the problem, and how they plan on solving the problem.  Once the students have a firm understanding of what to do, the students begin working.  First grade is when the students start to really develop math problem solving skills as the teachers guide them along through the process.  The students in this case would have to know that a bunny has two ears.  Usually the strategy the students will use to solve this problem is to make a diagram with a key.  This strategy allows the students to make a visual representation to solve the problem, but we also stress that the diagram needs to have a "math drawing" not drawing that they would make in art class.  The most common bunny made for this problem would be a circle for the head with two straight lines coming off the circle to represent the ears.  This brings up the importance of making a key to go along with their diagram.  The end result is the children draw 10 bunnies in total. 

When assessing this problem or when working with the students the teachers are looking for whether the child was able to get started after the whole class discussion, if the child use a problem solving strategy, and if the child know when to stop making bunnies, and lastly, was the child able to make a math connection about the problem.  A math connection could be anything mathematical; ranging from a pattern they noticed, odd and even numbers, an extension to the problem (What if Sarah saw 24 ears, how many bunnies would she have?), a number sentence/model about the problem, to name a few.

First grade is when a lot of growth can and will occur mathematically.  Be patient with your child as they think through a problem as the problem solving experience is just as valuable as solving the problem.
 
First graders do explore the concepts of multiplication and division through problem solving in their curriculum, but it is building the basic foundation of what multiplication and division truly represent and not the concrete concept. 

A couple problems to try with your children:

1.     This weekend I went to the zoo and saw some birds and bears.  Altogether I saw 18 feet.  How many birds and how many bears did I see?  Can you think of more than one answer?

2.    Brittany, Alex, Kim, Blake, and Lilly exchange Valentine cards.  Each friend gives one Valentine to each of the others.  How many valentines are there altogether?

Answers
1. This weekend I went to the zoo and saw some birds and bears.  Altogether I saw 18 feet.  How many birds and how many bears did I see?  Can you think of more than one answer?

There are many solutions to this problem and that is one of the main reasons teachers like these kinds of problems.  Students usually do this problem differently than their peers so it make for interesting discussion when sharing out the solutions.  Making students realize that sometimes a problem has more than one correct solution is difficult to understand for some.  The possible solutions would be: 9 birds-0 bears, 7 birds-1 bear, 5 birds-2 bears, 3 birds-3 bears, and 1 bird-4 bears.

 2. Brittany, Alex, Kim, Blake, and Lilly exchange Valentine cards.  Each friend gives one Valentine to each of the others.  How many valentines are there altogether?
Each person needs to hand out four valentines.  There are five people.  Therefore 4+4+4+4+4=20 total valentines. An extension would be to talk about multiplication 5 people x 4 cards each.






Problem Solving in the Second Grade

Second grade students will be using the following problem solving strategies to answer problems throughout the school year: diagram and key, model, tally chart, number line, table, organized list, tree diagram, area model, set model, pictograph, and line plot.

Second graders continue to work on all of the concepts from first grade with added requirements.  They should be able to read, write, and identify numbers up to at least 200, work with fractional benchmarks such as halves, thirds, and fourths, understands congruency, perimeter, area, extends patterns, can tell time to the closest quarter hour, measures with many different units, can determine the temperature given a thermometer and continue working on problem solving.

A common problem solving activity that is completed in second grade classrooms is:

Betty and Bo took their daughter, Barbara, and their twin boys, Billy and Bradley, to the beach.  Their dog, Bingo, and her four puppies went along with them.  Grandma Brown met them there.  Just how many legs were in the group on the beach?  Counting is the main focus of this problem, but the teachers can also bring in addition and subtraction by making connections and extensions.  For this problem the students may choose to draw a diagram with a key, make an organized list, or check track of the legs using a tally chart.  The students would have to count the number of people at the beach and the number of dogs at the beach.   In order to solve the problem students need to bring in their prior knowledge that people have two legs and dogs have four legs.  Depending on what problem solving strategy the student chooses to use in this case will determine how they will know how many legs are on the beach.  If they draw a diagram they will be able to count the legs on all the people and dogs to arrive at the solution.  If they made an organized list the students will also count up how many legs they made for each person or dog.  Lastly, if the student chose to do a tally chart they will need to count all of the tally marks.  Connections/extensions that can be made to this problem would be that the students could count legs by 2's, they could write a number sentence to represent the problem (2+2+2+2+2+4+4+4+4+4+2=32), students could also add more to the problem and then state how many legs there are in total (Grandpa showed up after work so now there are 34 legs.)     

Here are a couple problems to try!

1.     Kate loves apples and likes to eat them at lunch.  On the first day, Kate ate 1 apple and on the second day she ate 2 apples.  On the third day she ate 1 apple and on the fourth day she ate 2 apples.  If this continues, how many apples will Kate eat on the tenth day?  Kate's mom buys apples in a bag that holds a dozen apples.  If she buys a bag of apples in the morning of the first day, will she have enough apples for Kate to eat all ten days?

2.    Mr. Thomas has 6 classes for P.E.  He always begins with Kindergarten and then goes in order to the sixth grade.  The Kindergarten class starts at 8:30, the First grade starts P.E. at 9:00, the Second grade starts P.E. at 9:30.  If Mr. Thomas does not have any breaks, what time will the sixth grade class start P.E.?

Answers

1.     Kate loves apples and likes to eat them at lunch.  On the first day, Kate ate 1 apple and on the second day she ate 2 apples.  On the third day she ate 1 apple and on the fourth day she ate 2 apples.  If this continues, how many apples will Kate eat on the tenth day?  Kate's mom buys apples in a bag that holds a dozen apples.  If she buys a bag of apples in the morning of the first day, will she have enough apples for Kate to eat all ten days?

The strategy we would use for this problem in the classroom would be to either have the students construct an organized list or make a diagram with a key.  In 10 days Kate would have eaten a total of 15 apples.  Kate's mom would not have enough apples for 10 days if she only bought one bag.  Students here would need to know what the word dozen means.  One bag is not enough for Kate to eat apples in this pattern for ten days, she would only have enough apples for 8 days.

2.    Mr. Thomas has 6 classes for P.E.  He always begins with Kindergarten and then goes in order to the fifth grade.  The Kindergarten class starts at 9:00, the First grade starts P.E. at 9:30, and the Second grade starts P.E. at 10:00.  If Mr. Thomas does not have any breaks, what time will the fifth grade class start P.E.?

Students need to figure out that a class lasts for 30 minutes and when one class ends another class is arriving.  Kindergarten would start at 9:00 am, First starts at 9:30, Second starts at 10:00, Third starts at 10:30, Fourth starts at 11:00, and Fifth would then start at 11:30.  Another question would be to ask at what time would Mr. Thomas be done teaching P.E.?  An extension to this would be to start the first class at 9:15 am and then add in a break between two classes.





Problem Solving in Third Grade

Third grade students will be using the following problem solving strategies to answer problems throughout the school year: diagram and key, model, tally chart, number line, table, organized list, tree diagram, area model, set model, pictograph, line plot, bar graph, and linear models.

 Hopefully you are starting to see some resemblance between the problems as they progress through the grades.  The problems could all be revolving around patterns, but the complexity varies at the different grade levels.  We hope that so far you have been successful with the given problems, so we will continue on to the third grade.

 Third graders continue to work on reading, writing, and identifying numbers up to at least 1,000, work on fractional benchmarks (now including sixths and eights), along with being able to understand decimals in the context of money.  Multiplication is introduced as repeated addition and students head toward mastery of adding and subtracting with regrouping (same as borrowing and trading).  Students are also trying to develop strategies for mentally adding and subtracting numbers along with using estimation.  Geometry is entering into the picture now with using angles and sides of shapes to identify, describe, or distinguish among triangles, squares, rectangles, rhombi, trapezoids, hexagons, or circles.  The students continue to work on congruency and similarity among figures, along with being able to find the area and perimeter.  Spatial reasoning and visualization are being taught through giving directions between locations, on a map, or on a coordinate grid.  Lastly students are working on extending patterns, showing equivalence, determining missing values to make a number sentence true, and can interpret data from various graphical representations. A couple of items that can be easily practiced at home are measuring objects to the nearest inch or centimeter and reading time to the nearest five minute interval.

A common problem solving activity that is completed in third grade classrooms is: John was talking to his cousin, Patrick, who was visiting from Ireland.  John asked Patrick what dinner food was the favorite of his classmates.  Patrick said that 15 students like Irish Stew, 10 liked pork, and 5 liked Irish Stew and pork the same.  How many classmates does Patrick have?  For this problem teachers introduce students to using Venn Diagrams (two or more overlapping circles).  In this case we would use two overlapping circles.  The students would label one circle Irish Stew and then draw a second circle overlapping part of the first circle and label the second circle pork.  The students will then need to go back to the problem to review what information they were given.  The easiest way to begin is to start with students who like both Irish Stew and pork.  Have the students place the number 5 in the overlapping circle parts.  Then the students need to go back to how many people in total like Irish Stew, which is 15.  Since we already have 5 people inside the Irish Stew circle there are 10 people left who like Irish Stew the best.  Then have the students look at how many liked pork, which was 10.  Since we already have 5 people inside the pork circle there are only 5 people who like pork the best.  So there are a total of 20 students in Patrick's class.  Many students would just add up 15 + 10 + 5 =30 and say that there are 30 students in Patrick's class, which is incorrect.  Drawing out the Venn Diagram proves to be very helpful when organizing information that counts in two or more areas.

Here are a few problems for you to try at the third grade level!

1.     Sam lived in Alaska where the winter is very long.  Sam loves to throw snowballs.  He made a target and hung it on the side of his garage wall to practice his pitching aim.  On the first day, he hit the center of the target 2 times.  On the second day, he hit the center of the target 4 times.  On the third day, he hit the center of the target 6 times.  If this pattern continues, how many times will Sam hit the center of the target on the 10th day?  How many times will Sam hit the center of the target on the 20th day?

2.    Roberta wants to buy one chocolate chip cookie from the vending machine.  The cookie costs 35 cents.  She has nickels, dimes, and quarters in her hand.  What are the different ways she can make 35 cents?  Use pictures, numbers, and words to show how to solve this problem.

3.    Farmer Brown noticed that one of his animals must have a cut on its foot.  He needed to check the feet of each animal to see which one was hurt.  How many feet might he have to check before he found the poor animal that was hurt?  He has 7 chickens, 5 pigs, and 3 cows.  Using word, numbers, and pictures show and explain how to help Farmer Brown solve his problem.

Answers

1.     Sam lived in Alaska where the winter is very long.  Sam loves to throw snowballs.  He made a target and hung it on the side of his garage wall to practice his pitching aim.  On the first day, he hit the center of the target 2 times.  On the second day, he hit the center of the target 4 times.  On the third day, he hit the center of the target 6 times.  If this pattern continues, how many times will Sam hit the center of the target on the 10th day?  How many times will Sam hit the center of the target on the 20th day?

For this particular problem the students might consider making a table and looking for a pattern.  The pattern would be hitting the center of the target two more times each day.  The students will hopefully also see that the result of hitting the center of the targets is double the day Sam is on.  In other words, on day 5, he would hit 5 x 2 centers of the target, or 10 in total.  On the 10th day he would then hit the center of the target 20 times and on day 20 he would hit the center of the target 40 times.

2.    Roberta wants to buy one chocolate chip cookie from the vending machine.  The cookie costs 35 cents.  She has nickels, dimes, and quarters in her hand.  What are the different ways she can make 35 cents?  Use pictures, numbers, and words to show how to solve this problem.

There are six possible combinations of coins using only nickels, dimes, and quarters to make 35 cents.  One possible strategy is to make a table or an organized list of the possibilities.  To make a table one would need to make a quarter column, a dime column, and a nickel column.  Then start with one quarter and work your way through the table.  You must stay organized in order for this strategy to be the most helpful.  Your table might look like the following:



Quarter

Dime

Nickel

1


1


0


1

0


2


0


3


1


0


2


3


0


1


5


0


0


7



These are all the possible ways of making 35 cents using only quarters, dimes, and nickels.

3.    Farmer Brown noticed that one of his animals must have a cut on its foot.  He needed to check the feet of each animal to see which one was hurt.  How many feet might he have to check before he found the poor animal that was hurt?  He has 7 chickens, 5 pigs, and 3 cows.  Using word, numbers, and pictures show and explain how to help Farmer Brown solve his problem.

Students would need to determine how many total feet were on the farm.  There are seven chickens, therefore 7 x 2 feet = 14 total chicken feet.  There are five pigs, therefore 5 x 4 feet = 20 total pig feet.  There are three cows, therefore 3 x 4 feet = 12 total cow feet.  If we put all the animal feet together Farmer Brown would have to 14 + 20 + 12 = 46 feet on the farm.  He might have to check all 46 feet to find the animal that has a cut.





Problem Solving in Fourth Grade

Fourth grade students will be using the following problem solving strategies to answer problems throughout the school year: diagram and key, model, tally chart, number line, table, organized list, tree diagram, area model, set model, pictograph, line plot, bar graph, linear model, circle graph, line graph, Venn Diagram, and frequency charts.
 
Fourth graders continue to work on reading, writing, and identifying numbers up to at least 1,000,000, work on fractional benchmarks (now including fifths and tenths), along with being able to understand decimals in the context of money (to the hundredths place).  Division is introduced as repeated subtraction and students head toward mastery of adding, subtracting, multiplying (up to 2-digit by 2-digit) and division (with a 1-digit divisor).  Students are also trying to develop strategies for mentally adding, subtracting, multiplying, and dividing numbers along with using estimation.  Geometry is continuing with the third grade standards on shapes and attributes, but has added on the shape of octagon, along with being able to classify angles relative to 90 degrees as more than, less than, or equal.  They will identify, compare, and describe 3-D shapes such as: rectangular prisms, triangular prisms, cylinders, or spheres.  The students continue to work on congruency and similarity among figures where they have to match figures using reflections, translations, or rotations (flips, slides, or turns), along with being able to find the area and perimeter.  Spatial reasoning and visualization are being taught through giving directions between locations, on a map, or on a coordinate grid.  Students are working on extending linear patterns, showing equivalence, determining missing values to make a number sentence true (variables), and can interpret data from various graphical representations. A skill that is being developed is calculating the probability of an event.  In other words, how likely is it that something will happen.  A couple of items that can be easily practiced at home are measuring objects to the nearest inch or centimeter, conversions within systems, and if the basic addition, subtraction, multiplication, and division facts are not mastered this is the best time to accomplish this as it is essential to moving forward in mathematics.

A common problem that is done with fourth graders is what we call  "The Handshake Problem".  The problem is as follows: Amos, Brenda, Carrie, Derrick, Emily, and Francis are finalists in the School Spelling Bee.  Before the final round of the bee, each student must shake hands with each of the other students.  What is the total number of handshakes?  One way to start the children out thinking about this problem would be to model it with the class.  Have six students stand in the front of the room and have one person start and shake the hands of the other students, then ask how many hand shakes did that student make? (5 handshakes)  Then have the next student go and shake the hands of the other students, how many hands did he shake keeping in mind that you cannot shake someone's hand that you have already shaken? (4 handshakes) The process would then continue until everyone has shaken everyone's hand once, and only once.  So the solution would be 5 + 4 + 3 + 2 + 1 = 15 total handshakes are needed to have each of the 6 finalists of the spelling bee shake all the other finalists hands.

A couple problems to try at the fourth grade level:

1.      Mrs. Green decided to ask some students what their favorite party games were because she wanted to plan the right games for the class party.  12 students said they liked musical chairs, 20 students liked tossing games, and 10 students liked bobbing for apples.  There were 9 students who liked both musical chairs and tossing games the best, and 6 students who liked both tossing games and bobbing for apples the best.  How many students did Mrs. Green ask about their favorite party games?
2.      The Math Club has decided to have a class party.  They can have pizza, tacos, or hot dogs.  They can have milk or juice.  They can also have cupcakes or brownies.  If club members can select one meal, one drink, and one dessert to have at their party, how many different choices do they have to choose from?  If the Math Club wanted to offer more choices, should they add another meal or another dessert?

Answers
1.      Mrs. Green decided to ask some students what their favorite party games were because she wanted to plan the right games for the class party.  12 students said they liked musical chairs, 20 students liked tossing games, and 10 students liked bobbing for apples.  There were 9 students who liked both musical chairs and tossing games the best, and 6 students who liked both tossing games and bobbing for apples the best.  How many students did Mrs. Green ask about their favorite party games?

This problem would be most easily solved by making a Venn Diagram.  This particular version would have three circles in a straight line, with both outside circles overlapping with the center circle.

          Musical       Tossing      Bobbing

      
5208_101610_3.png 3 + 9+ 5 + 6 + 4 = 27 students
            
Place the students who like more than one game into the diagram first.  Then using the given information you can fill in how many students like only musical chairs, tossing games, or bobbing for apples.  Mrs. Green asked 27 students about their favorite games.

 
2.      The Math Club has decided to have a class party.  They can have pizza, tacos, or hot dogs.  They can have milk or juice.  They can also have cupcakes or brownies.  If club members can select one meal, one drink, and one dessert to have at their party, how many different choices do they have to choose from?  If the Math Club wanted to offer more choices, should they add another meal or another dessert?

There are a total of 12 different combinations.  A good strategy for this would be to make a tree diagram, an organized list or a table.  Let P=pizza, T=taco, H=hot dog, M=milk, J=juice, C=cupcake, B=brownie.  Then the following would be my 12 combinations: PMC, PMB, PJC, PJB, TMC, TMB, TJC, TJB, HMC, HMB, HJC, and HJB.  If the math club were to add another meal, for example salad, that would add 4 more combinations: SMC, SMB, SJC, and SJB.  If the math club were to add another dessert, for example ice cream, instead of adding another meal, they would have 6 more combinations: PMI, PJI, TMI, TJI, HMI, and HJI.  So if the math club wanted more choices they should add another dessert instead of another meal.




Problem Solving in Fifth Grade

 
Fifth grade students will be using the following problem solving strategies to answer problems throughout the school year: diagram and key, model, tally chart, number line, table, organized list, tree diagram, area model, set model, pictograph, line plot, bar graph, linear model, circle graph, line graph, Venn Diagram, frequency chart, and histograms.

 
Fifth graders continue to work on reading, writing, and identifying numbers up to at least 10,000,000, work on fractional benchmarks (now including twelfths), powers of ten, and percentage benchmarks of 10%, 25%, 50%, 75%, and 100%, along with being able to understand decimals in the context of money (to the thousandths place).  The student understands the meaning of a remainder with respect to division, has mastered multiplication and division facts up to a product of 144, and understands the math vocabulary factor, multiple, prime, and composite.  In Geometry the students will be using properties or attributes of angles (right, acute, obtuse) or sides (number of congruent sides, parallelism, or perpendicularity) to identify, describe, classify, or distinguish among different types of triangles, or quadrilaterals. They will identify, compare, and describe 3-D shapes such as: rectangular and triangular prisms, cones, cylinders, pyramid, and state how they compare to 2-D shapes.  The students continue to work on congruency and similarity among figures where they have to match using reflections, translations, or rotations (flips, slides, or turns), along with being able to find the area and perimeter.  Spatial reasoning and visualization are being taught through giving directions between locations, on a map, or on a coordinate grid (graphing in a 4 quadrants).  Students are working on extending and evaluating linear patterns, showing equivalence between two expressions, determining the value of a variable to make an equation true, and can interpret data from various graphical representations. A skill that is being developed includes calculating the probability of an event.  In other words, how likely it is that something will happen.  Please continue practicing your math facts!

A common fifth grade problem would be: Little Davey Dulce had eaten over 100 Whipple-Scrumptious Fudgemallow Delight bars, but did not find the golden ticket.  It was announced in the paper that Charlie Bucket had found the fifth and last golden ticket, allowing him to visit Willy Wonka's Chocolate Factory and learn all the secrets and magic it contained.  Davey arranged a special meeting with Mr. Wonka and cried huge tears until Mr. Wonka gave him another chance to win a golden ticket.  He tossed Davey a bag of delicious fun-sized M&M's.  Mr. Wonka told Davey he must guess the exact amount that was in the bag in order to win a ticket.  Davey asked 11 of his friends to buy a bag of M&M's and count how many were in each bag.  These are the amounts his friends reported: 23, 27, 24, 25, 23, 25, 26, 26, 25, 24, and 22.  Organize and display the information to help Davey win his golden ticket.  Tell Davey the: maximum, minimum, range, median, and mode for the data.  This is when the students really get introduced to statistics and have a chance to practice using data given to them.  The first thing the students need to do is put the data in order from least to greatest.  From there they can determine the maximum, minimum, and range.  Then when looking at the data, the students need to find the middle piece of data (median), and the data piece that occurred the most (mode).  These will then help Davey decide what number he should choose when telling Mr. Wonka how many M&M's are in his bag.  23, 23, 24, 25, 25, 26, 26, 27  max=27, min=23, range=4, median=25, mode=23, 25, 26  From this Davey needs to make his best estimate which may be 25 as it is the median and happened to be one of the amounts that happened the most.


Here are a couple problems to try at the fifth grade level.

1. John was talking to his cousin, Patrick, who was visiting from Ireland.  John asked Patrick what dinner food was the favorite of his classmates.  Patrick found out the following: 21 students like Irish Stew, 14 students like Pork, 7 students like both Irish Stew and Pork the same, 11 students like Corn Beef and Cabbage, and 3 students like both Corn Beef and Cabbage and Pork the same.  How many classmates does Patrick have?
2. How many possible ice cream choices do we have if we get to choose one ice cream flavor, one topping, and one type of sprinkles from the following menu?




Ice Cream Flavor

Topping


Sprinkles

Chocolate


Fudge

Rainbow

Vanilla


Caramel

Chocolate

Strawberry