Math Differentiation Strategies

(Definitions and Examples)

Curriculum Compacting   Grouping   Bloom's Taxonomy   Leveled Lessons   Dilemma   Choice Menus   Multiple Intelligences    Learning Contracts   Journaling   Reflection   Independent Study Project

The following is a list of strategies to differentiate, and/ or extend the curriculum in order for GT students to be engaged and challenged. Each strategy is followed by a specific example and its benchmark. The strategy can be used for any benchmark, depending on the concept you want to teach. Our focus is more on the strategies and not the benchmarks. 

Curriculum Compacting (Content) Curriculum compacting is a form of content acceleration that enables high-ability students to skip work they already know and substitute more challenging content.

1. Select the learning objectives for a given subject.
2. Find or create an appropriate way to pretest or alternatively assess competencies related to these objectives.
3. Identify students who may have mastered the objectives, or have the potential to master them at a faster than normal pace, or pretest all students in the classroom.
4. Pretest students-before beginning instruction-on one or more of the objectives.
5. Streamline practice, drill or instructional time for students who have learned the objectives.
6. Provide instructional options for students who have not yet attained all the pre-tested objectives, but generally learn faster than their classmates.
7. Organize and recommend enrichment or acceleration options for eligible students.
8. Keep records of the process and instructional options available to students whose curriculum has been compacted for reporting to parents and forward these records to next year's teachers. http://www.gifted.uconn.edu/nrcgt/vcurcomp.html

Grouping (Content, Process, Product) Placing students in small learning units to enrich curricula at all instructional levels.  Groupings may be based on academic goals, readiness, interests, or abilities.

Cluster – Use a combination of local and standardized identification materials to group students with similar ability, generally 3-6 students in each cluster. 

Flexible – Informally grouping and regrouping students in a variety of ways throughout the school day. Examples of Different Types of Flexible Groups
Readiness – Skill–based groups designed for students to learn specific skills and move between groups as needed

Interest – Students are grouped together based on similar interests, such as reading specific novels, studying a certain topic, or by learning style

Cooperative Learning – an instructional method which allows students to work in small groups in the classroom, often with a division of assignments of several specific tasks or roles.  This group strategy allows students to practice working in a group and take leadership.  Gifted students should be placed in cooperative groups ONLY with other gifted students.

Bloom’s Taxonomy: From lowest to highest order thinking - Knowledge, Comprehension, Application, Analysis, Synthesis, Evaluation. GT strategies focus on the highest 4.

Leveled Lessons:  A tiered lesson is a differentiation strategy that addresses a particular standard, key concept, and/or generalization, but allows several pathways for students to arrive at an understanding of these components, based on the students’ readiness.

Grades K-2:  When the class is studying number patterns, Tier 1 students would construct 3 to 5 patterns using three different objects.  Tier 2 students would construct 3 to 5 patterns using four different objects. Tier 3 students would construct 3 to 5 patterns using five or more objects. (II. BENCHMARK A: STUDENTS IDENTIFY, DESCRIBE, AND ANALYZE PATTERNS IN NUMBERS, SHAPES, AND DATA.)
Grades 3-5:  When the class is studying data and graphing, Tier 1 students gather data and graph various brands of shoes in the class.  Tier 2 will gather data, categorize shoes according to purpose, and graph. Tier 3 students will design an alternate graph to share results of which shoes are most popular. (III. BENCHMARK A: STUDENTS COLLECT, ORGANIZE, AND ANALYZE DATA USING SURVEYS, TABLES, AND GRAPHS.)

Grades 6-8: The students will be able to find the surface area and volume of right prisms and cylinders.  Tier 1 lesson has students finding the surface area and volume of wooden solid figures with any method possible.  Tier 2 Lesson includes students finding the surface area and volume of cereal boxes, oatmeal containers, and soup cans using formulas.  Tier 3 lesson has students finding the surface area and volume of the classroom or their house.  The students can explain how much paint will be needed to paint their house or classroom. 

(IV. BENCHMARK: (4.5) Solve problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions.)

K-2:  You know that there are often conflicts on the playground between groups of students.  Sometimes those conflicts arise because there is a limited amount of playground equipment.  If two children have 5 marbles to share, how would they share them equally?
I. BENCHMARK B: STUDENTS USE NUMBERS IN A VARIETY OF EQUIVALENT FORMS (I.E., FRACTIONS, DECIMALS, PERCENTS). 

3-5:  You have studied the conventional and metric systems of measurement.  Research which countries use either method.  Should the United States go to the metric system of measurement?  Be sure to think about the benefits and the costs of conversion.
V. BENCHMARK B: STUDENTS USE DIRECT AND INDIRECT MEASUREMENTS TO DESCRIBE AND COMPARE REAL-WORLD SITUATIONS.

6-8:  There has been discussion in the United States to get rid of pennies and round all prices to the nearest nickel.  Why might economists think this is a good idea?  Do you agree or disagree?  Research the use of pennies, the hoarding of pennies, and the reasons consumers might agree or disagree with this solution Back up your reasoning with math.
VII. Benchmark 7.E  Communicate the use of appropriate measurement techniques needed to solve problems and report the degree of accuracy required.

Choice Menus: Choice menus are organizers that contain a variety of activities which the students can choose from in order to learn a skill or develop a product.  Menus can be organized so that students are required to choose options that focus on several different skills. This is A strategy designed to allow for student choice in process and/or product while maintaining academic rigor. Menus may include tic-tac-toe or choice boards, RAFT, GRASPS, Engine-Uity cards, and cubing. Menus can be organized so that students are required to choose options that focus on several different skills.

Grade K-2:  Students will choose 6 objects from a variety of items to measure the length and width. (V. BENCHMARK A: STUDENTS USE LENGTH, CAPACITY, WEIGHT, MASS, TIME, TEMPERATURE, PERIMETER, AREA, VOLUME, AND ANGLE MEASURE TO SOLVE PROBLEMS.)

K-2 Addition – Use problems from an addition worksheet or a page from a math book.  Choose four of the strategies from the choice board to complete the addition problems.

I choose the following activities: # _______, # _________, # _________,  Date: _________________________

Student signature: ________________________________     Parent Sig. ______________________________

Project due date(s):  ____________________

VI. BENCHMARK A: STUDENTS MODEL AND USE THE FOUR BASIC OPERATIONS TO SOLVE PROBLEMS

Grade 3-5:  Students will choose 6 objects from the classroom to measure area, volume, and weight using the appropriate tools. (V. BENCHMARK A: STUDENTS USE LENGTH, CAPACITY, WEIGHT, MASS, TIME, TEMPERATURE, PERIMETER, AREA, VOLUME, AND ANGLE MEASURE TO SOLVE PROBLEMS.)
Grade 3-5:
VII. BENCHMARK B: STUDENTS COMMUNICATE THE USE OF PATTERNS AND FUNCTIONS NEEDED TO MODEL REAL-WORLD SITUATIONS AND SOLVE APPROPRIATE PROBLEMS.

Grades 6-8:
Students will demonstrate their knowledge of analyzing and interpreting data by creating a question or a problem to survey.  Students will pick a format to present the findings from the survey.  (III. BENCHMARK: (3.1) Read and construct displays of data using appropriate techniques (for example, line graphs, circle graphs, scatter plots, box plots, stem-and-leaf plots) and appropriate technology.) 
 

Independent Study Project (Content, Process, Product)
Students plan, design, and complete a project based on interest, ability, or learning style.  Teachers monitor and support students as they work towards an end product.  Consider using Paul’s Elements of Reasoning as a framework for an independent study project so that students consider the implications of a question connected to an area of interest rather than just a topical review.  http://cfge.wm.edu/TeachingModels/ReasoningWeb.pdf

K-2  Applying the strategy of Paul’s Elements of Reasoning, answer the following question: Some students can learn math facts very quickly and can finish their work early.  Their teachers want them to work on math during the math period.  What should those students do to learn more math during the time the rest of their classmates are working together?  Why?

3-5  Applying the strategy of Paul’s Elements of Reasoning, answer the following question:  Teachers require that students learn their basic math facts – addition, subtraction, multiplication, and division – without using a calculator.  Almost all adults, however, regularly use a calculator for basic math computations.  Should students be required to perform basic arithmetic with a pencil and paper?  Why or why not?

6-8  Applying the strategy of Paul’s Elements of Reasoning, answer the following question:  Should students be required to study basic economics in 8^th grade math class along with their “regular” math so that they are better prepared to deal with personal finances in the future?

K-2  Applying the strategy of Paul’s Elements of Reasoning, answer the following question: Some students can learn math facts very quickly and can finish their work early.  Their teachers want them to work on math during the math period.  What should those students do to learn more math during the time the rest of their classmates are working together?  Why?

3-5  Applying the strategy of Paul’s Elements of Reasoning, answer the following question:  Teachers require that students learn their basic math facts – addition, subtraction, multiplication, and division – without using a calculator.  Almost all adults, however, regularly use a calculator for basic math computations.  Should students be required to perform basic arithmetic with a pencil and paper?  Why or why not?

6-8  Applying the strategy of Paul’s Elements of Reasoning, answer the following question:  Should students be required to study basic economics in 8^th grade math class along with their “regular” math so that they are better prepared to deal with personal finances in the future?

Leveled Lessons (Content, Process, Product)

A leveled lesson is a differentiation strategy that addresses a particular standard, key concept, and/or generalization, but allows several pathways for students to arrive at an understanding of these components, based on the students’ readiness. 

K-2 Subject: Math  Concept: Patterns

All students will know and be able to construct and identify number patterns using a variety of objects.
II. Benchmark A: Students identify, describe, and analyze patterns in numbers, shapes and data.

3-5  Subject: Math  Concept: Patterns

All students will know and be able to gather, categorize, and graph data.
III. Benchmark A: Students collect, organize, and analyze data using surveys, tables and graphs.

6-8

Subject: Math  Concept:  Measurement

Students will know and be able to find the surface area and volume of right prisms and cylinders.
IV. Benchmark: (4.5) Solve problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions. 

The student has shown proficiency at finding the linear pattern and equation from a table and graph.  A contract is set up between the student, teacher, and parent with the student goals as the main focus.  The student has set a goal of finding out about different patterns in math and where they come from.  The student will investigate the Fibonacci Sequence and Pascal’s Triangle and report back to the class about what type of pattern he has discovered and where it can be found in the real world. (II. BENCHMARK: (2.1) Represent, describe, and analyze patterns and relationships using tables, graphs, verbal rules, and standard algebraic notation.)

Grades K-2: A student has pre-tested and mastered identification of basic two-dimensional shapes (square, triangle, circle, rectangle).  Student will independently search and identify additional shapes. Draw and label each shape. (IV. BENCHMARK B: STUDENTS CONNECT PHYSICAL OBJECTS WITH GEOMETRIC REPRESENTATIONS
Grades 3-5: A student has pre-tested on classifying lines and angles and has shown mastery of all concepts that have to do with lines but not angles.  The teacher will ensure the student receives instruction on angles and measuring tools. Then the student with construct 2-dimensional shapes using specific angle measurements. (V. BENCHMARK A: STUDENTS USE LENGTH, CAPACITY, WEIGHT, MASS, TIME, TEMPERATURE, PERIMETER, AREA, VOLUME, AND ANGLE MEASURE TO SOLVE PROBLEMS.)
Grades 6-8: Compacting: A sixth grade student has taken a pre-test and has shown that he/she is able to find the area and perimeter of all regular polygons.  The teacher and student set up a plan to compact and enrich the students understanding of geometry.  The plan includes the student explaining what happens to the area and perimeter when the length or width is double or tripled.  Is there a pattern when the length or width is increased or decreased? (IV. BENCHMARK: (4.5) Solve problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions.)

Acceleration:  A sixth grade student has demonstrated that he/she is proficient with all of the sixth grade standards and benchmarks.  The student is placed in an advanced math for acceleration. (All 6^th grade benchmarks.)

Grades K-2: When second graders are studying number sense, student would journal a list of different names for the same number using as many operations as they can think of (i.e. 5+5 =10, 2+8=10, 14-4=10, 2x5=10, etc.) (I. BENCHMARK C: STUDENTS KNOW THE PROPERTIES OF THE REAL NUMBER SYSTEM (I.E., COMMUTATIVE, ASSOCIATIVE, ADDITIVE, AND MULTIPLICATIVE).

Grades 3-5:  For a third grade class, students choose 6 letters of the alphabet, draw them in their journal and determine how many lines of symmetry and draw them for each letter.  Finally, using meta-cognition, students would journal how they determined these lines. (IV. BENCHMARK C: STUDENTS MAKE AND TEST CONJECTURES ABOUT GEOMETRY.)

Grades 6-8:

Students will keep a math journal that will keep all of the formulas and strategies that are used each day in class. (All benchmarks.)

Multiple Intelligences (Content, Process, Product)
The theory based on work by Dr. Howard Gardner which states that students exhibit talent and potential in a variety of ways including linguistic (word smart), logical-mathematical (number/reasoning smart), spatial (picture smart), bodily-kinesthetic (body-smart), musical (music smart), interpersonal (self smart), and naturalist (nature smart).

	Verbal-Linguistic intelligence: a sensitivity to the meaning and order of words. You may meet the needs of a student with this learning style through using books, stories, poetry, and speeches. A child might demonstrate this understanding through writing stories, scripts, poems or storytelling.
	Interpersonal intelligence: an ability to perceive and understand other individuals – their moods, desires, and motivations. Political and religious leaders, skilled parents and teachers, and therapists use this intelligence. You may meet the needs of a student with this learning style through teams, group work and specialist roles. A child might demonstrate this understanding through plays, debates, panels, or group work.
	Naturalist intelligence: refers to the ability to recognize and classify plants, minerals, and animals, including rocks and grass and all variety of flora and fauna. You may meet the needs of a student with this learning style through terrariums, aquariums, class pets, farm, botanical garden and zoo visits, nature walks and museum visits. A child might demonstrate this understanding through collecting, classifying, caring for animals at nature centers.
	Bodily-Kinesthetic intelligence: the ability to use one's body in a skilled way, for self-expression or toward a goal. Mimes, dancers, basketball players, and actors are among those who display bodily-kinesthetic intelligence. You may meet the needs of a student with this learning style through movies, animations, exercise, physicalizing concepts and rhythm exercises.  A child might demonstrate this understanding through dance recital, athletic performance or competition.
	Visual-Spatial intelligence: the ability to "think in pictures," to perceive the visual world accurately, and recreate (or alter) it in the mind or on paper. Spatial intelligence is highly developed in artists, architects, designers and sculptors. You may meet the needs of a student with this learning style through posters, art work, slides, charts, graphs, video tapes, laser disks, CD-ROMS and DVDs, and museum visits. A child might demonstrate this understanding through drawing, painting, illustrating, graphic design, collage making, poster making and photography.
	Intrapersonal intelligence: an understanding of one's own emotions. Some novelists and or counselors use their own experience to guide others. You may meet the needs of a student with this learning style through reflection time and meditation exercises. A child might demonstrate this understanding through journals, memoirs, diaries, changing behaviors, habits and personal growth.
	Logical-Mathematical intelligence: ability in mathematics and other complex logical systems. You may meet the needs of a student with this learning style through using exercises, drills, and problem solving. A child might demonstrate this understanding through counting, calculating, theorizing, demonstrating, and programming computers.
	Musical intelligence: the ability to understand and create music. Musicians, composers and dancers show a heightened musical intelligence. You may meet the needs of a student with this learning style through tapes, CD’s, and concert attendance. A child might demonstrate this understanding through performing, singing, playing and composing.

For further ideas on teaching with multiple intelligences go to: http://www.rogertaylor.com/clientuploads/documents/references/Product-Grid.pdf            http://www.thirteen.org/edonline/concept2class/mi/index.html

Grades 6-8: Multiple Intelligences

General Procedures:

Divide class into groups of about 6-7 students. Handout a worksheet to each group.

~Students are given a list of shapes and are asked to exactly reproduce the shapes using paper and pencil along with a compass and protractor.

~Students are given lists of coordinates and asked to graph the coordinates to get the desired geometrical shapes. They are then responsible for finding angle measures of the separate angles of the produced polygons.

~Each group will complete a write up on the procedures that they used to complete the assignment.

Multiple Intelligences Procedures:

	Linguistic: These students will complete the write-up portion of the assignment after the experimentation is completed
	Interpersonal: These students will act as the “overseers” of the group and its processes.
	Naturalistic: These students will be asked to walk through the school and around the school grounds to find objects that have similar shapes to the ones that they were asked to construct.
	Kinesthetic: These students will be doing the actual construction of the geometrical figures using the protractors and compasses.  These students will work closely with the Logical/Mathematical students.
	Visual-Spatial: These students would be asked to estimate the measure of certain angles or sizes of certain sides of objects, etc. to get an idea of the actual measurements and then measure them to assess accuracy.
	Intrapersonal: These students would be responsible for writing/overseeing a group self-evaluation. They would be responsible for evaluating the strategy that the group used and decide if there are any other strategies that may be more useful or efficient.
	Logical/Mathematical:  These students would be doing the actual paper and pencil calculations (or possibly using a calculator or computer) to find measurements and reproduce the figures.  These students will work closely with the Kinesthetic students.

Act it Out: Children themselves take the role of things to solve a problem. 

Act it Out Example: John, Lisa and Steven are going to the supermarket.  They all start at the park but there are 3 routes to get to the supermarket.  A diagonal through the park, down the west side block and take a left at the corner, or down east side of the block and take a right.  Show how each route could be the faster route. (VII. Benchmark 7.A Communicate the use of number sense, including estimations and mental math, needed to solve problems and determine the reasonableness of the solution.)

Choose the Operation: The process of choosing the operation involves deciding which mathematical operation addition, subtraction, multiplication, or division or a combination of operation will be useful. 

Choose the Operation Example: Jackie went to the store and bought 7 apples for $0.27 and 6 pounds of bananas where each pound is $0.89.  How much did Jackie spend at the store?  Show all your work. Which operation did you do first?  What was your last operation? (VII. Benchmark 7.F Communicate the use of the appropriate computational techniques needed to solve problems and determine whether the results are reasonable.)

Draw a Picture: The draw-a-picture strategy presents a nice concrete, visual representation of the problem. The picture need not be too elaborate. It should only contain enough detail to solve the problem. 

Draw a Picture Example: Find the area of a rectangle that has a length of 10 cm and a width of 5 cm. (IV. BENCHMARK 4.5:  SOLVE PROBLEMS INVOLVING PERIMETER AND AREA IN TWO DIMENSIONS, AND INVOLVING SURFACE AREA AND VOLUME IN THREE DIMENSIONS.)

Guess and Check: The guess-and-check strategy starts with an original guess for the problem. Students then use the structure of the problem to see if their initial guess works to solve the problem correctly. If their initial guess fails to work, they make another, it is hoped "better," guess and check to see if it works. They continue this process until they make an accurate guess.

Guess and Check Example: Sarah went to the store.  She wanted to buy gum and candy bars for her school.  Each piece of gum is $0.25 and a candy bar is $0.75.  If she bought 90 pieces of candy and spent $44.00 how many of each did Sarah buy? (VII. BENCHMARK 6.2:  CONSTRUCT, USE, AND EXPLAIN PROCEDURES TO COMPUTE AND ESTIMATE WITH WHOLE NUMBERS, FRACTIONS, DECIMALS, AND INTEGERS.)

Look for Patterns: is what mathematics is all about. We want to know how things are connected and how things work and this is made easier if we can find patterns. Patterns make things easier because they tell us how a group of objects acts in the same way.  

Look for Patterns Example: Mrs. Algebra put the following problem on the board and asked the students to complete the pattern. 

♣ ♣ ♣ ♣ ♦ ♪ ♪ ♣ ♣ ♣ ♦ __, ___, ___ (II. BENCHMARK 2.1:  REPRESENT, DESCRIBE, AND ANALYZE PATTERNS AND RELATIONSHIPS USING TABLES, GRAPHS, VERBAL RULES, AND STANDARD ALGEBRAIC NOTATION.)

Make an Organized List: A strategy which arranges items in such a way that there is some natural order implicit in its construction.   

Make an Organized List Example: Terry was running for class president and wanted to see if he could add some items to the lunch menu.   Terry asked 250 students what they liked to eat for lunch. What could he use to organize the information that he collected?  (III.  BENCHMARK 3.1:  READ AND CONSTRUCT DISPLAYS OF DATA USING APPROPRIATE TECHNIQUES (FOR EXAMPLE, LINE GRAPHS, CIRCLE GRAPHS, SCATTER PLOTS, BOX PLOTS, STEM-AND-LEAF PLOTS) AND APPROPRIATE TECHNOLOGY.)

Use Objects: any object that can be used in some way to represent the situation the children are trying to solve.

Use Objects Example: Find the surface area and volume of a cereal box. (IV. BENCHMARK 4.5:  SOLVE PROBLEMS INVOLVING PERIMETER AND AREA IN TWO DIMENSIONS, AND INVOLVING SURFACE AREA AND VOLUME IN THREE DIMENSIONS.)

Logical Reasoning: The process of using elimination and deductive thinking to solve problems. 

Logical Reasoning Example: You are given a basketball that weighs 1.5 pounds, a football that weighs 1 pound, and a soccer ball that weigh 2 pounds.  A box with balls in it weights 3 pounds.  What combinations of balls could be in the box?

Make a Table: Is a strategy in which information is placed in a table to help organized information to solve problem. 

Make a Table Example: Len, Maria, Frank, and Kim each have a favorite sport: bowling, softball, and football, but not necessarily in that order. Len’s cousin’s favorite sport is basketball. Frank and Kim do not like football.  Maria’s favorite sport is softball. Kim no longer likes bowling.

1. Which sport is Len’s favorite sport?

2. Make a table to organize your clues.

(III.  BENCHMARK 3.1:  READ AND CONSTRUCT DISPLAYS OF DATA USING APPROPRIATE TECHNIQUES (FOR EXAMPLE, LINE GRAPHS, CIRCLE GRAPHS, SCATTER PLOTS, BOX PLOTS, STEM-AND-LEAF PLOTS) AND APPROPRIATE TECHNOLOGY.)

Solve a Simpler Problem: When a problem seems complex, break it down to a smaller problem.  

Solve a Simpler Problem Example: How much paint would you need to paint a dog house (Dimensions = 2 feet x 5 feet x 3 feet), a shed (dimensions = 5 feet x 7 feet x 6 feet), and the house (Dimensions = 22 feet x 10 feet x 45 feet)? (Hint: find the surface area of each building and add them together.) (IV. BENCHMARK 4.5:  SOLVE PROBLEMS INVOLVING PERIMETER AND AREA IN TWO DIMENSIONS, AND INVOLVING SURFACE AREA AND VOLUME IN THREE DIMENSIONS.)Work Backwards: This strategy requires three steps: start at the end of the problem; reverse each of the steps in the problem, being careful to determine the amount at this step; and work the problem from end to beginning by performing the inverse operation at each step.
Work Backwards Example: A certain number of bottles were on the wall.  A door slams shuts causing 7 of the bottles to drop on the floor and break.  Next, someone came into the room and placed 12 more bottles on the wall.  A thief takes twenty of the bottles.  There are now 46 bottles remaining on the wall.  How many bottles were on the wall at the start of the problem?
(VII. BENCHMARK F: STUDENTS COMMUNICATE THE USE OF THE APPROPRIATE COMPUTATIONAL TECHNIQUES NEEDED TO SOLVE PROBLEMS AND DETERMINE WHETHER THE RESULTS ARE REASONABLE.)

Exact or Estimate:  Exact is strictly accurate or correct, precise. Estimation is the calculated approximation of a result which is usable even If input data may be incomplete, or uncertain.
Exact or Estimate Example:  From an aerial photograph of a herd of elk, students will take a 2”x 2” sample of the photo and from this sampling, estimate how many elk are in the whole picture. (VI. BENCHMARK C: STUDENTS APPLY THE APPROPRIATE COMPUTATIONAL TECHNIQUES TO SOLVE A VARIETY OF PROBLEMS AND DETERMINE THE REASONABLENESS OF THE RESULTS.)
Write an Equation: Develop a rule that can be used to solve similar problems.  

Write an Equation Example: You are using a function box in your classroom.  Your friend is inside of the function box ready to hand you a number.  If you put in a 2 and your friend gives you a 7, and  if you put in a 4 and your friend gives you a 9 what is the equation of the function box? (II. BENCHMARK 2.1:  REPRESENT, DESCRIBE, AND ANALYZE PATTERNS AND RELATIONSHIPS USING TABLES, GRAPHS, VERBAL RULES, AND STANDARD ALGEBRAIC NOTATION.) 

Use a formula: A set rule is used to find an answer to a problem. 

Use A Formula Example: Joe’s Dad is going to paint the dog house.  He is creating a custom color for the dog house and does not want to run out of paint because the color will be hard to match.  Joe’s Dad needs to know how big the dog house is so the paint store can give him the correct amount of paint.  If the height of the dog house is 3 feet, the length is 5 feet and the width is 7 feet what is the surface area of the dog house that needs to be painted?  (IV. BENCHMARK 4.5:  SOLVE PROBLEMS INVOLVING PERIMETER AND AREA IN TWO DIMENSIONS, AND INVOLVING SURFACE AREA AND VOLUME IN THREE DIMENSIONS.)

Reflection (Process, Product)

A thoughtful process used to challenge and guide students to examine issues and to assist them in finding personal relevance in their learning. Students at all levels can be challenged to find personal connections with non-fiction subjects. A few ways this reflection might be accomplished are thought response journals, class discussions, or graphic organizers such as a wheel and spokes.  Some possible questions for reflection:

How can I apply this math concept to other things we’ve learned in math to a situation I faced today?

            Is it possible for to have two different solutions to the same math   problem? Why/why not?

            What connections can you make in your world to this math concept?

            Explain the thought process you went through to solve this math problem.