Monica LenewayDecimal Differentiation

Here are some of the DI activities that I have made to use with decimals.  I’ve done the two bottom ones, but not the Tic-Tac-Toe.

Differentiated Learning Activity – Tic Tac ToeSubject:  Mathematics Topic:  DecimalsOutcomes:  As a result of the learning activity, student should meet the following key skills:  I can…(8) perform addition, subtraction, and multiplication to decimals, (9) perform division with decimals when the divisor is a whole number or a decimal, (10) apply the order of operations to decimal numbers, (11) apply problem solving techniques in application problems with decimals, and (12) develop application problems with decimals.Readiness Levels (Tiered Assignments):    Exceeds expectations    Meets expectations    Does not meet expectationsLearning Preference Model:    Visual Auditory Kinestheticx    Multiple Intelligences    Triarchic    OtherActivity Structure:x    Choice Board                            Learning Contract    Cube/Thinkdots                        Tri-mind    RAFT                                        Structured Academic Controversy    Profiler                                      Project/Problem Based Learning    Other                                         Tiered AssignmentDescription of Learning Activity:Students will each be given a tic-tac-toe board at the beginning of the unit.  It will be used as an anchor activity.  On the board, students will choose any three squares that complete a tic-tac-toe.  They may choose to do additional squares as well.Assessment:Each activity will be submitted individually, and assessed informally with feedback given.  There will be no grade, but feedback will be based on whether or not they did what the box asked them to do, and whether or not their “solutions” are mathematically sound.Closure/Sharing:Students will share their activities in small groups.  They will choose one of their activities to display in the classroom, and some will be used by the class for review.   

Tic Tac Toe BoardAnchor Activities (musical)Make a rhyme or chant to help you and others remember the order of operations or how to divide with decimal numbers.

(intrapersonal & verbal/linguistic)Create three story problems involving decimals.  As you write and solve each problem, write a think-aloud, including your reasons as to why you chose the problems and numbers that you chose.

(visual/spatial & logical/mathematical)Look at the story problems in the application section of the book.  Make a frequency table and histogram for the number of problems that are solved by addition, subtraction, multiplication, division, and multiple-step problems.

(kinesthetic & interpersonal & logical/mathematical)Get your family members together and have them make piles of all of their spare change.  Count and record how much money each person has.  Use these numbers to make and solve equations.

(free)You will find a creative way to review for the test.  Make sure your review includes at least two items from each section that we’ve covered in our unit.

(naturalist)Take a nature walk, looking for and recording, items that may have the golden ratio.  Then look the items up on the internet and see if they are indeed golden ratio examples.

(interpersonal & visual/spatial & verbal/linguistic & kinesthetic)Interview four family members or friends on how they use decimals in their everyday life.  Record your questions and their responses in a creative way (as a story, in a graphic organizer).

(logical/mathematical)Solve the puzzle in folder 8.  Then make another math puzzle (similar to it or a different kind), involving decimals.

(verbal/linguistic)With others interested in this activity, take turn reading the copied chapter of Where Do I Put the Decimal Point?.  Each of you will then write a summary of ways to reduce math anxiety based on the reading.  Copies of the chapter will be found in folder 9.

 Puzzle in Folder 8 This unit is devoted to the study of decimal numbers.  Use what you learn in this chapter to perform the operations shown in hints a-d.  Then use the hints to help you complete the puzzle. Each row and each column in the grid must use the numbers 1, 2, 3, 4, and 5 exactly once. Hints:a.  Simplify 0.8 + 12.12 + 7.33.  Place the tenths place digit in box a.b.  Simplify 60.75 ÷ 0.3.  Place the number of digits to the left of the decimal point in box b.c.  Simplify 1.7625 – 1.56.  Place the number of digits to the right of the decimal point in box c.d.  Simplify 8.1 × 0.25.  Place the thousandths place digit in box d.

       

1 3a 4

3 c5

d b

Differentiated Learning Activity – CubesSubject:  Mathematics Topic:  DecimalsOutcomes:  As a result of the learning activity, student should meet the following key skills:  I can…(8) perform addition, subtraction, and multiplication to decimals, (9) perform division with decimals when the divisor is a whole number or a decimal, and (11) apply problem solving techniques in application problems with decimals.Readiness Levels (Tiered Assignments):    Exceeds expectationsx    Meets expectations    Does not meet expectationsLearning Preference Model:    Visual Auditory Kinesthetic    Multiple Intelligences    Triarchicx    OtherActivity Structure:    Choice Board                            Learning Contractx    Cube/Thinkdots                        Tri-mind    RAFT                                        Structured Academic Controversy    Profiler                                      Project/Problem Based Learning    Other                                     x    Tiered AssignmentDescription of Learning Activity:Students will work in pairs that are assigned to them based on their ability/readiness level.  There will be an advanced cube and a basic cube.  Each student will take turns rolling.  Each problem must be solved, but will only be solved once (so if the problem appears more than once, the cube should be re-rolled).  The person rolling the cube is responsible for solving the problem; however, both members may discuss how to solve it.  Therefore, each student will turn in their own three problems on a sheet of paper.  See attached for the cube templates.Assessment:Students will be assessed by a rubric.  They will be assessed as a group, based on the processes used to solve each problem, as well as individually, based on each students’ answers to their own three problems.  Students will receive constructive feedback on their processes, as well as their final solutions.Closure/Sharing:Prior to turning their work in for assessment and feedback, students are already sharing with each other which processes should be used for each problem.  After feedback is given, students will pair back up to review the feedback, have a chance to re-work any incorrect problems together, and resubmit.  

Basic Cube

Boston had five snowstorms in one month, whose snowfall amounts were: 16.3 inches, 10.2 inches, 4.25 inches, 22.3 inches, and 8.9 inches.  Te normal amount of snow for the month was 22.35 inches.  How many more inches of snow than normal fell that month?

A butcher has 66 pounds of meat.  He wants to pack the meat into packages weighing 0.75 pounds each.  How many packages can he make?

Leticia used a digitized water collection device to take daily measurements of the rain that feel on her vegetable garden.  One week it rained 0.31 inches on Monday, 0.38 inches on Tuesday, and 0.26 inches on Wednesday.  What was the total rainfall for those three days?

Christine worked 38 hours last week at the department store.  She was paid a total $324.52 for the week.  How much was she paid per hour?

Armando and Luisa bought a rectangular building lot in a suburb of Austin, Texas.  It measured 71.6 feet by 96.7 feet.  What is its area in square feet?

Jose earns $13.90 per hour at his job painting houses.  He worked 18 hours last week.  Calculate Jose’s pay before taxes.

 

Advanced Cube 

Dennis rented a van to drive from Boulder, CO to Palo Alto, CA.  The cost was $300 for the first two weeks and $50 per day after.  He was not charged a mileage fee for the first 2000 miles, but had to pay 12 cents a mile for every mile after that.  The trip took 2 weeks and 5 days, and he drove 2350 miles total.  What was the total cost of the van rental?

Mike and Claire want to buy a home that costs $155,000.  They need an amount equal to 0.15 of the purchase price for the down payment.  They also need an amount equal to 0.01 of the purchase price to cover closing costs.  If they have saved $24,500, how much more money do they need?

Nancy earns $4.85 per hour selling TV’s and VCR’s in a large department store.  She also earns $15.50 commission for each TV she sells, and $12.75 for each VCR she sells.  One day she sold 3 TV’s and 4 VCR’s while working 7 hours.  How much did she earn that day?

One year, Gary’s height was measured with a yardstick as 62 inches.  An advanced laser measuring device used the next year showed that his height had increased to 65.490 inches.  According to these figures, how much had Gary’s height increased?  Round to the nearest hundredth of an inch if necessary.

The nutrition chart on a bag of flavored potato chips says that each serving contains 0.26 grams of cholesterol.  The chart also says that there are 4 servings in the bag.  How many grams of cholesterol are in the entire bag of potato chips?

Judy is planning a border for her triangular-shaped garden.  One side of the garden is 8.8 feet long, another side is 15.6 feet long, and the third is 12.1 feet long.  Find the amount of border material needed.

 

Differentiated Learning Activity – Tri-MindSubject:  Mathematics Topic:  DecimalsOutcomes:  As a result of the learning activity, student should meet the following key skills:  I can…(9) perform division with decimals when the divisor is a whole number or a decimal.Readiness Levels (Tiered Assignments):    Exceeds expectations    Meets expectations    Does not meet expectationsLearning Preference Model: Visual Auditory Kinesthetic    Multiple Intelligencesx    Triarchic    OtherActivity Structure:    Choice Board                            Learning Contract    Cube/Thinkdots                    x    Tri-mind    RAFT                                       Structured Academic Controversy    Profiler                                     Project/Problem Based Learning    Other                                       Tiered AssignmentDescription of Learning Activity:Students will choose one of the three tri-archic activities (see attached).  They will then have 2-4 minutes to brainstorm a solution, and another 5-8 minutes to write or draw it out.  Then, students will get into groups of three to share their solutions with each other.  Each student in the group will chose another student’s solutions to explain once they combine groups (forming groups of six).Assessment:Students will assess each others’ solutions based on mathematical soundness and proper understanding of average.; first in their group of three, and then, when they are part of a group of six.  During this sharing time, the teacher will be walking around to offer feedback as well.Closure/Sharing:As mentioned, students will share in a group of three, and again, share a different student’s solution in a group of six.  Lastly, two or three volunteers from each learning preference will be asked to share with the whole class. Tri-Mind Analytical

Write a definition for average.  Be sure to explain how the average of whole numbers will not necessarily be a whole number.

 Practical In the newspaper you come across a vertical bar graph, with a horizontal line, representing the average, as shown below.  Write a letter to the editor explaining the average shown is clearly not the arithmetic mean of the numbers, and defend this position.  Then, include a copy of the graph with where the correct average should appear.

 Creative Think of a way to visually show what average means.  If you are using a type of a graph, please label the graph with numbers, including the average.  Choose your numbers so that your average is a decimal.