Differentiated InstructionMathematics

Presented by: Leslie Humphreys, M.ed

Daily Warm-up

Reduce Math Anxiety

Teach vocabularyUse Math Wonders to increase

interest and engagement in mathEncourage multiple

solutions/answers

Teach Vocabulary

Define the term Use common language to

connect the term Encourage student’s language

when describing their process or asking questions

Math WondersBy: Alfred S. Posamentier

The Irrepressible Number 1

The Amazing Number 1,089

Number Patterns

Number Patterns

# One1x1 = 1

11x11 = 121111x111 = 2,321

1,111x1,111 = 1,234,321 11,111x11,111 = 123,454,321

Number Patterns

One #2

1x8+1 = 9

12x8+2 = 98

123x8+3 = 987

1234x8+4 = 9,876

12345x8+5 = 98,765

The Irrepressible #1

Use a number between (12 – 29)

Follow these 2 rules.

1.If the number is odd, then multiply by 3 and add 1.

2.If the number is even, then divide by 2.

Show each step on a separate line.

The Amazing Number 1,089

1. Choose any 3 digit number where the units and hundreds digits are not the same. [825]

2. Reverse the digits of the number you selected. [528]

3. Subtract the two numbers (larger from the smaller). [825-528=297]

4. Once again, reverse the digits of this difference. [792]

5. Now add the last two numbers. [297+792= 1,089]

The Big Four

Number Operations & Number Sense Data Analysis, Statistics, & Probability Measurement & Geometry Algebra, Functions, and Patterns

Eight Standards for Mathematical Practice (CCSS)

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Number Operations & Number Sense

WARSupplies:

Deck of playing cards for every two students.How to play:

Students each turn 1 card over, and race to mentally compute the solution.

Differentiate: Pairs use basic operations (add, subtract, multiply) up to

more complex calculations such as 2x + y =

War & The Common Core

“Mental Math War develops students’ capacity for “mental math” and enhances their fluency with numbers, expressions, and equations” (Silver, Brunsting, Walsh, & Thomas, 2012, p. 28).

Standards: MP 5 Tools: selecting from available, appropriate

tools when solving a mathematical problem MP 6 Precision: calculating fluently and efficiently

Project Based Learning

Allows for problem solving with real world applications.

Utilizes co-operative learning. Often interdisciplinary. Allows for differentiation within the group, while

every group member is making a valuable contribution to the solution.

“School Lunch Project”

Availability to food affects a populations growth rate.

This activity allows students to learn basic nutritional facts, while creating a project which allows them to utilize math, science, and writing skills.

In addition to the materials provided; you will need copies of current flyers from local grocery stores (I used Kroger and Foodland).

Nutrition Project Based LessonNutrition Project Based Lesson

Nutrition Project (Continued)

The challenge: Everyone has groused about school lunches for years It is your turn to plan one week of lunches for GED Elementary School.

You have been given $500.00 to spend for the week. You will need to plan to feed 30 students per day. (You will not need to purchase paper products.)

Use the nutrition pyramid to ensure you meet healthy meal requirements, and the grocery store flyers to determine the cost of your lunches. (You must use items listed in the flyers for your menus)

Nutrition Project (Continued)

You may not serve soda, Gatorade or other sugary drinks.

You may serve a treat (ice cream, cookie) once during the week.

You must calculate the servings you will get from each item on your shopping list to ensure you have enough to feed your students.

At the end of the week, we will vote for the most popular menu as well as, the most economical and nutritious menus.

School Lunch & The Common Core

Explaining solutions builds students’ reflecting, reasoning, and sense-making habits as they explain and communicate the problem-solving process.

MP1 Make sense of problems and persevere in solving them.

MP4 Model with mathematics.MP6 Attend to precision.

Data Analysis, Statistics, & Probability

M & M MathCan be done individually or in pairs.Differentiate by pairing stronger/weaker students.Remember! No sampling until data is recorded.

M & M Math and The Common Core

Using manipulatives to represent data allows students to make a deeper connection.

Creating representations of data and mathematical questions regarding data sets, demonstrates student understanding.

MP1 Make sense of problems and persevere in solving them MP4 Model with mathematics MP6 Attend to precision MP7 Look for and make use of structure

Measurement & Geometry

Geometry Yard

Differentiated measurement activity that reviews measurement fundamentals while reviewing geometric principles.

Formula Bingo

Students often do not have difficulty using a formula, but recognizing a problem that requires a formula to solve it. (This activity can be differentiated by allowing use of formula sheets for beginners, matching name of formula to the equation, and finally word problems requiring one of the formulas on the card to solve.)

Measurement/Geometry & The Common Core

Understanding measurements represent units allows students greater flexibility in problem solving.

Recognizing the need to solve via a given formula, leads to a quicker solution to the problem.

MP.1 Make sense of problems and persevere in solving them.

MP.4 Model with mathematics.

MP.6 Attend to precision.

Algebra, Functions & Patterns

Parachute Jump Activity

Reinforces coordinates on a plane, Pythagorean theorem, and calculating distance.

Battleship

Great for introducing the coordinate plane.

Reinforces the characteristics of each quadrant.

Algebra, Functions & The Common Core

Students who have the ability to concretely solve problems involving theorems gain a deeper understanding of the concept.

Modeling of this process aids developing students during small group work.

MP.2 Reason abstractly and quantitatively.

MP.5 Use appropriate tools strategically.

MP.6 Attend to precision.

MP.7 Look for and make use of structure.

References

Works Cited

Martin, H. (2006). Differentiated Instruction for Mathematics. Walch Publishing.

Posamentier, A. (2003). Math Wonders. Alexandria, VA: Association for Supervision and Curriculum Development .

Silver, Brunsting, Walsh, & Thomas. (2012). Math Tools. Thousand Oaks, CA: Corwin.