strategies and activities to engage kids in mathematics

12 Strategies to Engage Middle

School Kids in MathDr. Shirley Disseler

Assistant Professor Elementary & Middle Grades Education. STEM Coordinator, LEGO Educational Specialist

What is the goal today?

• Explore & share strategies for middle grades math

• Link to math practices

• Examine what is means to be a mathematically proficient

middle school student

Opening Activity: BTE

• What do you think it means to be a mathematically

proficient middle school student?

• Build a model that indicates your thoughts.

• Share

What Should the Focus

Truly Be?

• Use of Math Practices to create proficient math literate

citizens

• Contextual problem solving

• Collaboration and Communication

• Integration of math into other content through contextual

situations

Goal of Middle School

Mathematics

• Promote and Create “Mathematically Proficient

Students” ready for 21st mathematical

understanding and application.

• WHAT DOES THIS MEAN?

Mathematical Process

Skills (Math Practices)

• Make sense of problems and persevere in solving them.

• Reason abstractly and quantitatively.

• Construct viable arguments and critique the reasoning of others.

• Model mathematics understanding

• Use appropriate tools.

• Attend to precision.

• Look for and make sense of structure

• Look for repeated reasoning

How do we do it?

• 1) Get them motivated!

• 2) Get them engaged!

• 3) Assess them formatively and often!

• 4) Share ideas that work! GET OUT OF THE BOX!

Common Core Math

• More Integrated with other content

• Mathematical Practices MUST be addressed

conceptually.

• Use the unpacking documents : A better guide for

teaching and learning.

Getting Started with

Thinking: Strategy 1

• Appetizers:

• Logical thinking activities

• Playing cards

• Dominoes

• VENN Diagrams

WHAT ARE MATHEMATICALLY PROFICIENT STUDENTS?

• Students that can begin the math process by explaining to

themselves the meaning of a problem and looking for

ways to begin to solve problems.

• Analyze problems from the standpoint of what is

• Given

• Constraints

• Relationships (between and among variables)

• Goals

Let’s try it!

• How many ways can you name yourself?

• Think/ Pair/Share

• Look at the number 440.

• List all the ways you can name that number.

• Think /Pair /Share

This gets students prepared for what a ratio and a fraction

really represent.

How many ways can you name ¾?

Equivalent

Representations

6 + 4 = _____ + 5

2/3 + 4/5 = 4/6 + _____

Why do students struggle with these?

Strategy 2: Prime number

Models- Visualizing the Math

• Using 100 grids and linking cubes model prime

factorization.

• This helps students to see visually the prime components

of any number.

• Let’s try it!

Strategy 3: Contextual Problems

and organizers: Analyzing the Math

• http://worksheetsdirect.com/members/wp-

content/uploads/2011/08/simplifying_algebraic_expressions_gra

phic_organizer_1-1.pdf

A great site for using graphic organizers in algebra!

Strategy 4: Match Set Activities:

Collaborating with Math

Line students up equally on opposite sides of the room.

(one group as the symbolic representation of an event,

one has the the situation in mathematical terms and you

could have a third set with real world problems that can

be described by the expression) Set timer or play music

as students without talking walk around an pair up

with their match set.

What are Mathematically Proficient

Students?

• Students who can understand and use

assumptions, definitions, and previous results to

construct arguments and make conjectures.

• Analyze by breaking down examples and non-

examples

• Communicate to others and discuss

mathematically and explain reasoning

• Objects, drawings, diagrams and actions.

Strategy 5: Concept Formation

Examples Non-examples

2 (3+ 2 ) = 2 x 3 + 2 x 2 12- 3 + 2 = 12 ( - 3 + 2)

2 (x + 2x) + 3 = 2x + 4x + 3 3 x 2 = 2 x 3

4( x + 4x + 3x) = 4x + 16x + 12x 6 + 0 = 6

What is the concept?

Strategy 6: Concept

Attainment

Use 0 -9 cards, <, >, <, >

Display an inequality on the board such as: x < 4 or 5 > y <

3

Students create a yes/ no column on their desk. They place

the cards that satisfy the inequality in the yes column and

those that do not in the no column. Justify the no answers.

Strategy 7: Proportional

Rectangles

• Sort the rectangles into 3 families.

• Make sure all members of the same family are the same

shape and differ only in size.

• Arrange each group smallest to largest.

• What patterns do you see within each family?

• Stack each family with the left corner and bottoms lined

up.

• What new observations can you make.

Strategy 8: Rational and

Irrational Number Sort

• Using the number cards at your table sort them according

to rational and irrational.

• Have students then put them on a number line in correct

order. (Advanced)

• Discuss with your table the number sorts.

What are Mathematically Proficient

Students?

• Students can apply the mathematics they know to solve

problems in everyday society and in the workplace and

model situations.

• Describe situations algebraically

• Describe charts and graphs

• Reason proportionally: grade 6 should NOT use the cross

product algorithm.

Strategy 9: Games in Math

Proportionality with cards

• Using Card war proportionality.

What are Mathematically Proficient

Students?

• Students who can consider available tools when solving

problems and make a reasonable choice.

• Calculator Computer/tech tools

• Paper and pencil

• Models

• Ruler

• Protractor

• Spreadsheet

Strategy 10 : Using Tools

in Math

• Using cards to promote reasoning.

What are Mathematically

Proficient Students?• Students who can attend to precision in communication of

mathematics to others.

• Can clarify the symbols they use ( +, -. x, / , = etc)

• Careful to clarify units of measure and labels

• Calculate accurately

• Use a frame of reference to identify the context of a

problem.

What are Mathematically

Proficient Students?

• Students who can make sense of structure and discern

patterns within a problem.

• Students who notice notice if calculations are repeated

and look for shortcuts.

Strategy 11: Defining the

problem meaning

• How do you know that 4/6 = 2/3?

• Come up with at least 2 different explanations at your

table.

Possible Explanations

• 1) They are the same because you can simplify.

• 2) If you have a set of 6 items and only use 4 of them that would be 4/6 ; but you could take the 6 items and put them into into 3 groups and the 4 would then be 2 of those groups. This means 4/6 and 2/3 are the same.

• 3) If you start with 2/3 you can multiply the numerator and denominator by the 2 and get 4/6.

• 4) If you have a square cut into three parts and you shade 2 that is 2/3. If you cut these 3 parts in half that would be 6 parts with 4 shaded.

Different Thinking

• They are all correct but represent different types of

thinking about equivalent fractions.

• #2 and #4 are conceptual, although not efficient.

• #1 and #3 are procedural and efficient, but do NOT suggest

conceptual understanding of the concept.

• STUDENTS NEED A BALANCE! WHY?

What are Mathematically Proficient Students?

• Students that can bring together the abilities to

“decontextualize” (represent symbolically and manipulate) and

to “contextualize” (ask questions and rethink strategies as they

work)

Considers things like

• Units involved

• The meaning of quantities (not just how to compute)

• Using different properties of operations and objects.

Final Activity: LEGO

Making meaning of

learning math

Build a model that indicates your take- aways from today.

Comments?

• Thanks for coming today.

You can reach me at 704-798-1056 or at

sdissele@highpoint.edu

• New Book for 3-5: Strategies And Activities for

Activities for Common Core Grades 3-5.

• Middle School Book in progress!