strategies and activities to engage kids in mathematics
TRANSCRIPT
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
• New Book for 3-5: Strategies And Activities for
Activities for Common Core Grades 3-5.
• Middle School Book in progress!