Howard A Stern

Common Core is coming

Not Just the Standards  Algebra  Functions  Modeling  Geometry  Statistics

But Also the Practices  Make sense of problems and persevere in solving them  Reason abstractly and quantitatively.  Construct viable arguments and critique the reasoning of others.  Model with mathematics.  Use appropriate tools strategically.  Attend to precision.  Look for and make use of structure.  Look for and express regularity in repeated reasoning.

Particularly suited to Nspire  Construct viable arguments and critique the reasoning of others.  Model with mathematics.  Use appropriate tools strategically.  Look for and make use of structure.

Viable Arguments  As an end goal  As a means of formative assessment.

Argument Does Not Mean Rant

 Use student thinking to discover misconceptions  Use student understanding as a guide  Push them to make connections

Modeling  Mixing the four modes (graphical, textual, symbolic, and tabular)  Take mathematical action on a mathematical object and observe the mathematical consequences.

Use appropriate tools  Almost all handheld activies involve some level of strategic use of appropriate tools.

Structure  Table view  Function rules  Ability to drag and drop objects to organize the display

But …  How do we use Nspire apps to encourage these practices.

distributive_property.tns  On page 1.2 grab and drag points a, b, and c and come up with three observations about the relation to the expressions in blue.

Possible discussion points  Why is sign of b + c more important than individual b and c?  Does order of a, b, and c on the number line matter?  Did you try all combinations of positives and negatives?

CCSS?  Students will look for regularity in repeated reasoning  Students will use appropriate tools strategically

Points_on_a_Line.tns  On page 1.2 observe the horizontal and vertical changes you must make to point A to get it to point B.

Possible discussion points  Does direction matter? (moving both distance AND direction)  When moving, for example, up 7, is it okay to call it “positive 7?” How about “plus 7?”

CCSS?  Students will look for regularity in repeated reasoning  Students will use appropriate tools strategically  Students will model with mathematics

Simple_Inequalities.tns  Observe effect of dragging point P (below the number line) and changing the relationship symbol (upper left corner of symbol box)

Possible discussion points  What changes and what stays the same as you drag screen objects?  What is the significance of the open or closed circle?

CCSS?  Students will look for regularity in repeated reasoning  Students will use appropriate tools strategically  Students will look for and make use of structure

How_Many_Solutions.tns  Rotate and translate line 2  What do you observe about the number of intersections or points in common with line 1?

Possible discussion points  Remind about relationship between “slope” and “rate of change.”  How do you KNOW when lines are parallel?  What is the difference between “answer” and “solution?”

CCSS?  Students will look for regularity in repeated reasoning  Students will use appropriate tools strategically

Function_Notation.tns  Drag the number line points on pages 1.2, 1.3, and 1.4 and observe the effects on the “function machine.”

Possible discussion points  What do “x” and “f(x)” symbolize?  What is the relationship between function notation and simply evaluating expressions at given points?  Is y=[expression] always the same as f(x)=[expression]  What is the difference between the 2s in f(2)=y and f(x)=2

CCSS?  Students will look for regularity in repeated reasoning  Students will use appropriate tools strategically  Students will reason abstractly and quantitatively

Wrapping up  Many of us have already been using Common Core practices  A focus on how we ask questions is almost always appropriate  Technology can, but does not always, enhance our lessons

Thank you for attending  I will post the PowerPoint on my website  Activities used may all be downloaded from MathNspired (TI website)  I don’t always talk maths, but welcome twitter