Just for fun ... brain teasers

MTBoS BLAUGUST

Awesome Shelli asked early today if anyone has a slide show of brain teasers that could be used as an "away" screen on Google Meet.

Her ask resonated with me ... felt like a challenge that I wanted to tackle today.

So ... I pulled together a few brain teasers today that might be interesting to a wide range of students.

You are welcome to copy this slide show, use it, modify it, add to it!

The last slide has links to the resources from which I borrowed these teasers.  They are not original with me.  I don't have solutions for most of htem.

Resources to Extend Thinking with Quadratics

 

Here are a few activities that I've used to extend thinking in our work with the Quadratic Function ...

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True False Statements Sorting Activity - Characteristics of Quadratics

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Odd One Out Activities give students opportunity to analyze, build vocabulary, and develop a discerning eye for mathematics.

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Partner Discussions or "He Said She Said" Activity asks students to analyze 2 problems, discuss them and then debrief.

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Always, Sometimes, Never statements are great for helping students think deeply about quadratics.

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Last ... Here is a collection of questions to promote critical thinking:

1) Write three different quadratic functions whose graphs have the line x = 4 as an axis of symmetry but have different y - intercepts.

2) The points (2, 3) and (-4, 3) lie on the graph of a quadratic function.  Explain how these points can be sued to find an equation of the axis of symmetry.
3) Write a quadratic function that has as roots, x = 2a and x = -5b.

4) For what nonzero whole number m does the quadratic equation x^2 + 3mx + (9/2)m = 0 have exactly one real solution for x?

5) What characteristics are most easily determined from a quadratic function written in standard form?  In factored form?  In vertex form?

6) The point (1, 5) lies on the graph of a quadratic function whose axis of symmetry is x = -1.  Your classmate says the vertex could be (0, 5).  Is your classmate correct?  Explain.

Extending Thinking with Systems of Equations

 

Systems of Equations can be fun to explore.  

Here are some ideas for extending thinking...

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Odd One Out is always a great discussion starter!

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Another critical thinking activity ... "Partner Talk or He Said, She Said" ... students analyze problems on their own, pair up to discuss, and then debrief as a class:

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This Tic Tac Toe board offers students opportunities to explain their understanding of systems of equations.  How might you use something like this in distance learning?

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My Analysis Task asks students to complete several activities to demonstrate mastery of systems of equations:

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Last ... if you like using "Always, sometimes, never" statements, here are a set of 10!

Critical Thinking is a Favorite!

For this week's prompt ... "Your Favorite Math Task / Activity / Lesson" there was a clarification that it can be a small task or entire lesson. I'd like to share critical thinking questions that I use in various lessons for small group discussion and explanation.

In the last few years I worked with Pre-AP students.  We were encouraged to emphasize critical thinking, developing students' understanding and use of abstract notation ... in preparing students for AP Calculus.  

Here are a few questions that we used in various units:

Create equations for parabolas that fit these criteria:
a. Vertex in the first quadrant, concave down, and 2 roots with an axis of symmetry at x = 2.
b. Vertex in the second quadrant, concave up, and no roots.
c. Vertex on the y-axis, 2 roots, and concave up.
Explain how you determined each of your equations.

Find the value of b that will make the function pictured  have only 1 zero at -6. 

Find the value of k that makes the linear expression, x - 2, a factor of the cubic expression pictured. Explain your thinking.

We used multiple representations (word descriptions, tables, equations, and graphs) in comparison activities. I believe this one is from a textbook we used:

Consider the function, f(x) = log base b of x where b and x are real numbers. Can the domain include 0? Explain you thinking.

There are more questions/activities.

Parent functions are a huge topic in Algebra 2.  In this post I describe some ways we try to encourage critical thinking as well as just memorizing the functions.

I describe some other problems I considered rich tasks in this blog post.  I share a problem for several units in Algebra 2.

In addition, I used critical thinking structures in class.  Here are a few examples:

He Said, She Said ... Quadratic Attributes

Picture It with Error Analysis ... Quadratic Attributes

Problem Solving Strategy ... Quadratic Attributes

Networking  ... Special Right Triangles

Compare/Contrast ... System of Equations

All of the above questions/activities are noted in my blog somewhere :)

I do have a few additional activities for sale on TpT that address critical thinking in a few units of instruction.

How do you get students to analyze, compare, contrast, and problem solve?

Blogosphere Good Ideas Curated with elink!

Today I learned about a new tool ... super easy to learn! I like it because instead of just sharing links to great ideas, I can add visual appeal!  Check out https://elink.io/ ... and think about how you can use it with your students! Also check out the SIX great sites curated here! You won't be disappointed!

#MTBoSBlaugust Critical Thinking Strategies in the Math Classroom (Activities included!)

How do you encourage critical thinking in your classroom?

Critical thinking involves powerful verbs!
• Compare/Contrast • Classify • Categorize • Differentiate • Distinguish between/among • Evaluate • Justify valid reasoning • Analyze

For example a card sort activity could support thinking from each of the verbs above!

I love the Lead4ward strategies that were shared in some training I participated in a year or so ago. Check these out!

I chose a few of the strategies and created activities for a unit on the attributes of Quadratic functions.

He Said/She Said ... instructions and example ... link here for G Doc.

Odd One Out ... instructions and example ... link to Google Doc here.

Two other examples ... see instructions in the LeadForward file above.

Picture It

Problem Solving Strategy

Notice in each of the four examples students are talking math.  They are analyzing a prompt, but they are not just finding a solution.  Instead they are creating their own statements, justifying their thinking, recording questions, writing steps for themselves.

Will you share ideas for critical thinking activities in the comments??