May 2018 - Make Sense of Math


Keep Math Alive During Summer
Doing math worksheets is likely not on the list of activities your students or child wants to do this summer.  In fact, I read about a recent study from the Harvard Graduate School of Education that math worksheets during the summer do not actually improve a child's math performance. Instead, the Harvard Graduate School of Education suggests that by helping your child see and use math in every day life you can help prevent summer math loss.   You can read more about this study Here

Here are some great suggestions to keep math alive for your student during the summer. 

1. Real-World Integers - Take a picture of three examples of people or companies using integers in the real-world.   

2. Grocery Store Rates -  Go to the grocery store and take three pictures of unit rates on the labels.  Explain how you can use this information to save money. 

3. Interviews - Interview an adult who is a stay-at-home parent and how they use math in their life.  Write a short report about what you learned.  

4. Budgets - Learn how to make a budget through research and/or by talking to an adult who uses a budget. Create a fake budget for a salary of $2,500/month. 

5. Architecture -  Draw a scale drawing of your bedroom.  Include a scale, and at least three items in your room. Use the scale drawing to discover different ways to re-arrange the furniture in your room.

6. Real-World Fractions - Take a picture of three examples of people or companies using fractions in the real-world.   

7. Interior Design - Calculate the surface area of your bedroom walls.  How much paint will you need if you want to repaint the walls?

8. More Interviews - Interview a professional who uses math in their career.  Write a short report on what you learned.

9. Advertising - Search a grocery add and cut out three adds that advertise products as multiples/$, such as 2/$5. Figure out the unit cost of each product.

10. Math In Nature -  Learn about the Golden Ratio, and find examples of this ratio in nature. (I had my students do this once, and they loved it!  The Golden Ratio is so fascinating!)

Talk with Your Kids about Math
Adults often over look how often they use math in their lives: calculating distances, budgeting, area for gardens or decorating, cooking, etc... Talk with your child or students about how you use math every day and help them open their eyes to the math that lies at their fingertips.

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Save these tips and ideas to your favorite classroom Pinterest board. Come back and reference them for ideas on activities to develop procedural fluency in your middle school math classroom.


Keep Math Alive During Summer






How to teach exponent properties


How to Teach the Exponent Properties
The exponent properties can be super confusing for students if they do not make sense of them.  For example, when looking at the expression: x5xno where in the expression is their an addition sign, but if you know the property, addition is used to simplify the expression. I want to share some tried and true tips for successfully teaching exponent properties. 

First off, I want to discuss what is NOT effective:  I highly suggest not just telling your students the rules.  Having them simply copy down the rules then practice them will be ineffective, especially for students who struggle with memorization.

What IS effective:  I want to present a four-step process for helping students discover and make sense of the exponent properties. This process includes: helping students make sense of the expression, modeling the expression, simplifying the expression from the model, and noticing the pattern.

Let's look at the expression: x5x
1 - Make Sense of the Expression
I would start by asking my students, "What does this expression mean?"  Hopefully they could make sense that it is the product of x multiplied by itself 5 times and x multiplied by itself 3 times.

2 - Modeling the Expression
I would then have them write out the meaning of what they explained in the first step.  (x.x.x.x.x)(x.x.x).

3 - Simplifying the Expression
We would then talk about how (x.x.x.x.x)(x.x.x) is the same as x8

4 - Noticing Patterns
After doing a couple of the same types of problems following this method I would then ask the students to look for a pattern.  Hopefully they would notice that the exponent in the simplified expression is the sum of the exponents with the same bases.

Lets look at another expression x5/x
1 - Make Sense of the Expression
Ask your students the meaning of the expression

2 - Modeling the Expression
Write out in symbols what they said in words from the first step.   (x.x.x.x.x)/(x.x.x). 

3 - Simplifying the Expression 
You may need to review with your students that x/x=1, just as 2/2 = 1 or 5/5=1.  After canceling out, this will simplify to x.x = x2 

4 - Noticing Patterns
Again, do the process a couple more times with similar problems.  Ask the students if they notice a pattern or a "shortcut"  They should notice that the power in the simplified expression is the difference of the exponents in the original expression. 

I follow this method with every exponent rule.  With the negative exponents, I create a table with the positive exponents, and have them notice a pattern and continue the pattern to discover negative exponents. 

By following this method your students will make sense of the exponent properties.    The best part about using this method is that if a student doesn't memorize this property they can always go through the process of modeling and simplifying. Memorization is not required.  If their is an expression such as x50x30, and your student cannot  remember the rule, they probably don't want to model the expression either...that would be a lot of x's.  Instead of telling them the rule, I often write a simpler expression, have them go through the process of simplifying, modeling, and noticing the pattern, then apply their pattern to the larger expression. 

Exponent Properties Guided Notes for YOU

If you are looking for some guided notes on exponent properties I have taken then time to create some.  Students will discover all the rules through this method and apply their learning on expressions.  

In the mean time,
Happy Teaching!

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Save these tips and ideas to your favorite classroom Pinterest board. Come back and reference them for ideas on teaching the exponent properties.
How to teach exponent properties


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