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.

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Michelle Sigaran

How to Teach the Exponent Properties

Students often find exponent properties confusing, especially since addition is used to simplify expressions like $x^5x^3$ despite no visible plus sign. Instead of just telling students the rules, which is ineffective for those who struggle with memorization, a better approach is a four-step process:

1. Make sense of the expression
2. Model the expression
3. Simplify using the model
4. Notice the pattern

This method helps students discover and understand exponent properties conceptually.

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For the expression $x^5x^3$:

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 $x^8$.

4. Noticing Patterns
After doing a couple of similar problems following this method, I would then ask 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.

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For the expression $x^5{\mathrm{/x}}^3$:

1. Make Sense of the Expression
Ask students what the expression means, helping them recognize it represents division.

2. Modeling the Expression
Write it out as $(x.x.x.x.x)/(x.x.x)$ to represent what they described.

3. Simplifying the Expression
Review that $x/x = 1$, just like $2/2 = 1$ or $5/5 = 1$. After canceling, the expression simplifies to $x^2$.

4.Noticing Patterns
Repeat with similar problems and ask students to find a shortcut. They should see that the exponent in the simplified expression is the difference of the exponents in the original expression.

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I use this method for every exponent rule. For negative exponents, I create a table with positive exponents and guide students to extend the pattern. This approach helps students truly understand exponent properties rather than relying on memorization. If they forget a rule, they can always model and simplify instead. For complex expressions like $x^{50}x^{30}$, rather than modeling all the $x$'s, I give them a simpler expression to work through first, helping them recognize the pattern and apply it to the larger problem.

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.  

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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.

Read more »

Michelle Sigaran