Geometry in middle school opens up a world of exploration, giving students tools to understand shapes, space, and dimensions—all essential for visual problem-solving. Instead of boring worksheets, hands-on and creative problem solving tasks make these concepts much more engaging and will help with retention. Once students hit middle school, they move beyond simply naming & composing shapes.

Geometry topics cover everything from shape properties and angle relationships to calculating areas, perimeters, and volumes of 2D and 3D figures, as well as applying the Pythagorean Theorem. Building a strong grasp of these topics is crucial for students’ math confidence–and they’ll have more fun while learning!

If you’re ready to explore geometry in engaging, visual and hands-on ways, check out the full list of resources & ideas below. Resources are organized by math concept, making it easier to scan and find what you need.

14 Middle School Geometry Ideas & Resources:

To begin, take a look at some measurement activities, focusing on area, perimeter & circumference with 2D shapes, then find ideas for exploring measurements with 3D shapes.

Exploring 2D Shapes Activities: Understanding Shapes, Measurements & Angles

Explore 2D Shapes with Geoboards: When you’re ready to begin your geometry unit, start by creating, analyzing & calculating with shapes on a geoboard. In this post, you’ll find simple ideas to get started, along with free activity cards.

Explore Triangles with Geoboards & “The Greedy Triangle”: Want to help students understand triangles more deeply (including the triangle inequality theorem)? Create & compare triangles on a geoboard!

Exploring the Angles in Triangles: Dive deeper into triangle relationships as students cut up & measure triangles to discover some amazing triangle theorems.

Area of a Circle Exploration: Ready to dive into circle measurements? This hands-on, visual lesson combines a visual circle with a graphing calculator to consider what the area of a circle really means.

“Pass the Pi” Investigation of the Number Pi: Whether you are exploring circle measurements or just looking for a “Pi Day” activity, this lesson is a great way for students to discover the relationship between the circumference & diameter of a circle.

How Tall is a Building? Indirect Measurement Lesson: Lastly, once your students have learned about similar triangles, a great application is indirect measurement. In this activity, students are guided through using indirect measurement to find the height of their school building.

Exploring 3D Shapes Activities: Nets, Surface Area & Volume

Once students have a solid understanding of 2D shapes & their measurements, it’s time to move to 3D shapes. This opens up a new set of math to explore, and using hands-on discovery activities not only makes math more fun, it will help students better grasp the concepts.

Foldable 3D Shape Nets: Before you can begin measuring & calculating with 3D shapes, you have to understand the shapes themselves! I usually start by allowing students to decorate & fold their own set of 3D shapes using these nets, which we can then refer back to throughout our study of 3D shape properties & measurements.

Explore the Surface Area of Prisms & Cylinders: This hands on activity helps students connect the surface area to the area of each face & come up with their own formula.

Explore the Surface Area of Pyramids & Cones: This activity takes students a step further to explore pyramids & cones & how they are different from prisms.

Which Cup will Hold the Most Hot Chocolate?  As an introduction to the volume of cylinders, you might try this interesting question. This is a great warm-up and an opportunity for students to think about how the width and height affect volume.

Explore the Volume of Prisms & Cylinders: Once again, this activity is hands-on, allowing students to see & discover volume themselves, and make sense of how it differs from surface area.

Exploring Pythagorean Theorem: Hands-On Activities & Real Life Application

Lastly, if your 8th graders are ready to learn all about Pythagorean Theorem & how it can help solve real life math problems involving right triangles. Once they’ve proven, understood and mastered this theorem, they will be ready for more complex calculations in high school geometry class!

Prove the Pythagorean Theorem with LEGO Bricks: This hands-on activity will help students ‘see’ the theorem and understand what all the letters & measurements mean.

Pythagorean Theorem in the Real World: Find two different printable sets to help students actually use and apply this theorem in real life.

• 3 Real World Examples to Explore Pythagorean Theorem
• Pythagorean Theorem Word Problem Task Cards

I hope that gives you lots of engaging, hands-on & creative ways to make geometry come alive for your students! Don’t just list out formulas to memorize. Discover formulas, properties, theorems & more through play & exploration! Have FUN with these middle school geometry ideas!

Want more engaging & creative teaching ideas for your middle school students?

You might want to check out Math Geek Mama+, my all-access membership, which includes hundreds of ready to use materials for grades 5-8. There are even more geometry resources ready for you to download inside Math Geek Mama+.

LEARN MORE ABOUT MATH GEEK MAMA+ HERE.

The post 14 Creative Middle School Geometry Ideas {Tips & Free Resources!} appeared first on Math Geek Mama.

I find that a lot of textbooks barely skim the surface when it comes time to solve linear inequalities. After all, once students are comfortable solving linear equations, this is just more of the same, right? Wrong! Inequalities are more complex and have greater depth of meaning than equations, and although the algebra involved in solving them may look similar, it takes a lot of work to actually understand what’s going on. Plus, students have to know when to “flip the inequality symbol.” What does that even mean, and why do we do it? But once you’ve done the hard work of sense-making and students are ready to practice, grab these silly riddle pages for Low-Prep Solve Inequalities Practice.

Understanding the Solution to Inequalities:

One of the biggest differences between a linear equation and an inequality is the solution.

In both cases, the solution is the value(s) that make(s) the statement true.

However, most students are used to solving an equation in which exactly one number makes the equation true. (Yes, a linear equation can also have no solution or infinite solutions, but in early middle school students are solving an equation to find exactly one number that makes it true).

An inequality, on the other hand, will have a whole range of numbers that make the statement true.

For example, if the solution is x < 2, that means that the solution is not 2. The solution is ANY number that is less than 2. So it could be 1.9. It could be 0. It could be -100.

It’s important that as students solve inequalities they model the solution on a number line so they can visualize the entire set of numbers that makes the inequality true.

Although this set of riddles practice pages do not include number lines, you may want to have students sketch a number line next to each solution as well so they can show you they understand the solution and what set of numbers is part of the solution.

Solve Inequalities Practice Pages: Easy to Differentiate

This download includes 3 practice pages, gradually increasing in difficulty.

You will find the following inequalities to solve:

• Solve one-step inequalities (use with 6th or 7th grade)
• Solve two-step inequalities (use with 7th or 8th grade)
• Solve multi-step inequalities (use with 8th or 9th grade)

If you have students who are struggling or need to get back to the basics, start with the first page of one-step inequalities.

But if you have more advanced students who are ready for a challenge, let them try the multi-step page! This page includes variables on both sides of the inequality symbol as well as the distributive property.

Plus, as students solve each inequality they can self-check as they look for the solution at the bottom of the page to determine the answer to the silly riddle!

If you’re looking for resources to teach solving inequalities, check out Math Geek Mama+, our ad-free option that includes inquiry lessons to help students make sense of algebra topics such as solving inequalities.

There are visual lessons to help students see and understand what inequalities mean and WHY the inequality symbol flips.

Plus, you’ll find more engaging and easy to use practice pages like this one!

LEARN MORE ABOUT MATH GEEK MAMA+ HERE

Ready to use these riddle pages with your students? Just use the link below to grab it in my shop.

{Click HERE to go to my shop and grab the FREE Solve Inequalities Practice with Silly Riddles!}

Plus, find more resources for solving equations and inequalities at the links below:

• Summer Algebra Review: Solve Equations Practice
• Writing Algebraic Expressions: FREE Practice Pages
• DIGITAL Solving Linear Equations Error Analysis {FREE}

The post Solve Inequalities Practice – Silly Riddles for 7th-8th Grade appeared first on Math Geek Mama.

One of the most challenging topics in middle school math is making sense of rational numbers in all their forms-fractions, decimals, repeating decimals-and knowing how to convert between various forms. Throw in positive and negative signs and things get really crazy! In this simple rational numbers activity, students will use lots of different math skills and strategies to compare rational numbers.

What Are Rational Numbers?

Rational numbers is a set of numbers that includes any number that can be written in fraction form. Thus, every rational number can also be written as a repeating decimal or a terminating decimal (meaning it stops, such as 0.5). Rational numbers also include integers, meaning both positive and negative numbers.

That means rational numbers include many different forms or sets of numbers, such as:

• Positive and negative whole numbers
• Positive and negative fractions and mixed numbers
• Positive and negative decimal values, as long as they either repeat or terminate

Although students begin comparing fractions and decimals as early as 4th grade, 7th or 8th grade students look at much more complex rational numbers. More challenging comparisons are what’s included in this sorting challenge.

Compare Rational Numbers Sorting Activity

This printable activity includes 12 rational number comparisons.

This means students are trying to determine less than, greater than or equal to with each pair of rational numbers.

Some of the problems compare two fractions, some compare a fraction to a decimal, and some compare two decimal values.

Adding to the challenge, some of the numbers are positive and some are negative.

Students should use a variety of strategies to compare the quantities, such as:

• Are both positive or both negative? If one is positive and one negative, they know right away which is larger, regardless of the number forms
• If the numbers are both fractions, they might rewrite them to have common denominators or use other strategies such as comparing each to a benchmark such as 1/2 or one whole
• If the numbers are both decimals, they should pay attention to place value
• If the numbers are in different forms, they can rewrite one so they are in the same form (such as both decimals) or they can compare the a benchmark, or consider place value
• If they’re looking for a visual, they could put the numbers on a number line

The goal is for students to find ways to compare the quantities and then determine how to correctly complete the comparison statement (<, > or =).

How to Use the Rational Number Sort:

This is designed to be a printable cut and paste activity, however there are other options as well depending on what will work best for your students.

Printable Cut and Paste Activity:

To use as a cut and paste activity, print the sorting mat (one per student or one per pair–this works well as a partner activity).

Then print the page of comparison problems. There are two sets per page, so print enough so you have a complete set for each student or pair of students.

Students then cut out each expression, compare the rational numbers and determine if it goes in the “Less Than,” “Equal To,” or “Greater Than” column on the sorting mat.

Encourage them to sort all problems first and then let you check it before they glue the final answer down.

Once students have corrected sorted each comparison statement, they glue them down and they’re done!

Math Center Option:

If you would prefer to prep this one time and use it again and again, you can print the sorting mat on colored card stock paper and laminate for durability.

Then print the comparison statements on another color of card stock paper and laminate. Cut out all the comparison statements to go along with the sorting mat.

Students then work sort the statements onto the mat, but don’t glue them down.

Then store the comparison statements in a ziplock bag along with the sorting mat for another group to use later!

Lastly, one final option is to print the sorting mat and cards on card stock paper. Laminate the sorting mat or place it in a page protector and give students a dry erase marker.

Then students can simply write the comparison statements onto the sorting mat, no cutting or pasting required.

(You can also do it this way as an individual review. Just print a page for each student on regular paper and let them write in their comparisons to turn into you). 

When they finish, be sure they erase their answers from the mat and store the mat and comparison statements for another day.

I hope this provides a helpful challenge as your students learn to work with & compare rational numbers.

If you enjoy this activity, become a Math Geek Mama+ member and gain access to the entire ad-free library of engaging activities like this one, with hundreds of math games, digital practice, and low-prep review worksheets for grades 5-8!

Learn more about Math Geek Mama+ right HERE.

If you’re ready to grab it, use the link below to head to my shop to get a free copy!

{Click HERE to go to my shop and grab the FREE Compare Rational Numbers Sort for 7th & 8th Grade!}

Looking for more rational numbers resources? Check out the links below!

• {FREE} Get Them in Order: Comparing Fractions Game
• Adding and Subtracting Integers {FREE Lesson!}
• Multiply & Divide Integers Lesson {FREE}
• Compare Decimals Cut & Paste Sort {FREE!}

The post Compare Rational Numbers Sorting Challenge – Grades 7-8 appeared first on Math Geek Mama.

Translating words and phrases into “math language” is an important skill because it will help them prepare for algebra and higher levels of math. But getting kids comfortable and confident with that takes time and practice. Whether you’ve got 5th graders working on numerical expressions or 6th and 7th graders writing algebraic expressions with variables, this low-prep and engaging partner challenge is a great warm-up!

What are Expressions?

Before jumping into this activity with your students, be sure you (and they) understand what expressions are.

Here’s a short, helpful definition of a numerical expression:

Numerical expressions are number sentences involving one or more operations.

Some examples include: 5 + 7 or 15/8 + 12 or (16 + 3) x 18

Numerical expressions contain NUMBERS and math OPERATIONS.

What about algebraic expressions? What’s the difference?

Algebraic expressions are similar to numerical expressions in that they include numbers and operations, but they also include at least one VARIABLE, which represents an unknown number.

Some examples of algebraic expressions are: 3x or 9 – 12y or (4 + p) – 15r

The key thing to note is that expressions include numbers and math operation symbols but NO EQUALS SIGN.

When you have two expressions that are equal to each other, it forms an equation. But that’s a post for another day. If you’d like to move on to finding equivalent expressions try this cut and paste equivalent expressions activity.

Introducing Expressions to Students

Although I shared some definitions and examples for you above, I would encourage you to NOT start there with your students.

Instead, give them the chance to think about their own way of translating situations, words and phrases into expressions using this partner challenge.

Walk around the room and listen in on student conversations to hear how they think about the wording and the math. Listen to student disagreements and how they justify their answers.

This will give you insights into what students already know, what they may need help with, and any misconceptions that you need to clear up after they finish the activity.

Writing Expressions Activity: Which Version Will You Use?

To use this in your class, all you need to do is choose which version is best (numeric expressions or algebraic expressions) then print a set for each pair of students.

But which version do you need for your students? Option one includes numerical expressions only. This is best for 5th grade students who are not yet ready to work with or think about variables.

But you might also use this version with older students who struggle with word problems, need further clarification on different math operations or who need a refresher before including variables.

Option two is to help introduce students to writing algebraic expressions. This is a fun warm-up for 6th or 7th grade students before you get into your expressions chapter or unit, or as a quick refresher before working on more challenging expressions and word problems.

If you enjoy this activity, become a Math Geek Mama+ member and gain access to the entire ad-free library of engaging math activities like this one, hundreds of math games and low-prep practice worksheets for grades 5-8!

Learn more about Math Geek Mama+ right HERE.

How to Use the Writing Expressions Partner Activity

To begin, pair students with a partner and print a worksheet for each partner. One student should have ‘Partner A’ and the other student should have ‘Partner B.’

The post FREE Writing Expressions Activity: Partner Challenge – Grades 5-7 appeared first on Math Geek Mama.

Multiplying and dividing integers seems like such a straightforward process at first. If both integers are positive or both integers are negative, the result is positive. If the integers are opposite signs (one positive and one negative) the result is negative. Easy, right? Of course I’m about to complicate things, LOL. What about when you’ve got more than two integers? What about when the numbers get really large or really small? What if you’re dealing with exponents?? To help students tackle more complicated expressions without getting bogged down in the numbers (or relying on a calculator), use this Multiply & Divide Integers Sort.

*Note: This post contains affiliate links which help support the work of this site. Read our full disclosure here.

Setting Up the Integers Sorting Challenge

IN order to complete this challenge, students do have to have some prior knowledge of the ‘rules’ for multiplying and dividing integers. I recommend using this guided lesson to walk them through an introduction to multiplying & dividing integers. Then they’re ready for this sorting challenge!

This is a very simple activity to set up, but will hopefully prove especially useful for students.

To begin, you will need to print the sorting mat & expression cards (included in the download).

I recommend printing on card stock paper and laminating for durability.

Then cut out the expression cards (there are 24 expressions altogether) and you’re all set!

Reasoning with Integer Operations

Once you have the materials ready for students, they simple use their reasoning skills to determine if each expression will result in a positive value or a negative value without doing any calculations.

The goal here is for students to internalize the ‘rules’ for integer multiplication and division and also look for patterns (such as with exponents).

The post {FREE} Multiply & Divide Integers Sorting Challenge appeared first on Math Geek Mama.

Fraction operations. Whew! Just typing that out feels stressful! Over and over again I hear from teachers whose students struggle with fraction sense and fraction operations. While I do encourage teaching and modeling with hands on tools, pictures and real life contexts, kids also just need lots of practice and exposure. So the next time you’ve got an early finisher, need some low-prep sub plans or want some extra practice to send home, grab this free add fractions color by number activity!

Materials Needed for the Fraction Addition Color by Number:

• Coloring page for each student
• Fraction Addition Task Cards printed & cut (there are 12 altogether)
• Colored pencils, markers or crayons

Once you’ve got the materials printed and prepped and gathered some coloring supplies, you’re all set!

How to Complete the Color by Number Activity:

This low-prep math practice is pretty straightforward. To begin, students solve the fraction and mixed number addition problems on the task cards.

If they find the correct solution, it will be on the task card with the COLOR to use for that task card. They then color the color by number page using the task card number.

For example, the solution for task card #2 is labeled GREEN. In this case, students would color all the 2’s on the color by code page GREEN.

This may be the one thing to note for students before they begin. The FRACTION ANSWERS will not be on the coloring page, only the number of each task card.

Once they have all 12 cards solved, they will be able to color in the design on the coloring page.

One final note about the coloring page: a design was chosen specifically so that students could not just guess the colors and therefore guess the answers. It is a unique design, full of color, rather than a picture of a known object.

If you enjoy this lesson, become a Math Geek Mama+ member and gain access to the entire library of engaging math lessons like this one, hundreds of math games and low-prep practice worksheets for grades 5-8!

Learn more about Math Geek Mama+ right HERE.

Ways to Use the Add Fractions Color by Code:

Although you could assign this as an individual activity, you could also put students in small groups or use this as a math center.

In this case, put students in groups of 3-4. Print a coloring page for each student, but only print and cut out ONE set of task cards.

Then students will each choose 3-4 task cards to solve individually. They can then help each other if they get stuck, and check each other’s work as they go.

Once they have all completed their task cards, they swap to know how to color in the additional spaces on the coloring sheet.

Although this does not provide as much practice for each student, it does allow the activity to be completed faster, requires less printing, and allows students to work collaboratively.

Of course you can also assign this as individual practice or review. Here are some ideas:

• Keep on hand for ready to go sub plans
• Offer as a choice board option
• Activity for early finishers
• For struggling learners who need more practice
• To send home for tutors or parents to practice/review with their kids

However you use this, I hope it provides a new or different option for your kids who need to review addition with fractions and mixed numbers!

Ready to grab the download for yourself? Head to my shop at the link below.

{Click HERE to Go to My Shop & Grab the FREE Add Fractions Color by Number Activity!}

Looking for more fraction resources? Check out these additional freebies:

• {FREE} Candy Bar Fractions: Hands On Fraction Practice
• Add & Subtract Fractions Cut & Paste Activity {FREE}
• Hands On Adding Fractions Game for Kids
• Missing Addend with Fractions: Challenges for Google Slides {FREE}

The post Add Fractions Color by Number: Unlike Denominators & Mixed Numbers appeared first on Math Geek Mama.

As a math teacher, I firmly believe in teaching math through problem solving and investigation. This means I try to present an interesting problem or question to students and let them play around and explore before we dig into formal definitions or algorithms. And when I can combine an important math topic with Skittles candy? That’s definitely a math win! This lesson starts with a real life data set related to baseball in the United States. Students then model the survey using Skittles candy to see how population sampling can lead to general inferences about the population as a whole. I hope this provides a fun statistics lesson for your students!

Materials Needed for Baseball Survey Inference Lesson:

• Bowl of exactly 100 Skittles candies with 25 RED and 75 other colors for each small group (or you could do this as a whole class)
• Student handouts for each student (grab this FREE using the link at the end of the post)

Get Students Thinking About Sampling & Inference:

Before running the experiment in small groups or as a class, present the results of the survey to students: according to YouGov survey of 1,000 adults, 25% of adults in the U.S. watch baseball on TV.

Then allow students time to think about and discuss the following questions:

• Why do you think the organization did not poll every single adult in the United States?
• Do you think these statistics are an accurate representation of the population as a whole? Why or why not?

Oftentimes, statistics are presented as fact and if we’re not careful, we can accept the results as general truths without diving deeper into the methods & sample size used.

The goal of this lesson is to help students see that statistically, using a sample can provide an accurate generalization about the population as a whole, BUT sample size plays an important role.

If the sample size is too small, the results may be skewed.

I hope this provides an important hands on, visual lesson for your students to see where statistics come from and how they can be helpful (or sometimes not so helpful!).

Setting Up the Statistical Inference Experiment:

To begin the experiment, students take turns drawing 12 Skittles out of the total ‘population’ of 100 Skittles candies.

They then create a table of their samples, noting how many are red and how many are not.

The goal is to see that because the ratio of reds to the whole population is 1:4, in a sample size of 12, we would expect 3 to be red.

Of course, using random sampling, this will not always be the case, so not every sample accurately models the whole population.

After running the experiment once, students answer a set of discussion questions and create a histogram of their data before trying it again, this time drawing a sample size of 24.

The goal then is to see that in a larger sample size, a larger percentage of samples closely model the population as a whole.

After running the experiment a second time, there are further discussion questions which students can answer on their own, in their small groups and together as a whole class.

Extension Ideas for the Sampling & Inference Lesson:

If you have time and your students are interested in exploring further, here are some ideas to extend learning:

• Have students run the same baseball survey with a sample of students at their school to compare results to the given survey
• Discuss how you might use Skittles candies to model the other results of the survey
• Discuss simulations and see how technology can simulate various experiments quickly
• Compare experimental probability and theoretical probability

Most of all, have fun diving into statistics, sampling and population inference together as a class!

If you enjoy this lesson, become a Math Geek Mama+ member and gain access to the entire library of engaging math lessons like this one, hundreds of math games and low-prep practice worksheets for grades 5-8!

Learn more about Math Geek Mama+ right HERE.

Ready for more statistics & probability lessons? Try one of the resources below!

• Fun Probability Experiment with Dice {FREE}
• Analyzing Data Worksheet for Middle and High School
• Fidget Spinner Math Activity: Probability & Graphing
• Simple Coloring Probability Worksheets for Grades 4-6 {FREE}

Want to grab this free lesson? Use the link below to grab it from my shop!

{Click HERE to go to my shop and grab the FREE Baseball Survey Sampling & Inference Lesson!}

The post Candy Math: Sampling & Inference Lesson – Grades 7-8 appeared first on Math Geek Mama.

Do you have a stash of geoboards collecting dust in your closet? Well, get ready to pull them out as your students create images to celebrate Earth Day! This set of hands on math challenges will help your students compose shapes, count, add and create a simple bar graph. This is a great way to take a break from your normal math routine & focus on ways to care for our planet (while also weaving in some important math concepts ;)). And as a bonus, little learners can strengthen those fine motor skills too!

*Note: This post contains affiliate links which help support the work of this site. Read our full disclosure here.*

Materials Needed for Earth Day Geoboard Activity Pages:

• Geoboard for each student (you can grab a set on Amazon here if you don’t have any yet)
• Large bag of rubber bands in a variety of colors (you can likely find rubber bands at the dollar store, but for a good variety of colors, try this set or something similar)
• Printed student handouts (grab for free in my shop using the link at the end of the post)

How to Use the Earth Day Geoboard Pages:

This download includes 10 different images for students to create using rubber bands on their geoboard. To begin, students choose a picture and recreate it on their geoboard.

Images Included:

• Leaf
• Sun
• Flower
• Earth
• Trash Can
• Tree
• Lightbulb
• Plant
• Watering Can
• Faucet

Once they’ve created the image with rubber bands, they create a bar graph by counting the number of rubber bands they used for each color in their design.

Finally, they add all the values together to find the total number of rubber bands.

The activity is pretty straightforward once you print and gather all the materials.

A quick note: Color images AND black and white images are included, allowing you to choose how to present this to students.

If you have matching colors and you think it will be easier for students to see & recreate the pictures, give them the color pages and corresponding colors of rubber bands.

However, if you want this to be more open ended & allow for more creativity from your students, provide the black and white pictures.

Students can then choose their own colors to create each design and everyone’s bar graphs will be different.

One final note: You may also want to encourage students to create their own design for a particular object, rather than copying the design shown exactly.

This will challenge them to find another way to make a picture on their geoboard and see new ways to compose shapes.

For example, you may have them design their own flower and then compare it to the flower picture shown on the activity page.

Discussion Questions: Earth Day Math

As students create their designs, or after everyone is finished, it would be good to discuss the activity together, both to reflect on Earth Day and also tie in some math concepts. Here are some ideas to get you started:

• How does your picture relate to Earth Day? How does it remind you to care for our planet?
• Which picture used the greatest number of rubber bands?
• Which picture used the least?
• What shapes do you see in your picture?
• How many rectangles do you see? How many squares? How many line segments?

I hope this provides a fun Earth Day math challenge for your students! But if you’re wanting even more ways to combine math + Earth Day, check out the resources below. There’s something for a variety of ages!

• Earth Day Math Board Games (add, subtract, multiply & divide)
• Earth Day Color a Fraction Challenge
• 50+ Spring Math Activities for Grades K-8

And if you’re ready to try out the Earth Day Geoboard Activity, use the link below to grab it FREE in my shop! Enjoy!

{Click HERE to go to my shop and grab the FREE Earth Day Geoboard Activity for Grades K-2!}

The post {FREE} Earth Day Geoboard Activity – Grades K-2 appeared first on Math Geek Mama.

There are so many fun, hands on math topics to explore in geometry. And the best part? It doesn’t have to wait until high school! Laying the foundation for high school geometry begins in upper elementary and middle school. Before students can understand relationships between the angles in a triangle, or discover exterior angles, they need to understand what an angle is. This free set of angles worksheets covers angle vocabulary, measuring angles with protractors, classifying angles and even spotting angles in real life.

Understanding Angles: Angle Vocabulary

Once students have been introduced to the idea of angles, it’s important that they learn some new vocabulary terms. This includes the following:

Right Angle: An angle measuring exactly 90 degrees

Acute Angle: An angle measuring less than 90 degrees

Obtuse Angle: An angle measuring more than 90 degrees

The above terms are the most common and terms students will likely learn first. These are important because these same terms are used to classify triangles based on their angles. Additional terms to know:

Straight Angle: An angle measuring exactly 180 degrees (easy to remember because it looks like a straight line!)

Reflex Angle: An angle measuring more than 180 degrees

Full Rotation: A complete circle, or an angle that measures exactly 360 degrees (you might relate this to snowboarding or ice skating and how they measure their spins)

As you teach and discuss these terms with your students, talk about how the math term relates to the everyday meaning of the term and how that can help them remember (for at least some of them).

For other terms, it will simply require lots of practice and exposure to get the terms and their meanings to stick.

Luckily, I’ve got several angles vocabulary worksheets to help you in this free printable pack!

Classifying Angles:

Once students know the terms, they can practice classifying angles based on their angle measures.

To help with this, this angles practice set includes a page to classify angles as acute, obtuse or right.

In addition, there is a page for students to create their own angles of various types. This is a fun way for students to better internalize what these terms mean as they think about what their examples might look like.

Students can either draw angles freehand based on what they know about each type of angle, or they can use a protractor to draw angles and label their exact measurements.

This is totally up to you!

Measuring Angles Worksheets

Another important skill for students is to learn how to measure angles using a protractor.

This is a completely new idea for most students, as their experience with measurement thus far has most likely been measurements of length or time.

Angles are measured in a new unit called degrees.

Spend some time looking at a protractor together, noticing and wondering things about it.

Talk about benchmark measurements such as 45 degrees, 90 degrees and 180 degrees.

Then talk about how they might estimate angle measurements based on certain benchmarks.

Lastly, ensure students understand that the measurement on the protractor can begin from either side, so they need to ensure they are starting at zero when they begin to measure.

Once students understand the basics of how a protractor is set up and how it works to measure angles, it’s time for practice!

You’ll find a worksheet to practice measuring angles in this printable pack, but you might also like this set of measuring angles puzzles!

Angles in Real Life:

Finally, to help students begin to see angles in the world around them and recognize this new and different form of measurement, you can look for examples of angles in real life.

Angles are all around us, so you might ask for students input, or here are a few ideas to get started:

• The angles formed by opening and closing a door (swing the door slowly on its hinges to watch as the angle changes
• Right angles used in buildings: door frames, windows, corners where two walls meet
• Ice skating, snowboarding or skateboarding tricks: look up some different tricks and consider the angles with your students

More Angles in Real Life:

This printable set of angles worksheets includes several more examples of real life angles for students to consider. This includes:

• Angles formed by the hands on a clock
• Angles found inside a variety of polygons
• Angles formed by everyday household objects

Download the FREE set of 8 Angles Worksheets:

This set of angles worksheets includes 8 pages, covering a wide variety of skills and vocabulary.

Included in the Download:

• Naming Angles Cut & Paste Worksheet
• Angle Vocabulary Crossword Puzzle
• Classifying Angles Worksheet
• Draw Your Own Angles Worksheet
• Measuring Angles Worksheet
• Identify Angles in Polygons
• Identify Angles in Clocks
• Identify Angles in Everyday Objects
• Answer key for each worksheet

I hope this provides an easy way to learn & review these important geometry skills with your students.

Ready to try it out? Use the link below to grab this free download from my online shop!

{Click HERE to go to my shop and grab the FREE All About Angles Worksheets Set!}

Find More Engaging Geometry Resources Below:

• Measuring Angles Activity: Simple and Fun Puzzle Set {FREE}
• Understanding the Angles in Triangles
• Exploring Triangles with “The Greedy Triangle!”
• Geoboard Activity Cards {FREE Geometry Challenge}
• Explore Angles with Sir Cumference

The post {FREE} All About Angles Worksheets: Classify & Measure Angles appeared first on Math Geek Mama.

One of the biggest overarching math concepts in middle school is proportional relationships. We see proportional relationships in real life all the time, and it’s important that students can recognize them, but more than that apply proportions to solve real problems. There are a lot of applications, but one easy way to show students a proportional relationship is through indirect measurement. By creating similar triangles, we can create proportions to find a good estimate of things that are too tall or difficult to measure more precisely. In this lesson, Find the Height of a Building, students will apply their knowledge as they get outside and see it in action.

What is Indirect Measurement?

Indirect measurement means finding an unknown measurement of an object that is difficult to measure directly, with a ruler or measuring stick.

When you cannot directly measure an object, you can use other measurements to indirectly estimate the measurement you’re looking for.

For example, you may not be able to easily measure the height of a tree in your back yard, the height of your house or the height of an office building downtown.

These things are significantly taller than you, so you can’t simply hold up a measuring tape to find the height.

You can, however, use a very clever application of similar triangles to estimate the heights of these objects. This is known as indirect measurement.

Applying Similar Triangles to Indirect Measurement:

What does it mean for two triangles to be similar? Before we can begin our lesson on indirect measurement, we have to understand similar triangles.

Similar triangles have the same shape, but are different sizes. This means all corresponding angles are equal, but corresponding side lengths are not equal. This is what makes similar triangles different from congruent triangles.

Congruent triangles have equal corresponding angles and equal corresponding sides. So they are the same shape and the same size.

Although similar triangles do not have equal corresponding sides, they have an interesting relationship that we will put to work in our indirect measurement lesson: corresponding sides all have equal ratios. In other words:

Similar triangles have equal corresponding angles and all sides are of equal proportion.

Because we can create a proportion out of the corresponding sides of similar triangles, we can use that proportional relationship to find the measurements of known side lengths.

So how in the world does this relate to finding the height of a building?? Let’s find out.

Finding the Height of a Building: An Indirect Measurement Lesson

To use indirect measurement, we will need two similar triangles.

The fun part of this lesson is that when you step outside on a sunny day, you (and other objects around you) cast a shadow on the ground.

Using your height and your shadow, you can create a right triangle.

The best part? At that moment, everything that is casting a shadow on the ground now has created a similar right triangle to you and your shadow.

Materials Needed:

• Student handout for each student (grab it free in my shop!)
• Clipboard
• Measuring tape for each pair/small group

Overview of the Lesson:

So the basic premise of this lesson is that you can use direct measurement to find the height and shadow length of an object that is easily measurable.

Then, you measure the shadow length of the object that is too difficult to measure directly.

Then you set up a proportion using the two similar triangles to solve for the unknown measurement (in this case, the height of a tall building).

Although the basic idea is pretty straightforward, the lesson includes a few more parts to help guide students and make sure they understand what they’re doing and why it works.

Lesson Steps:

In step one, students will briefly review similar triangles and using proportions.

I recommend reviewing this problem in your classroom and discussing it together before you head outside.

In step two, students will use direct and indirect measurement to find the height of something small and measurable.

The goal of this step is to compare their measurements and begin to think about why precision matters and see how close their estimate is to the actual measurement.

This is also another opportunity to review measuring and creating proportions with similar triangles.

In step three, students will measure the shadow of their school building and once again create a proportion to estimate the height of the building.

In step four (which you can do back in your classroom), students answer some questions as they reflect on what they did and what they learned.

Indirect Measurement Lesson Wrap-Up:

Once all students have completed the tasks, head back inside to compare and discuss.

When I used this lesson with my 8th grade students, we will in a brand new school building. Lucky for me, I knew the builder and I was able to reach out and get the actual, exact height of our new school building.

We were able to turn this into a little competition, with the group finding the closest estimate to the actual height earning a prize.

Although this is certainly not necessary, it definitely helps to be able to wrap up the lesson by revealing the actual height of the building.

This naturally leads into a discussion of why the estimates were different from each other and also different from the actual.

You can also find the average of all the estimates. Is this closer to the actual? Why?

Lastly, you can discuss other possible applications for indirect measurement.

And once you’re finished, if your students need additional practice with similar triangles, proportions and indirect measurement, you might try this similar triangles classroom scavenger hunt.

It includes 10 problems to post around your room. Students walk around solving them and finding the solutions until they have completed all 10.

It also includes two independent practice worksheets, which you can use for informal assessments or review.

Learn more and grab the Similar Triangles Scavenger Hunt HERE.

If you enjoy this lesson, become a Math Geek Mama+ member and gain access to the entire library of engaging math lessons like this one, hundreds of math games and low-prep practice worksheets for grades 5-8!

Learn more about Math Geek Mama+ right HERE.

Ready to get started? Click the link below to go to my shop and grab this free math lesson!

{Click HERE to go to my shop and grab the FREE Indirect Measurement Lesson!}

More Middle School Math Resources to Try:

• Real World Pythagorean Theorem Practice {FREE}
• Understanding the Angles in Triangles
• Simple Ideas for Introducing & Exploring Functions in Middle School
• {FREE} Middle School Back to School Math Challenge

The post Height of a Building: Indirect Measurement Lesson | Grades 7-8 appeared first on Math Geek Mama.