10 End of Year Math Projects

The end of the school year is the perfect time to incorporate real world math and engaging activities.  I love using projects to keep students focused the last few weeks of school.

projectblog

Below are some of my favorites.  Each one involves math and creativity!

 

Slide1

Using Transformations as an Architect

Math Skills: Area of Irregular Figures, Transformations

Students design an apartment based on requirements, calculate the area of rooms, and then use transformations to create an entire floorplan of apartments.

 

Slide2

College and Career Research Project

Math Skills: Real World Cost Calculations

This eye-opening research project has students investigating future careers and college options while calculating costs.

 

Slide3

Design a Boat

Math Skills: Volume, Density

Density and buoyancy are tested as students create boats and experiment with how many coins they will hold.

 

Slide4

Classroom Makeover Project

Math Skills: Measuring, Scale Drawing, Surface Area, Cost Calculations

Students measure their own classroom and then design their dream classroom, all while using important math concepts.

 

Slide5

Plan a City

Math Skills: Graphing Lines, Systems of Equations, Parallel and Perpendicular Slope

Many cities are planned with a grid systems.  Students use parallel and perpendicular lines, along with other graphing skills to create their own cities.

 

Slide6

Sports Stats Scatter Plots

Math Skills: Graphing and Analyzing Scatter Plots

Description: Statistics can be revealing and interesting, especially when applied to sports.  With this project, students look for trends and make predictions based on the data.

 

Slide7

Geometric Sculpture Project

Math Skills: Measurement, Volume

Students design a sculpture involving a variety of 3D figures.  They build it, measure it, and calculate the volume.  Students love getting creative with this project!

 

Slide8

Apartment Floor Plan

Math Skills: Area and Perimeter of Irregular Figures

Students get to see how area and perimeter can be used in a real world application as they think about materials required for an apartment.

 

Slide9

Population Density Exploration

Math Skills: Population Density

Students explore and calculate population densities of cities, including their own.  They compare benefits and drawbacks of densely populated areas.  Research and writing is included as well!

 

Slide10

3D Dilation Art

Math Skills: Graphing points, dilations

Math and art combine as students learn how to use dilations to create 3D drawings.  They love this activity and always want to create more!

 

Hope you have been inspired to incorporate some of these ideas into your math class!

 

Thanks for reading.

-Rachael

 

 

 

 

Advertisements

Preparing Students for the Next Grade Level of Math

As the end of the school year draws near, we may start asking if we have done enough to prepare our students for the next grade level.

First of all, I have realized I could always use more time to teach more material.  At some point, however, the year ends and the students must move on.

After reflecting over my experiences teaching 8th graders, Algebra I students, and Geometry students, I began to make a list of skills that I wish students had from previous grades.  I have also spent the past school year observing 5th, 6th, 7th, and 8th grade students, noting how certain prerequisite skills can either make or break a new concept.  Additionally, I reached out to teachers everywhere for feedback on the skills they thought were essential for their grade level.  Through this process, I have created checklists of skills and concepts needed before students start 5th grade math through high school Geometry.

checklists1

I hope these lists will help you prepare your students for the next grade level of math.

Are You Ready for 5th Grade Math?

  • I can use mental math strategies to add and subtract 2-digit numbers.
  • I know my times tables.
  • I can multiply multi-digit numbers.
  • I can divide with 2-digit numbers.
  • I can draw visuals to represent fractions and mixed numbers.
  • I can add and subtract fractions with the same denominators.
  • I understand place value of whole numbers.
  • I can round whole numbers to a given place value.

Download the list for free here.

 

Are You Ready for 6th Grade Math?

  • I can use mental math strategies to add and subtract 2-digit numbers.
  • I know my times tables.
  • I can multiply multi-digit numbers.
  • I can do long division.
  • I can add, subtract, and multiply decimals.
  • I understand the meaning of a fraction; I can compare fractions, change improper fractions to mixed numbers, and reduce fractions.
  • I can add and subtract fractions with unlike denominators.
  • I can multiply fractions and mixed numbers.
  • I can find multiples and factors of numbers.
  • I understand place value, including decimals.
  • I know how to use a ruler to measure.
  • I can round and estimate solutions.

Download the list for free here.

 

Are You Ready for 7th Grade Math?

  • I can use mental math strategies to add, subtract, multiply, and estimate solutions.
  • I can locate fractions, decimals, and negatives on a number line.
  • I can do long division.
  • I can find equivalent fractions.
  • I can add, subtract, multiply, and divide fractions.
  • I can add, subtract, multiply, and divide decimals.
  • I can calculate unit rates.
  • I can solve one-step equations.
  • I can graph points in all four quadrants on the coordinate plane.
  • I can calculate areas of rectangles, triangles, parallelograms, and trapezoids.
  • I can calculate volume of rectangular prisms.
  • I can use a protractor to measure angles.
  • I can convert between fractions, decimals, and percents.

Download the list for free here.

 

Are You Ready for 8th Grade Math?

  • I can use mental math strategies to add, subtract, multiply, and estimate solutions.
  • I can add, subtract, multiply, and divide integers (positives and negatives).
  • I can convert fractions to decimals with long division.
  • I can add, subtract, multiply, and divide fractions.
  • I can add, subtract, multiply, and divide decimals.
  • I can use order of operations including exponents and parentheses.
  • I can solve two-step equations.
  • I can graph simple two-variable equations.
  • I can translate words into algebraic expressions.
  • I can calculate the volume of prisms.
  • I can find areas of polygons and circles.
  • I can find missing angle measures involving supplementary and vertical angles.

Download the list for free here.

 

Are You Ready for Algebra 1?

  • I can add, subtract, multiply, and divide integers.
  • I can add, subtract, multiply, and divide fractions.
  • I can add, subtract, multiply, and divide decimals.
  • I can solve multi-step equations.
  • I can graph lines given an equation.
  • I can explain what a real world graph means using axis labels and an understanding of slope.
  • I can substitute a value for a variable and simplify an expression using order of operations.
  • I can translate words into algebraic expressions.
  • I can find multiples and factors of whole numbers.
  • I can solve problems with percents.
  • I can solve and graph simple inequalities.
  • I can estimate and determine if solutions are reasonable.

Download the list for free here.

 

Are You Ready for Geometry?

  • I can add, subtract, multiply, and divide integers.
  • I can add, subtract, multiply, and divide fractions.
  • I can add, subtract, multiply, and divide decimals.
  • I can solve multi-step equations.
  • I can graph linear equations in any form.
  • I can estimate and determine if solutions are reasonable.
  • I can calculate areas of polygons and circles.
  • I can calculate volumes of 3D figures.
  • I can use the Pythagorean Theorem to calculate missing lengths and distances.
  • I know the names and properties of polygons.
  • I can use a protractor and understand angle relationships.
  • I can translate, reflect, rotate, and dilate figures on the coordinate plane.

Download the list for free here.

 


These checklists could be used at the end of the year, sent home with students over the summer, or used at the beginning of the new school year.

Each one was determined by studying the CCSS standards, surveying teachers through Instagram, observing and teaching students, and preparing materials for math teachers.

Of course, many skills are important for success in each level of math.  I hope these checklists give you a place to start.  I also encourage you to develop your own custom lists at your school working with other grade level teachers!


Below are some bundles of resources that can help prepare your students for the next grade level.

7threadycover ready8thcover readyalgcover georeadycover

Thanks for reading!

-Rachael

Word Problems: 4 Ways to Make Students Think

Slide6How would your students answer this question?

Robert Kaplinsky has brought recent attention to this word problem.  In his study, 75% of students answered incorrectly.  Students look for key words, operate on the numbers given, and supply an answer.

Getting students to break this habit is no easy task.

I have found 4 strategies that can force (or at least encourage) students to do more thinking (and less mindless solving) when given a math word problem.

Slide1

Slide2

 

1. Draw a picture.

Drawing is one my favorite math strategies.  Drawing helps students visualize what is going on.  To draw a picture requires a student to think about what the problem says.  Plus, it is fun.

Tips for making this strategy work:  If drawing in math is new for students, they likely will start out drawing elaborate, literal pictures.  This is okay at first, and it will make the strategy enjoyable.  As you use the strategy more and more, show students examples of simple drawings that get the point across.   A quick drawing helps students organize information and make sense of the math.

 

Slide3

2.  Remove the question.

If you already have sets of word problems, simply remove the question.  Then, the students’ task is to read the story and write 2-3 math questions that can be answered.

Tips for making this strategy work: This strategy is great for group work.  Display or pass out word problems that have no questions.  Give groups a few minutes to read and write their own questions.  Then, select a few questions for everyone to answer.  Challenge students to write difficult questions.  (You might even display Bloom’s Taxonomy to encourage them to write different types of questions!)

 

Slide4

3.   Provide unnecessary information.

If students are in the habit of picking out numbers and operating without thinking, a sure way to stop this habit is to give unnecessary information and numbers.  This strategy will force students to slow down and think about what information is important.

Tips for making this strategy work:  Begin with fairly simple word problems and questions.  Students will likely get frustrated if they are confused by the math while they are trying to pick out necessary information.  The unnecessary facts can even be silly.

 

Slide5

4.   Remove the numbers.

Brittany from Mix and Math talks about how she stops students from finding the numbers and performing random operations by giving numberless word problems.  When the numbers are removed, students cannot rush through the problem to get an (often incorrect) answer.

Tips for making this strategy work: This strategy is perfect for tricky numbers like fractions or numbers in scientific notation.  Take those numbers out.  Then, students are free to think about the meaning without focusing on the numbers.  Once students think about the operations required, fill in the numbers.

 

 

I am always looking for strategies that make students think in math.  I hope some of these can be used in your math class.

People are not calculators.  We want to teach students to be thinkers and problem solvers. 

 

Learn more about the shepherd problem and Robert Kaplinsky’s study here.

The task cards shown with unnecessary information are part of the following resource:linearcover

 

Thanks for reading!

Rachael

Pi Day: Help Students Discover Circumference and Pi

pi day circumference1

I love inquiry lessons and helping students learn concepts that will stick with them.

Pi Day is the perfect opportunity to allow students to discover pi.  Here’s an outline for a Pi Day lesson.  It is most suited for around 7th grade when students are learning the formula for circumference, but it also incorporates graphing and measurement skills.

 

Materials:

You will need several circles. These could be items already in the classroom (like a clock, cup, table) or you could cut different size circles from paper.  Label the circles with numbers.  Students will need string and rulers.

 

Lesson:

Pair students up and assign them a circle to measure.  They will measure and record the diameter and circumference.  To measure the circumference, they should wrap the string around the circle, and then measure the length.

Once everyone has measured a circle, they should find a new circle to measure.  Or, have each student share their measurements with the class.  Create a large table of values on the board to record each diameter and circumference.

Next, students graph the points to create a scatter plot.  They can use graph paper to create a graph with the diameters as the x-axis and circumferences as the y-axis.

Then, have the students look at the pattern and try to write an equation for the relationship.

They will discover the circumference of a circle is always about 3 times the diameter.  This can lead to great conversation about pi and the actual circumference formula. Bonus: The students will actually remember the circumference formula!

 

I love that this lesson is hands-on and helps students truly understand the circumference formula.  Find an easy student template for this lesson in my Teachers Pay Teachers store:

circumexperimentcover


Looking to practice circumference, area of circles, and working with pi on Pi Day?  Check out this collaborative poster activity:

pi

Hope you’ve enjoyed these ideas for Pi Day lessons that don’t involve pie!

Slide2

Thanks for reading! Happy Pi Day!

-Rachael

 

Valentine’s Resources for Secondary Math

slide2


Doing something a little different is a great way to boost engagement.  Below are some of my favorite math activities around Valentine’s Day.  They may just look fun, but they are educational too.


 

slide7

Practice graphing on the coordinate plane, working with line plots, and decimal addition with this Valentine pack of activities from Cameron Classroom.  Perfect for 4th – 6th grade students.

 

 

 

 

slide6

 

Translating words into inequalities is a challenging skill.  Make practice a little more fun with these Valentine task cards from To the Square Inch.  6th grade students (or above) would really benefit from this activity.

 

 

 

slide9

In my experience, most students enjoy a good mystery graphing picture!  Hayley Cain creates all kinds of them, and this rose would be great for the week of Valentine’s Day.  Students in 6th grade or above would love this practice.

 

 

 

 

slide12

 

Integer operations can be a struggle when students learn them in middle school.  Many high schoolers could still use the extra practice.  In this activity, students add and subtract integers to create ordered pairs, which they graph to create a mystery picture.

 

 

 

slide14

 

Need to practice two step equations? In this activity, each solution reveals an interesting fact about Valentine’s Day.  Decimals, fractions, and negatives are involved, making this perfect for 7th and 8th graders.

 

 

 
valentine1

 

 

Practice writing equations of lines when given two points with this fun activity from 4 the Love of Math.  The lines make a heart when graphed.  (And this is a freebie!)

 

 

 

slide8

 

Slope-intercept form is so important in 8th grade math and Algebra 1.  These graphing exercises from Scaffolded Math and Science turn into a cute Valentine decoration when complete!

 

 

 

 

valentine3

 

This Broken Hearts activity from 8th Grade Math Teacher has lots of options for approximating square roots.  Have students find their partners with matching values or make a giant number line with roots of irrational numbers.

 

 

 

slide3

 

 

Need a fun way to practice using the quadratic formula?  This collaborative activity from Algebra Accents will have students eager to work out the solutions.

 

 

 

 

slide11

 

Want to challenge high school students?  These multi-step equations will do the trick.  Each one reveals a cool fact about Valentine’s Day.

 

 

 

 

 

slide13

 

Practice congruent triangle theorems with this coloring activity from Kacie Travis.  Geometry students will enjoy it, and you will be able to quickly see if they are solving correctly.

 

 

 

These activities are perfect to use in February to reinforce concepts.  I love resources like these for early finishers too!  Anything that adds a little motivation and engagement is a win.


 

Here are two more resources that are just for fun!

slide5

 

How cute are these cards from iteachalgebra?!  Hang them as decoration or let students hand them out.

 

 

 

slide15

 

Students often ask why they need math.  This Valentine door decoration will give them plenty of reasons to love math.

 

 

 

 

 

Thanks for reading!

-Rachael

What I’ve Learned from Using Multiple Representations

In math, we allow and push students to represent their thinking in multiple ways.  In 7th grade math, 8th grade math, and Algebra I, this strategy is very beneficial when exploring the relationship between two variables.  Teachers often ask students to use equations, graphs, tables of values, and descriptions.

slide1

Teaching 8th graders, I realized many students struggled with linear relationships, and many were totally lost when I presented systems of linear relationships.  I turned to multiple representations as a way to help the struggling students.  If they couldn’t understand the equations, maybe they could at least understand a graph or create a table of values.

Many standards focus on solving systems with graphs and with algebra (substitution or elimination), but few mention working with tables.  However, tables were the key to my students’ success with systems.  Once students read a story, many felt comfortable creating two tables of values and looking for a match to solve the system.  Some went on to understand the algebra (and others did not), but the tables allowed them to makes sense of the whole idea of a system.

slide2

Through this experience, I learned to use tables to help struggling students.  However, just this year, I realized something else.

slide3

I recently watched an 8th grade Algebra I class work through a system of linear equations problem.  They were not given any direction on what procedure or representation to use.  Would these students just use equations and arrive at an answer (which they were capable of doing)? No!  Most students created tables of values.  They were trying to understand their solution (because their teacher surely would ask them to defend it) instead of just solve it.

 

What did this teach me?  Well, for one, tables are a great tool, but I already knew that.  More importantly, I learned that good strategies are good strategies, no matter what the ability level of a student.  Tables are a way that students can make sense of linear relationships and systems.  When problem solving, everyone needs to make sense of what they are doing.

 

I am realizing more and more that a good strategy is a good strategy for every student.

systems pics4

Thanks for reading!

-Rachael

 

The following are some multiple representation resources I have created:

proprcover piecewise cover systems graphmr quadcover

The question referenced in the Algebra I class can be found at map.mathshell.org.

 

Study Guides: The Negative Side Effect on Classroom Management

A study guide: a harmless way to help students prepare for a test.  FALSE.

study guide pics3

Let me start by describing how I wanted my classroom to work.  I created challenging tests that assessed true understanding of my standards.  I planned engaging and rigorous lessons to prepare students for those tests.  I wanted students to participate and learn everyday.  I wanted students to enjoy class but also put all their effort into all their work.  Classroom management would be… manageable.

That is how the year started, but it quickly deteriorated.  Effort dropped, behaviors worsened, and students did not seem to be learning or retaining anything.

What happened?

I would have changed many things looking back now, but let me explain how study guides played a key role in my problem.

In the beginning of the year, students did participate in the lessons I prepared, and they learned.  However, I was too concerned about their grades on that first test.  I wanted them to ace it.  So I made a study guide.  I always liked when teachers gave study guides.  I told students, “If you complete the study guide, you will be prepared for the test.”  Then, I went over the problems step by step.

Is there anything wrong with the story above?  I didn’t think so, at the time.  However, let me repeat what I told them: “If you complete the study guide, you will be prepared for the test.” That was the problem. 

Why participate in class?  Why try my hardest to understand?  Why do homework and practice?  Why ask for help?  Why do anything at all?  Why not just wait for that study guide and memorize the types of problems I will see?

My study guide ruined any motivation to work hard to understand the material.

I did not realize the effect of study guides until many years later when I stopped giving them in the format I once had.  Of course, students need to know what to expect on a test.  A better study guide outlines the topics to study, notes to reference, and maybe practice (that is different from the test).  I stopped worrying about test grades.  If I have prepared good lessons and have monitored my students along the way, I will know if they are prepared.  Students know each day is important for learning and understanding.

Lesson learned: If a student can use a study guide to ace a test on Friday, they probably will not show up (mentally) the rest of the week.  
Study GuideDownload this Study Guide format here: Study Guide.

 

Thanks for reading!

-Rachael