Math Lesson Ideas

Elementary Classrooms

Grade: 1-4
Subject: Math (place value)
Objective: The student will be able to identify digits as ones, tens, hundreds, or thousands.
Original Post: The $55 Interactive Whiteboard

Most teachers find that base ten blocks are a perfect start for studying place value. But it’s difficult to use them for whole-class lessons since not everyone in your class can see the set you hold at the front of the class. That’s why the digital base ten blocks found at the National Library of Virtual Manipulatives are perfect add-ons for any place value lesson.

Grade: 3-5
Subject: Math (algebraic thinking)
Objective: The student will be able to verbalize his/her understanding of the mathematical meaning of the equal sign.
Original Post: Harness the Power of Social Networking in Your Classroom, Safely and for FREE

One thing that we teachers rarely do is ask simple questions, just to see what our students are actually thinking. One of the most eye-opening days of my career was when I gave my fourth-graders a paper with a simple question on it: “What does = mean?” The answers were more varied than I expected, and that worksheet turned into a weeks-long discussion that’s documented here. (Sorry — I didn’t have a social network at the time, so I had to document the conversations from memory.)

Give students a worksheet with three questions:

1.)    What does = mean?

2.)    True or False: 4 + 3 = 7

3.)    True or False: 9 = 5 + 4

After they complete the worksheet, have students log onto the class’s social networking site, where you’ve posted the same three questions. Ask students to post their responses and reply to at least two other students. (The reason for the worksheet first is to give students time to form their own opinions before they read other students’ answers.)

Based on students’ responses, continue to post questions like this: “True or False: 5 + 4 = 7 + 2″ and encourage discussion. Keep posting similar questions, trying to lead students to the conclusion that the equal sign means “the same amount as.” Don’t just tell students what it means — ask the right questions to lead them to discover the meaning for themselves. When they come to the conclusion on their own, their understanding will be much greater.

Lessons like this have two benefits, as I see it. First, in order to understand math, it’s extremely important for students to learn to verbalize their mathematical thinking and be able to explain it, step-by-step. Second, having students’ thinking documented online will give you and your students some great insights. It is also a good tool for parent-teacher conferences, as well as when identifying learning disabilities in students.

Grade: K-5
Subject:
Math (or Science)
Objective:
The student will be able to explain and demonstrate how things change over time.
Original Post: Moving Beyond Bar Graphs with Data Visualization

With younger students, I think it’s important that they still create their own charts and graphs by hand. But visualization tools can allow teachers to take students a little further into data analysis.

As a 4th-grade teacher, I always taught a math unit called “Changes Over Time.” As part of the unit, students grew small plants and collected data for graph creation. Students started by each planting their own seed in a small paper cup (or re-used milk carton) filled with soil and labeled with the plant’s name (I had students name their plants).

Every day, students would record the overall height of their plant, the number of leaves, and the date. After about a month, each student would make a simple graph demonstrating how their plant’s height changed over time.

With the Google Motion Chart Gadget, though, I could have taken this lesson a lot farther. Students could have shared their data and then compared how the entire class’s plants grew.

To create a visualization, a teacher could create a Google spreadsheet document and label the columns as follows: The “A” column should be the plants’ or students’ names. The “B” column should list the dates that you recorded data. Then label a column for each of the remaining variables – plant height and number of leaves. Depending on your students’ level and your equipment availability, here are some ideas for how you could create a class-wide data visualization:

  • share the Google spreadsheet, and have students open it individually to add their data
  • project the Google spreadsheet on the board, and call students up to enter their data, one by one (after the first few students, you might want to have the class start working independently on an activity, such as creating their hand-drawn graphs, as students enter their data because it will take a while)
  • project the Google spreadsheet on the board, and have students read their data aloud as the teacher enters the data (again, you may want to have students working independently after the first few students model what to do)
  • have each student (or student group) create their own Google spreadsheet; the teacher creates one as well, and projects it on the board; the teacher enters all students’ data into his/her spreadsheet as a model; and students copy all students’ data into their individual spreadsheets

Once all the data is entered, click insert > gadget > motion chart to create the playable graph that will show students’ named (and colored) dots moving as time passes. You can use the chart to start a conversation about how the variables are connected, how the plants changed over time, and how different students’ plants compared to one another at different times. (When played, students will likely see the visualization as a race, watching their dot overtake or fall behind their classmates’.)

Grade: 2-12
Subject: Math
Objective: The student will be able to use grade-level appropriate mathematical operations to solve a problem.
Original Post: Reverse and Improve Your Instruction with Screencasts

Often in math class, a student will struggle with a particular operation or problem type. In 4th grade, a few of my students had consistent problems with subtraction and division. Screencasts are perfect for offering these students one-on-one tutoring, without having to schedule the time.

Create a screencast with a sample problem involving the operation the student has trouble with. Give the struggling student a worksheet with an identical problem, but with the numbers slightly different. Have students follow the screencast step-by-step, pausing it to complete each step on their own worksheet (for younger students, it might be a good idea to tell students when to pause the screencast during the recording).

You can create one such screencast and use it with several students over several years. The students can watch the screencast in class, using headphones, or at home, with parental support.

Middle School Classrooms

Grade: 6-8
Subject: Pre-Algebra
Objective: The student will be able to:

  • determine the identity element;
  • decide if there is an inverse for each element;
  • determine if an operation is commutative or associative

Original Post: The $55 Interactive Whiteboard

When I was in school, I wasn’t a fan of math — too much boring memorization and drill and kill for me. Those arbitrary rules never seemed to make sense. So when I started teaching math, I took a completely different approach. I felt it was important for students to understand the why behind all those rules. Process over product became my mantra, and the TERC Investigations curriculum gave me some great tools to work with.

So I was really excited to find the Illuminations Web site, created by the National Council of Teachers of Mathematics. It offers lessons and applets ideal for teaching the why, and many of their applets are perfect for use on a Wiimote Whiteboard.

To introduce the ideas of identity, inverse, commutative, and associative, Illuminations offers a lesson that uses shapes to explain the principles. Check out the lesson, and be sure to find the applet link, which would be a perfect fit on a Wiimote Whiteboard.

Grade: 5-8
Subject: Geometry
Objective: The student will be able to use ordered pairs to describe points on a coordinate grid.
Original Post: From Trash to Treasure: Three Easy Steps to Convert Corporate Garbage into FREE Classroom PCs

Students can use Scratch, a FREE open-source logic-based computer programming tool, to explore coordinate grids with a real-world connection. Based on their level, you can create easier or more difficult questions and tasks. Use a worksheet to guide students through the activity.

For example, in this lesson by Karen Randall, you can have them answer the following questions (see worksheet on page 2 of this document), with a focus on the vocabulary quadrant, ordered pair, x coordinate, y coordinate, X-axis, Y-axis, and origin:

  1. What is the default location of the cat when you open a project? How does that location change when you drag the cat to other places on the screen?
  2. How can you draw lines by changing the x and/or y coordinate for the location of a sprite?
  3. How can you draw a line by changing one coordinate?
  4. How can you draw the x and y axis of the coordinate grid by using coordinate pairs?
  5. How can you use coordinate pairs to draw specific shapes, such as your initials?

For more Scratch lesson plans, check out http://wiki.classroom20.com/Scratch+Lesson+Plans.

You can also find Kig geometry lesson plans at https://wiki.edubuntu.org/Lessons/Kig.

Grade: 5-8
Subject: Math
Objective: The student will be able to use the language of mathematics to communicate his/her math thinking coherently to peers, teachers, and others; and analyze and evaluate the math thinking and strategies of others.
Original Post: Use FREE Blogging to Increase Your Students’ Writing Scores 20 Percent

Blogging is clearly an amazing tool for the writing classroom. But it doesn’t have to stop there. Reading teachers can use blogs to start discussions about books read in class; science teachers can have students explain their understanding of an in-class experiment; social studies teachers can have students write letters to their congress people and post them on their blogs.

Blogs are also the perfect place for students to learn to communicate their mathematical thinking. For students to progress in math, it’s extremely important for them to be able to articulate exactly how they solve word problems and why they chose this method. In addition to strengthening students’ mathematical understanding of a concept, it can point teachers to common misconceptions.

In essence, blogs can allow you to have every student complete a problem on the board. Here’s a possible math lesson:

  • Post a word problem for your students to solve.
  • On their blogs, the students are expected to explain their thinking step-by-step (i.e.. “when I read the problem, I thought this. So I…”) – this may require some pre-teaching.
  • As they explain their thinking, students should show their math calculations (for some students, the math calculations might be a drawing that you photograph and post on the blog).
  • For their next assignment, students should be expected to comment on other kids’ blogs. These comments might be a specific piece of praise, like “I like how you said that the problem reminded you of marbles grouped inside of cups. That helped me think about the problem differently.” Or they could be constructive criticism, like “the problem said he had four groups of five pencils. Why did you decide to divide? Maybe you could draw four groups of five pencils to help you.”

Grade: 4-6
Subject: Math
Objective: The student will be able to find the perimeter and the area of an object.
Original Post: Let Them Play: Video gaming in education

First, spend one day teaching students about perimeter. The next day, introduce the idea of area. Then, take students out onto the playground. Tell them to walk on the PERIMETER of the playground (generally, students will walk in a line around the outside of the playground). Then, ask them to walk in the AREA of the playground (they run around in the middle of the playground). Keep switching your directions — having students walk along the PERIMETER, and then inside the AREA. Afterwards, discuss what students noticed — were the perimeter and area the same? Etc.

Next, have students play the Cyberchase game Cyberspaceship Builder. In the game, students are given a set perimeter. Then they have to create shapes with various areas using the same perimeter. As students play, have them take notes about their findings. You might want to make a worksheet where students must demonstrate the different perimeters and areas they create. With older students, you could have them record their findings in their math notebooks.

After the lesson, discuss what students discovered, any questions they have, and have connections they made. (This is a good time to connect area to multiplication arrays and ask students if they found a more efficient way — other than counting — to find the area. For older students, ask about strategies for finding the area of oddly shaped spaceships.)

Grade: 5-8
Subject: Math
Objective: The student will be able to eliminate incorrect answers using logic and reasoning skills.
Original Post: iPad Dream at Realistic Price: the $250 Android Tablet

Have students use the FREE Sudoku app that comes with the Nook Color to practice their logic and reasoning skills. The app allows students to pencil in notes and use a “pen” when they’re certain of an answer. If they mark something that can’t possibly be correct based on the numbers already filled in, the number turns red, which can help scaffold understanding. The app also allows users to choose their difficulty level and pause play, so students can come back to the same puzzle day after day. The app times them, so they can see how long it takes them to complete a Sudoku puzzle and track their progress as their speed improves.

Grade: 2-12
Subject: Math
Objective: The student will be able to use grade-level appropriate mathematical operations to solve a problem.
Original Post: Reverse and Improve Your Instruction with Screencasts

Often in math class, a student will struggle with a particular operation or problem type. In 4th grade, a few of my students had consistent problems with subtraction and division. Screencasts are perfect for offering these students one-on-one tutoring, without having to schedule the time.

Create a screencast with a sample problem involving the operation the student has trouble with. Give the struggling student a worksheet with an identical problem, but with the numbers slightly different. Have students follow the screencast step-by-step, pausing it to complete each step on their own worksheet (for younger students, it might be a good idea to tell students when to pause the screencast during the recording).

You can create one such screencast and use it with several students over several years. The students can watch the screencast in class, using headphones, or at home, with parental support.

High School Classrooms

Grade: 2-12
Subject: Math
Objective: The student will be able to use grade-level appropriate mathematical operations to solve a problem.
Original Post: Reverse and Improve Your Instruction with Screencasts

Often in math class, a student will struggle with a particular operation or problem type. In 4th grade, a few of my students had consistent problems with subtraction and division. Screencasts are perfect for offering these students one-on-one tutoring, without having to schedule the time.

Create a screencast with a sample problem involving the operation the student has trouble with. Give the struggling student a worksheet with an identical problem, but with the numbers slightly different. Have students follow the screencast step-by-step, pausing it to complete each step on their own worksheet (for younger students, it might be a good idea to tell students when to pause the screencast during the recording).

You can create one such screencast and use it with several students over several years. The students can watch the screencast in class, using headphones, or at home, with parental support.

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