Category Archives: Math

Game Board: Festival

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Add your own title or directions, and use this game board to review basically anything- math, phonics, review for a test. Use paper clips, buttons or pieces of colored paper as markers.
To get this game board, just right-click, “save as” and save this image to your computer. Resize the image to fit the paper you’re printing it on. Ta-da!

Game Board: Barefoot Fun

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I always use blank game boards for review and practice of a concept (anything from math facts to phonics practice). This one’s really cute and you can throw your own title, directions or comments on the tag at the bottom right.

To get this game board, just right-click, “save as” and save this image to your computer. Resize the image to fit the paper you’re printing it on. Ta-da!

Fractions are Everywhere! (Lesson Plan)

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This lesson was kinda fun. It shows students that you can find fractions everywhere… even in Hershey’s chocolate bars.  I wish I had been rich and could give each student their own chocolate bar to give the lesson extra punch, but alas, I am a teacher… 
 
Context
Name: XXXXXX                         Date: March 12, 2009                         Grade level: 3rd
Subject/topic: Fractions                Length/minutes: 20-30 minutes          Group size: whole class
Sequence: ongoing
Purpose
Standard/core: UtahStandard 1, objective 2, indicator b
Standard 1
Students will understand the base-ten numeration system, place value concepts, simple fractions and perform operations with whole numbers.
Objective 2
Use fractions to communicate and compare parts of the whole.
a.   Identify the denominator of a fraction as the number of equal parts of the unit whole and the numerator of a fraction as the number of equal parts being considered.
b.  Define regions and sets of objects as a whole and divide the whole into equal parts using a variety of objects, models, and illustrations.
Learning goal: Students will understand that they can make fractions out of anything.
Major concepts:
Fraction- part or portion of a whole
Denominator- bottom number of a fraction; the number of pieces in the whole  
            Numerator- top number of a fraction; number of pieces we are looking at
            Equivalent fractions- same size; equal fractions; fractions with the same portion of the whole shaded
Assessment
Given a worksheet, students will be able to draw a fraction (illustrated with objects of their choice).
Management
Self starter: none
Expectations: Sit and raise hands (no calling out); Students will focus on the topic; No sharpening pencils, getting out of seats going to the bathroom during the lesson.
Procedures: work with your table buddy; raise hands to speak.
Fast finisher: Color your picture if you finish early.
Instructional Strategies

Attitude Orientation: You probably already use fractions more than you realize. Name some ways you personally have used fractions…

Tell objective: “Today, are going to see how many things we can make fractions out of.”
Schema Orientation:
Using a Power Point Slide, show pages from The Hershey’s Fraction Book that illustrate common fractions. Use the following outline to help move through the Power Point. Italics indicate speech.
Slide 2: Picture of a Hershey’s candy bar. The candy bar is the whole.
Slide 3: How many pieces make the whole? Wait and let students count the pieces in the bar.
Slide 4:Point out each piece. 12 pieces make up the whole.
Slide 5: How do we write this as a fraction?
Slide 6: Since we just counted 12 pieces, that’s how big each piece is, 1/12 of the total. The total number of pieces goes at the bottom. Remember how we used the cubes yesterday during centers? The denominator told us which size piece we had. That’s our denominator, which goes on the bottom of the fraction. (Write it on the board). Now for the top of the fraction. How many do we have? We just counted 12, so that’s the numerator. (Write it on the board).
We can use this candy bar to make more than one fraction.
Slide 7: If we eat one piece, what fraction of the bar is left?
Slide 8: Let’s see. There are still 12 pieces total, so that’s our denominator. (Write it on the board). But our numerator has changed. Now how many are there? There are 11 left. So what’s the fraction left? 11/12.
Slide 9: Can we make fractions out of other things?
Slide 10: discuss how there are 5 cows on the page, and one of them is brown. 1/5 of the cows are brown.
Slide 11: Is there anything else that we can make into a fraction?
Slide 12: Cacao beans. Explain how 1/8 of the beans are falling out of the tree.
Slide 13: So, you can make fractions out of anything!
Activity:
Model how to use manipulative:
For example, if I found these leaves on the ground, I can make a fraction out of them. Put them on the board and show how to make a fraction. Model finding the total, and then the number that are different (example: 3 of the 9 leaves are orange). Give students the thought process behind finding a hidden fraction in a set of objects.
Since we just learned that we can make fractions out of anything, let’s try to make some.
(Pass out bags of objects- one per student).
 Slide 13:Find the hidden fraction in your set of things.  Teacher may want to suggest ways to look at fractions (by color, by type of object, etc.)
            Check for understanding:
            As students make their hidden fractions, walk around the room and see if students are understanding the concept.
Independent practice:
Slide 14: Draw a picture of the fractions on your worksheet.
Pass out worksheet and ask students to draw objects of their choice to illustrate the fractions.
Closure: Lead a class discussion about the importance of fractions and the ways we see them in everyday life. So now that you know how to make anything a fraction, see how many fractions you can find around you every day! 
Accommodations
            Visual learners- Power Point visuals, charts, drawing assessment
            ELL students- Modeling, pictures to match the words, hands-on activities
Resources
Power Point presentation
Projector
Computer
Manipulatives
Worksheet
Reflection
Step 1: (Instruction and Management) What went well? What should be improved?
Step 2: (Student Learning) What did the children learn? How do you know?
What have you found helpful when teaching fractions?

Division Using Arrays (Lesson Plan)

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This lesson plan uses arrays to explain division. If you don’t have the “Array A Day” worksheets, you can use regular graph paper to help you draw arrays. 

Division Using Arrays
Context
Name: XXXXXXX                            Grade level: 3rd                     Group size: whole class
Date: March 10                                   Length: 20 minutes                 Sequence: introductory
Subject/topic: Division using arrays
Purpose
Standard/core: Standard 1, Objective 3a

Demonstrate the meaning of multiplication and division of whole numbers through the use of a variety of representations (e.g., equal-sized groups, arrays, area models, and equal jumps on a number line for multiplication, partitioning and sharing for division).

Learning goal: Students will know how to see a division problem in an array.
Major concepts: Arrays can be divided into groups of a certain size, or into a certain number of groups.
Assessment
Given a blank array worksheet, students will be able to divide the array into groups of a size and a number of groups.
Management
Self starter: N/A
Expectations: raise your hand to talk
Procedures: Watch the teacher and do what the teacher does on your own paper.
Fast finisher: draw more problems on the back of your worksheet
Instructional Strategies
Anticipatory set: “We have been building arrays with multiplication problems, but is there a way to divide an array?”
Tell objective: “We are going to learn what how to break up or divide an array into groups. Division is easier than you think!”
Instructions:
Input: “Let’s say we have a problem that looks like this… (write “18 divided by 3”)When we first look at a division problem, there are two parts we need to identify. The first number tells us the number of groups we have. There are 18 dots. So draw in 18 dots.”
           
Modeling: Write out the problem. Identify and label the parts. Draw in the dots (3 rows of 6 in each) on the array sheet.
           
Check for understanding: “Which one of these positions tells us how many we have? Show me with your fingers which spot has the total?”
                       
Input: “The second spot tells us how we are going to group the dots. This says 3, so we want 3 groups. How can we make 3 equal groups?”
           
Modeling: Circle the dots so there are 3 groups of 6 dots each.
           
Check for understanding: “Show me with your fingers how many groups we have. How many dots are in each group?” Watch to make sure students have the correct numbers.                     
Input: “Now where do we write our answer? On the line. The answer is 6, so we write that on the line. Now what’s cool about this? Look at your picture and see if we can group them another way, maybe using the number 6. Look! We can also make 6 groups of 3 each!”
           
Modeling: draw circles around groups 3 each. There should be 6 total groups.
           
Check for understanding:  “So, How many equal groups can we make with this problem? Show me with your fingers.”
Guided Practice: done as teacher does it on the overhead.
Independent practice: Have students do their own problem using a new worksheet (20 divided by 5)
Closure: “So now that we know what to do when we look at a division problem, we won’t be as scared, huh? We can use our array sheets to solve the problem.”
Resources
Array-a-day worksheet (2 copies per student)
Overhead worksheet, pens
Reflection
What went well?
What didn’t?
Improvements for next time?
Anyone else have good ideas for teaching division with arrays?

Geometry: Intro to Angles (Lesson Plan)

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I love teaching geometry. It’s the most fun of the math categories, in my opinion, since there’s so much geometry around us in the classroom every day! This is one way to introduce the basic types of angles. I’ve also used Bendarooz (wax sticks) to teach angles, but this lesson plan was from before I discovered those.


Context
Name: XXXXX                                  Date: March 25, 2009                         Grade level: 3rd           
Subject/topic: Angles                          Length/minutes: 20-30 minutes          Group size: whole class
Sequence: Introductory
Purpose
Standard/core: UtahStandard 3, objective 1, indicator d
Standard 3 Students will describe and analyze attributes of 2-dimensional shapes.
Objective 1Describe and compare attributes of 2-dimensional shapes
d.      Identify right angles in geometric figures, or in appropriate objects, and determine whether other angles are greater or less than a right angle.
Learning goal: Students will be able to identify right, obtuse and acute angles.
Major concepts:
Right angle: an internal angle which is equal to 90°
Obtuse angle: an internal angle which is greater than 90°
Acute angle: is an internal angle which is less than 90°
Angle: Two rays that share the same endpoint
Assessment
Given a worksheet with pictures, students will be able to identify angles with 100% accuracy.
Management
Self starter: none
Expectations: Sit and raise hands (no calling out); Students will focus on the topic; No sharpening pencils, getting out of seats going to the bathroom during the lesson.
Procedures: come back to desks when activity is over; raise hands to speak.
Fast finisher: make a list of things that have right angles.
Instructional Strategies

Attitude Orientation: (transition from lines lesson) We learned yesterday about lines, rays and points.  What happens when a line shares a point? Well…

Tell objective: “Today, are going to learn the about different angles.”
Schema Orientation: When you have two rays that share the same endpoint form an angle. How do you say “angle” in Spanish? (ángulo)
There are three basic kinds of angles…
Right angles:
            Put up word card that says “right angle” so students can see how the term is spelled.
            Draw a picture of a right angle.
Explain that when you draw a right angle, you can put a square I the corner to show that it has 90 degrees. You haven’t learned about degrees yet, but just know that there are 90 degrees in a right angle.
Have students stand up and make a right angle with their arms.
–          put one arm out sideways
–          then put your other arm straight up
Obtuse angles:
            Put up word card that says “obtuse angle” so students can see how it’s spelled.
            Draw a picture of an obtuse angle.
Explain that obtuse angles have more degrees than a right angle. They have to have more than 90 degrees to be obtuse angles.
Have students stand up and make a obtuse angle with their arms.
–          put one arm out sideways
–          then put your other arm leaning to the other side
Acute angles:
Put up word card that says “acute angle” so students can see that it’s an acute angle (not a cute angle).
            Draw a picture of an acute angle.
            Explain that acute angles are smaller than right angles, so they have less than 90 degrees.
Have students stand up and make a right angle with their arms.
–          put one arm out sideways
–          then put your other arm across the body to the side of the first arm
Activity: Now we’re going to go on an angle search. Pass out note cards and have students draw right angles in the corners.
Have students go around the room and use their note card to see if angles in the classroom are greater or smaller than the right angle on their note card.
Model how to compare the note card angle to something in the classroom such as a book, or edge of other supplies.
Check for understanding: Let the students have a few minutes to explore the angles in the classroom. Guide the class by having each student find a right angle, then an obtuse angle, and finally an acute angle. Have students find an angle and call on students to show the class their angle.
             
(Independent practice: Have students practice drawing angles.)
Assessment: pass out worksheet that asks students to label different angles as right, acute an obtuse.
Closure: Lead a class discussion about where you can see angles in everyday life.
Accommodations
            Visual learners- Power Point visuals, picture of the angles, drawing assessment
            ELL students- Modeling, word cards, picture of the angles
            Kinesthetic learners- use arms to make angles
           
Resources
Word cards
Notecards
Worksheet
Reflection
Step 1: (Instruction and Management) What went well? What should be improved?
Step 2: (Student Learning) What did the children learn? How do you know?