Using manipulatives in math Professional Development October 21

Why Hands on? Then Now Students memorize how to calculate. Many do not understand how and why…. Students experience math and manipulate materials allowing them to see math away from the pencil and paper. A deeper understanding of why and how are developed. Hands on experiences mesh with the new BC Curriculum.

How do I evaluate this? Older methods Newer methods Teach, practice with pencil and paper. Teacher tests students and moves on- even if it is clear a student doesn’t understand Teach, practice with manipulatives. The teacher can circulate and see who understands and doesn’t. Maybe not every concept needs to have a test… This doesn’t mean no pencil and paper. With a deeper understanding, students will have less difficulty with pencil and paper and unit tests. You know who to help ahead of time. WIN/WIN!

Excellent resources for hands on math Carole Fullerton Resources Developed in Campbell River by a BC Teacher Excellent resources for hands on math John Van De Walle Resources

Online resources The NCTM site has an amazing array of math resources Explore learning ( Gizmos) is another awesome site that teaches math and science concepts with simulations. This is a pay site- school district 35 funds all interested teachers… A bit dry, but the Khan academy is well done Google brings up anything… ( I love google!) Online resources Many hands on math resouces are online as well http://www.explorelearning.com/ Show gizmos accout

Let’s start with integer disks First go over the zero principal with integers. If two integers are opposite ( + and -), they cancel each other out. +1 and -1 equal zero. Move into adding integers and line them up in zero pairs- (-3) + (+2) (+5) + (-6) Students will come to understand that they line up the zero pairs and what is left over is the answer. Let’s start with integer disks Integer disks can be used to improve student understanding of positive and negative numbers, and how they are added and subtracted. For these questions, we will assume that red represents positive and yellow represents negative.

Subtracting integers What happens with subtraction? (-7) – (+2) When we start out, we have no positive to take away. But wait! We can add zero pairs to our equation because they do not change what the equation equals- they add to zero. Now I add two zero pairs to get enough positive to take away. Now I can successfully take away +2 When I take away the positive disks, I end up with 9 yellow disks- my answer is -9 Subtracting integers Remember to begin with the emphasis on the zero principal… Opposite integers cancel each other out and equal zero

Practice a few in your table groups (+5) + (-7) (+3) + (-2) (-3) – (+6) (+10) – (-4) Make up a few to test yourself… Practice a few in your table groups Spend about 5 minutes going over subtraction and addition questions. Let Mike and I know if you need help…

Lets move on These are very versatile materials…. You have cuisinaire rods in front of you. Take a few minutes to mess around and figure out their properties… It is ideal to have enough sets in your classroom for each pair or trio to have a set. In fours they try to split them up… One class set of 15 cuisinaire rod boxes in your math room would be awesome.

Let’s start simple-take the red rods and make a single train from them. Have students describe the train as a repeated addition sentence and skip count to ensure they are right. Say the sentence to match the collection- 6 groups of 2 are 12 or 6x2= 12. ( The order of the numbers matters in this case-they have actually built 6 groups of 2 not two groups of 6) Start small and move up Cuisinaire rods will help students to see division, multiplication and ratios. Often students have a limited understanding of these concepts. You can decide where to start with your students depending on their general mathematical literacy. We will start with basics and move up quickly…

Have students use 2 – 6 sided dice Have students use 2 – 6 sided dice. The left die tells how many rods to collect. The right die says the length of the rods. A 6 and a 4 means to collect 6 magenta rods. The student can line them up against a ruler- this will give them the answer- 6 x 4 = 24 Try a few with your partner Second task Roll and Multiply.

Start with an orange rod-how many times will a yellow line up with the orange? Since they line up and match, we can say that 5 is a factor ten. How many other colors line up exactly with the orange? These are all factors of 10. 10 is also a multiple of 5. So 2 is a factor of 5 and 10 is a multiple of 5. ( I used factor plus factor = multiple as a mnemonic with some students Common Multiples The Line it Up Game

You can use other colors or multiples How many other factor and multiple groupings can you build? What are the factors of 9? What happens with prime numbers? Can you find the factors of 24? You can use other colors or multiples For example, an orange and a red = 12

Lowest common multiple Have students compare a dark green and a blue ( 6 and 9) Since they don’t line up, we know that 9 is not a multiple of 6 and 6 is not a factor of 9. keep building your greens and blues until you get two matching trains. What do you get? How does this show an lcm? Try this with other colors Lowest common multiple You can teach lcm with these rods and cement the understanding with a math game using a spinner of 10 or 2 ten sided dice. Each student rolls and they use the rods to find the lcm of the two numbers that they got. Page 21

Division- from cuisinaire rods to fair shares Start with cuisinaire rods- use a 10 (orange) Divide evenly first- use the red rods- 10 / 2=5 Show what happens when we divide by 3- space is left but the next rod goes beyond. Use white to fill the space All division really consists of is splitting a larger number into fair shares with (often) some left over. Division- from cuisinaire rods to fair shares Division is hard for kids that do not know their times tables.

The successive subtraction idea USING THE ‘LEFT’ ‘EACH’ METHOD, LETS TRY A FEW LARGER NUMBERS 57/4 138/6 202/5 YOUCAN USE BASE 10 BLOCKS TO MODEL THESE AS WELL…. The successive subtraction idea CUISINAIRE RODS WORK WELL FOR SMALL NUMBERS- HOW DO WE ‘FAIR SHARE’ LARGER NUMBERS. YOU NEED TO HAVE A MULTIPLICATION GRID FOR SOME STUDENTS. MOST WILL NOT NEED IT. PICTURE PAGE 41 FAIR SHARES

Beginning algebra Here you can really begin to see algebra at work. What do you take away from 3 yellow to make a blue? How can you explain this algebraically? Can you solve these with numbers?

The object is to take up as much area on the graph sheet as you can. Each student has their own color. When they roll, they make a square on the graph paper that is the number times itself ( also teaching the squaring principal) The idea is to be strategic. I have the students write over the square they shade in how many spaces they took up ( 8= 64) AREA and squaring GAME USE 10 SIDED DIE, PENCIL CRAYONS AND A SHEET OF GRAPH PAPER Graph paper, pencil crayons

Take some time to work with the manipulatives Take some time to work with the manipulatives. Today was a glimpse into what can be done…. Questions? Thanks for coming today!