Pattern Blocks Why are we using PB. Research in math has shown concrete to abstract when teaching. Teachers will use manipulatives such as algebra tiles, and fraction bars. Pattern blocks allow you to do the concrete to the abstract. Conceptual to procedural. Have participants get out the pattern blocks and play with them. Give one bag to every two people, ask them to look at what they have.

Region Relationships

is what fraction of the blue rhombus? The green triangle is what fraction of the blue rhombus? Previous slide. Region relationships teaching them the concepts of fractions and size. Previous slide. How many does it take? It takes two, if it takes 2 green, green is what fraction of the blue? It is ½ 1 2

is what fraction of the yellow hexagon? The red trapezoid is what fraction of the yellow hexagon? Read to them and have them cover the yellow with the red. Red is what fraction of yellow. What is your student going to be asking you. How can they both be one half? This is the discussion you have to have. What is red to yellow? One half. They are different sizes and shapes. Reason they are a half if because they are half of the whole. Half of the original piece. Why do we like to use these instead of fraction bars? With these manipulatives you can show these are half the original size with different size originals. 1 2

How can and both be equivalent to ? 1 2 Explain that both cover one half.

is what fraction of the yellow hexagon? The blue rhombus is what fraction of the yellow hexagon? How many blues does it take to cover a yellow? Blue is what fraction of the yellow. 1/3 Participants are doing this. 1 3

is what fraction of the red trapezoid? The green triangle is what fraction of the red trapezoid? Do the same practice. 1 3

How can and both be equivalent to ? 1 3 practice

is what fraction of the yellow hexagon? The green triangle is what fraction of the yellow hexagon? It means six of these take up one whole. 1 6

1 6 What pattern block represents when you use two yellow hexagons as the whole? Ask the question above. Now one is a whole and two is a whole. If two yellows make a whole. What pattern block represents one sixth? You had to use six pieces. What it means to have a fraction. A whole is two yellows.

How can two different pattern blocks both be equivalent to ? 1 6 It depends on the size of the whole. It takes 6 greens when the whole is one yellow. It depends on the original size.

Now use two yellow hexagons as the whole. From now on 2 yellows is a whole

2 yellow hexagons = 1 whole. The yellow hexagon is what part of the whole? How many yellow hexagons . This is another example of ½ They would have to stack because they are not the same color. 1 2

2 yellow hexagons = 1 whole. The red trapezoid is what part of the whole? Red tr. How many reds to cover 2 yellows. Doing the same thing change the size of the whole. What does it means to be one half. Relation to size. What does it mean to have a sixth, need sixth to have a whole. 1 4

2 yellow hexagons = 1 whole. The blue rhombus is what part of the whole? If there is two it is one sixth. 1 6

2 yellow hexagons = 1 whole. The green triangle is what part of the whole? It is 1/12 1 12

Now use three yellow hexagons as the whole. Now do it all over again but now we are doing with three as a whole. Participants practice this.

3 yellow hexagons = 1 whole. The yellow hexagon is what part of the whole? Practice 1 3

3 yellow hexagons = 1 whole. The red trapezoid is what part of the whole? The size of the original whole determines the size of the fractional part. 1 6

3 yellow hexagons = 1 whole. The blue rhombus is what part of the whole? Practice 1 9

3 yellow hexagons = 1 whole. The green triangle is what part of the whole? Practice 1 18

Using Pattern Blocks to Add and Subtract Fractions GLE 0506.2.4 Develop fluency with addition and subtraction of proper and improper fractions and mixed numbers; explain and model the algorithm. Check 0506.2.3 Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals. Check 0506.2.6 Add and subtract mixed numbers. SPI 0506.2.5 Solve addition and subtraction problems involving both fraction and decimals. SPI 0506.2.6 Add and subtract proper and improper fractions as well as mixed numbers. It is important that students are giving the time to practice . If you go to fast they will not have the conceptual but teachers tend to jump into add and subtract . You can ‘t start in the middle. Can’t assume they understand. One yellow hexagon is equivalent to one whole.

Show: + + = = 1 3 1 3 2 3 Shade on each hexagon, combine like shapes. GLE 0506.2.4 Develop fluency with addition and subtraction of proper and improper fractions and mixed numbers; explain and model the algorithm. Check 0506.2.3 Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals. Check 0506.2.6 Add and subtract mixed numbers. SPI 0506.2.5 Solve addition and subtraction problems involving both fraction and decimals. SPI 0506.2.6 Add and subtract proper and improper fractions as well as mixed numbers. Here is the whole. Yellow Is nothing more then a whole. Ask question, put one third on the yellow, Is that one third. Put both of the blues on the yellow. Move it over and can you do anything to those blues or is that is as small as that can get. Can you replace any blues with any pattern blocks. How many thirds are there? There are two thirds. You have two one third pieces and now have two thirds. 2 3 = Shade on each hexagon, combine like shapes.

Show: 2 3 + 1 2 + = GLE 0506.2.4 Develop fluency with addition and subtraction of proper and improper fractions and mixed numbers; explain and model the algorithm. Check 0506.2.3 Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals. Check 0506.2.6 Add and subtract mixed numbers. SPI 0506.2.5 Solve addition and subtraction problems involving both fraction and decimals. SPI 0506.2.6 Add and subtract proper and improper fractions as well as mixed numbers. We need to put two one thirds and the one half on the right. Now we are going to have a problem. Pieces are going to overlap. We need to use the same piece on both. Teachers are gong to say we are getting a common denominator. We don’t use the cm. Teach that later. When we teach the procedure. Now what we are going to do . Bring all the greens over at one time. We fill the yellow completely up. One green left over. We just pull down another yellow block. How many greens did we have left over. Notice how we went from adding simple Not for teachers to use Move into this after you have common denominator. Can have other pieces on table-extraneous information. 1 6 =1

Show: 3 2 + 1 6 + = GLE 0506.2.4 Develop fluency with addition and subtraction of proper and improper fractions and mixed numbers; explain and model the algorithm. Check 0506.2.3 Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals. Check 0506.2.6 Add and subtract mixed numbers. SPI 0506.2.5 Solve addition and subtraction problems involving both fraction and decimals. SPI 0506.2.6 Add and subtract proper and improper fractions as well as mixed numbers. Students can do addition with common denominator first then move to next and then to mixed number and so on. In past had problems. New standards. Bring over and put together. Make all the same size. Could you use a bigger piece. Not the biggest piece. Don’t use the word reduced yet. I used less pieces that is why it is getting bigger. Number of pieces is reduce. Doesn’t have anything to do with smaller pieces just less pieces. 2 3 =1

Show: 2 3 - 1 2 = GLE 0506.2.4 Develop fluency with addition and subtraction of proper and improper fractions and mixed numbers; explain and model the algorithm. Check 0506.2.3 Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals. Check 0506.2.6 Add and subtract mixed numbers. SPI 0506.2.5 Solve addition and subtraction problems involving both fraction and decimals. SPI 0506.2.6 Add and subtract proper and improper fractions as well as mixed numbers. We are going to do take aways. What is two thirds. It is 2 blues. If I want to take half of the yellow. How? Can’t do it cover it with greens. When you cover it greens can you take half of the greens away. How many greens are left? Anther way to show it. Just do take away. If you take away one green, then that is one sixth. 1 6 =

Show: 1 1 2 3 1 2 + + GLE 0506.2.4 Develop fluency with addition and subtraction of proper and improper fractions and mixed numbers; explain and model the algorithm. Check 0506.2.3 Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals. Check 0506.2.6 Add and subtract mixed numbers. SPI 0506.2.5 Solve addition and subtraction problems involving both fraction and decimals. SPI 0506.2.6 Add and subtract proper and improper fractions as well as mixed numbers. Mixed number addition which is fifth grade. First you model. What are you going to do. Bring down the wholes then I am going to cover what is left with greens, bring down and cover, what do I have left. # and one sixth. Spend time on front. Show low functioning then switch to calculators. Give same time as general ed. Don’t jump straight to calc in sp ed. = 1 6 =3

- Show: 1 1 2 3 1 2 GLE 0506.2.4 Develop fluency with addition and subtraction of proper and improper fractions and mixed numbers; explain and model the algorithm. Check 0506.2.3 Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals. Check 0506.2.6 Add and subtract mixed numbers. SPI 0506.2.5 Solve addition and subtraction problems involving both fraction and decimals. SPI 0506.2.6 Add and subtract proper and improper fractions as well as mixed numbers. Asked to remove 1 ½ Cover and take away. Left with a single sixth. Don’t do mixed number subtraction until they know mixed number addition. This where you do worksheets etc.

- Show: 1 1 2 3 1 2 GLE 0506.2.4 Develop fluency with addition and subtraction of proper and improper fractions and mixed numbers; explain and model the algorithm. Check 0506.2.3 Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals. Check 0506.2.6 Add and subtract mixed numbers. SPI 0506.2.5 Solve addition and subtraction problems involving both fraction and decimals. SPI 0506.2.6 Add and subtract proper and improper fractions as well as mixed numbers. same

- Show: 1 1 2 3 1 2 GLE 0506.2.4 Develop fluency with addition and subtraction of proper and improper fractions and mixed numbers; explain and model the algorithm. Check 0506.2.3 Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals. Check 0506.2.6 Add and subtract mixed numbers. SPI 0506.2.5 Solve addition and subtraction problems involving both fraction and decimals. SPI 0506.2.6 Add and subtract proper and improper fractions as well as mixed numbers. same 1 6 =

Using Pattern Blocks to Multiply Fractions GLE 0606.2.1 Understand and explain the procedures for multiplication and division of fractions, mixed numbers, and decimals. Check 0606.2.2 Use area models to represent multiplication of fractions SPI 0606.2.1 Solve problems involving the multiplication and division of fractions SPI 0606.2.2 Solve problems involving the addition, subtraction, multiplication, and division of mixed numbers. One yellow hexagon is equivalent to one whole.

1 3 Find of 1 2 Show 1 2 Show 1 3 of 2 1 3 X 2 1 6 =

Two yellow hexagons are equivalent to one whole. Double Hexagon Model GLE 0606.2.1 Understand and explain the procedures for multiplication and division of fractions, mixed numbers, and decimals. Check 0606.2.2 Use area models to represent multiplication of fractions SPI 0606.2.1 Solve problems involving the multiplication and division of fractions SPI 0606.2.2 Solve problems involving the addition, subtraction, multiplication, and division of mixed numbers. Two yellow hexagons are equivalent to one whole.

1 3 Find of 1 2 Show 1 2 Show 1 3 of 2 1 3 X 2 1 6 =

1 3 Find of 1 4 Show 1 4 Show 1 3 of 4 1 3 X 4 1 12 =

Using Pattern Blocks to Divide Fractions GLE 0606.2.1 Understand and explain the procedures for multiplication and division of fractions, mixed numbers, and decimals. Check 0606.2.2 Use area models to represent multiplication of fractions SPI 0606.2.1 Solve problems involving the multiplication and division of fractions SPI 0606.2.2 Solve problems involving the addition, subtraction, multiplication, and division of mixed numbers.

Find 4 1 3 Four hexagons represent 4. 1 3 4 = 12 6 7 9 10 12 2 5 8 11 To divide by 1/3, think “How many 1/3’s are in 4?” 1 3 4 = 12

Find 4 2 3 Four hexagons represent 4. 2 3 4 = 6 1 2 2 3 4 5 5 6 1 3 4 6 To divide by 2/3, think “How many 2/3’s are in 4? 2 3 4 = 6

Find 4 3 1 2 Shade four and one half blocks 1 2 1 2 4 3 = 1 Divide the shaded area into 3 equal parts. 1 2 1 2 4 3 = 1

Find 2 2 3 2 3 Shade two and two thirds blocks 2 3 2 3 2 = 4 1 2 2 3 4 1 3 4 Think “How many 2/3 are in 2 2/3?” 2 3 2 3 2 = 4

6th, 7th, and 8th grade GLE 1.4: Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies. 5th, 6th, and 7th grade GLE 1.8: Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts.

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