8E Math Activities Training teacher's guide English July 2009

A WORLD of MATHEMATICS

Math Activities

Grades 1-2-3

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This Training Guide was made possible by the support of the American people through the United States Agency for International Development (USAID) under the terms of Award No. 306-A-00-06-00518. The content is the responsibility of the Partnership for Advancing Community Education in Afghanistan (PACE-A) and does not necessarily reflect the views of USAID or the United States government. PACE-A is a consortium composed of four international NGOs: CARE, IRC, AKF and CRS.

له مخې شمیره تون A-00-06-00518-306د (USAID) پرمخت د ادارې نیوאل د امریکا د متحده ایالاتو دې په مالي مرسته چد خلکو متحده ایالاتو د امریکا ا لارود د روزنې دد اویاUSAID د ېده چه او حتمی ن دیمسؤلیتې ادار د (PACE-A)وند پاره پرمخت ل د محلي وونې او روزنې دې په افغانستان ک محتویاتغه لارود د د. دی ترتیب شوی،برابریي

. کيحکومت نظر رند د متحده ایالاتو امریکا د د

.دیائتلاف شوی یو خه جوCRS او CARE ،IRC ،AKF ـدولتي مؤسسونیوالو نالورو د)(PACE-Aون پرمخت لپاره د محلي وونې او روزنې دېپه افغانستان ک

پروگرامPACE-A د: تهیه او ترتیب

لمریز کال هجري ١٣٨٧ لیند/ December 2008

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Introduction for Teachers The world is full of mathematics. Counting, shapes, patterns and puzzles are everywhere. Everything we see and hear can be used to teach mathematics to young children. The shape of the mosque minaret, the patterns in a carpet and the seeds a farmer plants all require mathematics. Puzzles are problems that have one or more solutions. If two birds are singing, there is a pattern to the sounds that each of them makes in turn. Students in Grades 1-3 need to be actively engaged in math lessons to make sense of numbers representing real world situations. If the family has 3 loaves of bread and they eat two for breakfast, how many loaves are left for lunch? If the father in a family has 8 siblings and 3 are brothers, how many are sisters? If each pomegranate costs 20 Afs, how many pomegranates can you buy for 100 Afs? These questions are part of every day life and we need to understand mathematics to solve them. Mathematics learning for younger children needs to include activities with:

Movement of children (kinesthetic)

Objects that children move/the Base Ten Blocks (tactile)

Colorful pictures (visual) Each activity in this guide will tell you if it is visual, tactile or kinesthetic at the top of the page. The Base Ten Blocks have ones, tens, hundreds and thousands for adding, subtracting, multiplying and dividing.

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USING BASE TEN BLOCKS

Each block counts as one in addition, subtraction, multiplication and division problems. The teacher can show 1 + 2 on the board. The students take 1 block and add 2 blocks more, showing 3 blocks in total. The blocks are tangible and represent the numerals. Each block can also represent one item in a picture, giving students blocks to move around (tactile) when the teacher shows a picture and asks a math problem. The teacher can show a picture of balls and ask the students to count one block for each ball in the picture. If the total number of balls is 10, then the students count ten blocks. The teacher can tell the students to subtract 4 red balls from the picture and writes 10-4 on the board to represent in numerals what is being asked. The children remove 4 blocks from their group of 10 and have 6 remaining, the answer to the problem, 10-4=? 2X3=? Students take 2 blocks three times, having three groups of 2. By adding all the blocks they see that 2X3=6. 6÷3=? Students take 6 blocks and divide them into groups of three, seeing that they have 2 groups. 6÷3=2 The ten, one hundred and thousand blocks are used when higher numbers are used in problems. Students in the 2nd and 3rd grades can use them to begin learning amounts greater than 100.

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Activity 1 Visual/Grade 1

Teacher Directions Possible Questions Answers How many colored butterflies do you see?

10

How many blue butterflies are there? How many orange butterflies are there? How many green butterflies are there? How many yellow butterflies are there?

4

3 1 1

Is there another color of butterfly in the picture? What color is it?

Yes Lavender/purple

Use the picture of butterflies in the math picture book on page 1. Hold the picture up and walk close to the children so they can easily see the picture. Then stand in the front of the room so all children can see the picture. Ask the questions on this page, giving children time to count the different colored butterflies.

How many green and blue colored butterflies are there altogether?

5

If we add the yellow and the green butterflies, how many do we have?

2 Ask the children to pay attention and think hard.

If we add the orange and the blue butterflies, how many do we have?

7

Teacher: Use the colors and numbers of butterflies to ask more addition questions. Use the Base Ten Blocks (ones) so children can have a tactile activity also. Each child should have 10 ones-blocks because there is a total of ten butterflies in the picture.

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Activity 1 Tactile & Visual/Grade 2 & 3

Teacher Directions Possible Questions Answers

Count out one block for every colored butterfly you see in the picture.

Children should have 10 ones blocks.

Subtract one block for each blue butterfly in the picture. How many blocks do you have left?

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Put the ten blocks together again. Subtract one block for each yellow butterfly you see. How many blocks do you have left?

9

Use the picture of butterflies in the math picture book on page 1. Use the Base Ten Blocks (the ones). Hold the picture up and walk close to the children so they can easily see the picture. Then stand in the front of the room so all children can see the picture. Ask the questions on this page, giving children time to count the different colored butterflies and to count out their blocks.

Count one block for each blue butterfly and put them together in a group. Count out one block for each orange butterfly and put them in a separate group together.

4 blue 3 orange

Which group has more, the orange or the blue?

The blue Greater than [>] and less than [<] symbols should be introduced to students. How many more blue butterflies are

there than orange butterflies? 1

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Activity 2 Tactile & Visual/Grade 1


How many green flowers are there? 4 Count out 4 blocks. How many pink flowers are there? Count out 3 blocks and place them below the 4 blocks. How many purple flowers are there? Count out 3 blocks and place them below the other 3 blocks.

3

3

How many green and pink flowers are there altogether? Put the blocks for each colored flower together and count them. Place the blocks back into groups of 4, 3 and 3.

4+3=7

Use the picture of flowers in the math picture book on page 2, and the ones blocks. Before showing the picture, have students count out 10 blocks. Then show the picture to the students.

How many purple and pink flowers are there altogether? Put the blocks for each color together and count them.

3+3=6

Say to the students, “6+4 and 7+3 both equal 10”. Divide the 10 blocks into a group of 6 and 4. Divide the blocks into a group of 7 and 3.

Which 2 sets of flowers make 6? Which sets of flowers make 7? How many plus 6 make 10? How many plus 7 make 10?

Purple & Pink Green & Pink/Green &Purple

4 3

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How many flowers are blooming? How many buds are there? Which is >, the blooming flowers or the buds?

10 11

The buds

Using the blocks, show the number for the blooming flowers. Now, show the number of buds with blocks. How can we make the number of blocks equal (=)?

One tens block or Ten ones blocks

One tens and one ones

Take one away (subtract) one from the blocks of buds.

Yellow buds + green flowers =? 10

Use the picture of flowers on page 2, and the ones blocks. Before showing the picture, have students count out 10 ones blocks and 1 tens block. Then show the picture to the students. There are 10 flowers in bloom. There are 11 flower buds (yellow, pink and green).

Yellow buds – purple flowers=? 3 Make up any subtraction problems using buds and flowers amounts.

Use the picture and the counting blocks in each problem.

Kinesthetic Activity: Have the children be a ‘flower garden’. Children stand up and are given a name: yellow bud, green flower, purple flower, pink bud and so on. Then tell the flowers to blow in the wind and children sway and move their arms. Then the teacher says, “Oh no, a purple bud has blown away!” and that child sits down. Have the group of flowers still standing count their total number. Repeat until all children (flowers) have blown away.

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Count one ones block for each 6 sided black shape. How many blocks do you have?

16

Count one ones block for each red four sided shape. How many do you have? How many blocks do you have altogether? 16+18=?

18

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How many points does the blue star in the center have?

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Using the picture of shapes on page 3 of the math picture book, tell the students they are going to work with the 6 sided black shapes and the four sided red shapes and the pointed blue star in the middle.

Is that half the number of the black or red shapes? Use the ones blocks to check your answer.

Black shapes

If we subtract the number of blue points from the number of black shapes, how many do we have? How much does 8+8=? 16-8=?

8

16 8

Kinesthetic Activity: Have children stand in groups of six and stretch out their arms to touch and make a hexagon. Then have them stand in groups of four to make quadrilaterals. Does the length of children’s arms differ?

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Are the six sides of each hexagon the same length?

No, some sides are longer.

(Teacher uses two fingers and points to sets of hexagons.) Count aloud by 2’s until we have counted all the hexagons. Repeat counting by 2’s with blocks.

2, 4, 6, 8, 10, 12, 14, 16

2, 4, 6, 8, 10, 12, 14, 16 Are the 4 sides of each quadrilateral the same length?

No, the sides are many different lengths.

Using the picture of shapes on page 3. Tell students that a 6 sided shape is a hexagon. A four sided shape with different lengths, like the red ones in the picture, is called a quadrilateral. Count the sides of four or five of the black and red shapes, so children see that each color has the same number of sides in each shape even though the length of each side is not the same. Use ones and tens blocks.

(Teacher uses two fingers and points to sets of quadrilaterals.) Count aloud by 2’s until we have counted all the quadrilaterals. Repeat counting by 2’s with blocks.

2,4,6,8,10,12,14,16,18

2,4,6,8,10,12,14,16,18 The picture also looks like a puzzle. The teacher can have the children draw and color a copy of the picture, cut it up along the black lines and try to put the puzzle together again, matching the picture.

Use 2 tens blocks for students to use two fingers to count by 2’s up to 20. Practice counting backwards aloud with students.

2,4,6,8,10,12,14,16,18,20

20,18,16,14,12,10,8,6,4,2

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Hexagon A hexagon is a six-sided figure. Bee hives have hexagonal cells.

Quadrilateral A quadrilateral is a four-sided figure. The square, rectangle, rhombus, trapezoid, kite, and parallelogram are quadrilateral.

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How many red squares are there? How many yellow squares? How many white squares? How many light blue squares? How many squares have a black outline? What colors are the black outlined squares?

3 4 2 3

3 Light blue and red

Use the picture on page 4 of squares in the math picture book. Talk about the different colors in the picture (light blue, white, yellow, red). Hold the picture up for all students to see.

Is there a pattern to the colors? Do the colors go; red-yellow-white-blue in every row? Do the colors go blue-red-yellow-white in every row?

No No

No

Use the ones blocks Count one block for the red squares.

Count one block for the blue squares. Count one block for the white squares. Count one block for the yellow squares. 3+3+2+4=?

3 3

2

4 12

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How many squares are in each row going up and down?

3

How many squares are in each row going across?

4

Let’s count the squares going up and down by 3s together aloud. Repeat.

3,6,9,12 3,6,9,12

The blocks are ‘cubes’ and have six equal square sides. Squares have four equal sides and are flat. Use the picture of colored squares on page 4 of the math picture book and have each child count out 21 ones blocks. Teacher counts aloud with students to count the number across and up and down. Teacher uses three fingers to count the squares in the picture by 3s.

Put your blocks in rows of 3. How many rows do you have? Now let’s count higher by 3s by counting each of your rows of blocks. Let’s repeat. Count with a partner next to you.

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3,6,9,12,15,18,21

3,6,9,12,15,18,21 3,6,9,12,15,18,21

What is the difference between our blocks and the squares in the picture?

The blocks are solid. The blocks have six sides. The squares in the picture are flat. The squares in the picture have four sides.

Kinesthetic Activity: Have the children line up by 3s in rows behind each other. The first row shouts 3, the second row 6 and so on. After a row has shouted out their number, they move behind the last row of 3. See how high the children can count by 3s this way without making a mistake.

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Teacher Directions Possible Questions Answers What is the total number of hearts in the picture?

14 Use the picture with hearts on page 5 of the math picture book. The various sizes of the hearts will be counted; largest, large, medium, small and smallest. Teacher points to each different size when she says the name. Give children 15 ones blocks and 1 tens block each or to partners.

Using the blocks, count out 14 two different ways. How many of the largest size heart do you count? How many of the large size heart do you count? How much does 4+1=? Count with blocks. How many of the medium size hearts do you count? Add 5+4 with blocks. What is the total number of blocks now? How many small hearts do you count? Add 2 blocks to the 9 blocks you already have. What is the total? How many of the smallest hearts do you count? Add 3 blocks to the total of 11 you already have. What is the total?

1 tens block and 4 ones 14 ones blocks.

1

4

5

4

9

2

11

3

14 Using the blocks, have children subtract certain sizes of hearts from the total of 14 for practice in subtraction.

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Teacher Directions Possible Questions Answers How many hearts do you have altogether? Is this the same amount as the total number of hearts in the picture? Which number is more? Is 25>14? How much more is 25 than 14? Take 14 hearts away from your group of 25. How many are left?

25

No

The cut hearts Yes 11

11 Look at the picture and count out with your cut hearts: The number of largest hearts in the picture. The number of large hearts in the picture. The number of medium hearts in the picture. The number of small hearts in the picture. The number of the smallest hearts in the picture.

Largest# < large #

Large# = medium#

Medium# > small#

Small# < smallest#

Smallest# >largest#

Give children pieces of paper that are folded in half. With scissors, the children cut different sized hearts out of their paper. Cutting half a heart shape will make a whole heart when the paper is unfolded. Have the students organize the hearts from the whole class into groups by size. Have 5 different groups; largest, large, medium, small and smallest. Children will use the hearts to count with instead of blocks. Use the picture on page 5 of the math picture book and show the students the largest, large, medium, small and smallest hearts in the picture so they are clear when they do the exercises. Work in small groups, giving each group 5 of each sized heart they have cut. Practice < and >. How many cut hearts do you have? 14

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How many sculptures do you count? 5 Use the picture of iron sculptures on page 6 of the math picture book. This is a modern sculpture in Paris, France, one of the most beautiful cities in the world. The sculptures will teach categorizing by tall, average and short.

What differences do you see in the sculptures? Let’s talk about the height. How many heights do you count? How many of the tall sculptures do you count? If there are 5 altogether, 3 tall sculptures means the majority are tall. (more are tall than any other height)

Height, shapes on top, colors

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Children line up by height from the shortest at one end to the tallest on the other end. Children decide which children in between are short, average and tall. Count how many children fit in each category. At the end of the school year, have children line up again to see how they have grown and recount.

There is one sculpture that is medium height. Medium means between tall and short. Describe what the medium sculpture looks like. Describe what the short sculpture looks like.

It has an 8 sided shape on top (called an octagon) with 3 circles cut out. It’s yellow with circles cut out.

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Describe the rectangle in the picture.

Dark green background, blue circle inside, with a red circle inside the blue circle.

Describe the octagon in the picture. Dark green (may look black) with 3 circles cut out.

Describe the circle in the picture. O It is round with 3 arches cut out.

Use the picture of sculptures on page 6 of the math picture book. See the note in Grade 1 activities on the previous page. Tell the students about the picture. This lesson is about shapes. Each sculpture has a different shape on top; rectangle (4 sides, 2 sides longer than the other 2 sides), diamond, circle, octagon (8 equal sided shape), triangle (3 sided fan shaped on top).

Describe the diamond in the picture. There is a red circle inside a black circle on a blue background.

Kinesthetic Activity: Look in the classroom and outdoors for these shapes in objects or nature. See how many of each shape the students can find in real objects around them. Make a chart of each shape and the number found.

Describe the triangle in the picture.

It is yellow, shaped like a fan, with 3 circles cut out.

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Let’s find out how many balls there are by counting each color. Count out blocks for each total we reach.

Use the picture of balls on page 7 of the math picture book. This activity helps children classify by color, and add larger double digit numbers. Use the counting blocks to represent each different color. If a ball is not completely pictured, still count it as one of that color. Teacher counts out loud with all students, pointing to each ball of certain colors as she counts.

Let’s count the orange balls. Let’s count the green balls. Count the blocks for orange and green and add them together. Let’s count the yellow balls. Add the yellow balls blocks to the total of orange and green. Let’s add the blue balls. Let’s add the white balls. Now add the pink and red balls together.

20 14

20+14= 34

11 34+11= 45

6 4 6

If there is time, let the children add and subtract numbers and blocks for all the possible combinations of colors.

What is the total of blue, white, red and pink balls? How can we find the total number of all the balls using the blocks?

16

Add the total of 45 to 16. 45+16= 61

Kinesthetic Activity: Have children use crayons and color a piece of paper with their favorite color. Children get in groups according to matching colors. Which group color has the most? The least? Are any groups equal in number?

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Teacher Directions Possible Questions Answers Look at the picture and tell me which color you see the most of.

orange

There are twice as many orange balls as yellow. There are almost three times as many orange balls as blue balls. We see orange as the dominant color in this picture because there are many more orange balls.

# yellowX 2= # orange # orange ÷ 2 = # yellow # blue X 3= # orange

# orange > # any other color

Use the picture on page 7 of the math picture book of colored balls. Balls are solid spheres. This activity will use colors for addition and subtraction of larger numbers and > and < and =. Make seven groups of students and give each group a color and the number of balls of that color; yellow (11), orange (20), blue (6), green (14), white (4), pink (3) and red (3). Use counting blocks to represent the number of balls for each color, whether the picture shows a complete ball or just part of a ball. It is difficult to count the different colors of balls. If children come close to the numbers above, use the number they see.

Using the blocks for each color group, ask groups if they are > or < or = the other groups by counting the blocks. Have each group keep a written chart of their color compared to other groups. As a whole class, compare all the charts and see if they match.

Have groups subtract their totals from other groups to determine the differences between numbers.

Orange 20-yellow 11= 9 (example)

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What is this shape? What is the arrow sitting on in the picture? Try to make an arrow sitting on a cube out of your blocks.

An arrow

A cube

How many arrows are in the picture? How many cubes are in the picture?

1 2

Count the windows in the tall building. How many are there?

32

Use the picture on page 8 of the math picture book of the buildings. There are 5 different shapes in the picture. Use the ones, tens and hundreds blocks for groups to try and make the same shapes out of blocks. Count out 32 ones blocks. Count out 15 ones blocks. Subtract 15 blocks from the group of 32. Add 32 blocks plus 15 blocks.

Count the windows in the other building. How many are there?

15

Subtract and add the number of windows using blocks.

32-15= 17 32+15= 47

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Activity 8 Tactile & Visual/Grade 2 & 3 Teacher Directions Possible Questions Answers

Do you remember how to count by 3s? Let’s practice again, counting the ‘threes’ in the picture.

3,6,9,12,15,18,21

3 blocks are stacked up. Let’s add those too. Let’s count backwards by 3s.

3,6,9,12,15,18,21,24

24,21,18,15,12,9,6,3 The windows in the tall building have 4 across. Let’s practice counting by 4s. Repeat.

4,8,12,16,20,24,28,32

4,8,12,16,20,24,28,32

Using the picture on page 8 of the math picture book of buildings, children will learn to count by 4s, learn more about shapes: rectangles, triangles, cubes, arrows and cylinders. Use ones blocks for counting by 4s activities. Review counting by 3s by putting your fingers on the 3 black dots in the buildings and counting out loud with children Then introduce counting by 4s with the ‘windows’ on the tall building.

Put rows of 4 blocks in front of you and keep adding rows until you have 32. How many rows of 4 do you have? Count the blocks by 4s.

8

4, 8, 12, 16, 20, 24, 28, 32

Count backwards by 4s. 32,28,24,20,16,12,8,4 Ask students to make some of the shapes with the blocks and the puzzle pieces.

How many cubes are there? 2

How many rectangles do you see? 8 How many arrows? 1 How many cubes do you see? 2 How many triangles do you see? 2

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How many strawberries are there in total in the picture?

17

Is 17 > 20? How do you know? How many + 17 = 20? How much does 17 + 17= ? How much does 17+ 20= ?

no there are not enough ones blocks to

make 2 tens. 3

34 37

Use the picture of strawberries on page 9 of the math picture book. Each student counts 17 ones blocks and has 1 ten block to work with. Have children work in pairs.

How many more strawberries does the picture need to make 37?

20

Using paper and crayons, let the students draw strawberries on a paper. Use 100 blocks, tens and ones.

Count all the strawberries everyone has drawn. How many do we have altogether? Who has the most strawberries on their paper? Who has the least number of strawberries on their paper? Count enough blocks to equal the number of strawberries children have drawn.

?

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How many strawberries are in the picture?

17

How much does 17 X 1=? 17 X 2=? 17 X 3=? 17 X4=? 17 X 5=?

17 34 51 68 85

Which answers are even numbers? 34, 68

Use the picture of strawberries on page 9 of the math picture book. Students should work in groups of 5 and use all their blocks together to solve the problems you ask. Give each student 17 ones blocks and 1 ten block and 1 one hundred block. Which answers are odd numbers? 17,51,85 Multiplication practice. Using blocks as a group.

If 17 is multiplied by an odd number is the answer odd or even? If 17 is multiplied by an even number is the answer even or odd?

Odd

Even

Division practice. Using blocks as a group.

How much is 85 ÷ 5? 85 ÷ 17? How much is 68 ÷ 4? 68 ÷ 17? How much is 51 ÷ 3? 51 ÷ 17?

17, 5 17, 4 17, 3

Kinesthetic Activity: Have the students stand up and count off until each of them has a number (1,2,3…). Tell them to remember their number. The teacher will call out two numbers (6 and 9 for example). The students with numbers 6 and 9 have to add their numbers and multiply their numbers. If they are correct they stay in the game. If they are incorrect, they sit down. The last pair standing is the winner.

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How many colors do you see? 4 Green, blue, orange, yellow

Use the picture of bottle caps on page 10 of the math picture book. Students should each have 25 ones blocks and 2 tens blocks. Some bottle caps are partially hidden, so students need to count carefully.

Count each color, even if a cap is partially hidden. How many of each color do you see? Count one block for each bottle cap. Subtract the blue from the green. Subtract the orange from the green. Subtract the yellow from the blue. What answer will be the same if you subtract yellow from another color?

9 green 9 blue

5 orange 1 yellow

24 total blocks 0 4 8

green Only use the blocks. Have students count the blocks for each problem you give them.

How much does 9+9=? How much does 9+5+? How much does 9+1=? 9 + an odd number always equals an even number. What does 9+ an even number equal?

18 14 10

An odd number

Kinesthetic Activity: Have students form groups of odd and even numbered groups. Then have them join together to make odd and even numbered totals.

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How many blue squares are there in one row that go across the picture? How many blue squares go up and down in one row? If you multiply the two numbers, what is the answer?

6

7

42

How many cubes are there in total in the picture? How many squares are there in total in the picture?

42

7X6X3= 126

Use the picture of stacked cubes on page 11 of the math picture book. This picture is an ‘optical illusion’. If you stare at it, it looks like the cubes are stacked, facing the left or the right, depending on where your eyes focus. The combination of colors on the cubes causes us to see two different versions of the same picture. The eyes play tricks on us!

How much is 126÷3? 42 Have the students look at the picture for a few minutes and talk about what they see. Use the counting blocks for multiplication and division problems.

How much is 126÷7? How much is 6X3? What do you notice about the numbers in the problem 7X6X3?

18 18

They can be multiplied in different ways to get the same answers.

What elements cause an optical illusion?

Color, shades of colors, shapes

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Teacher Created Activities Teacher Directions Possible Questions Answers

Kinesthetic Activity:

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Teacher Created Activity Teacher Directions Possible Questions Answers


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مشاركت "تهيه شده است و دفتر , فراهم مي شود) USAID (" اداره انكشافي بين المللي ايالات متحده آمريكا"اين رهنمود قسماً توسط كمك مالي مردم ايالات متحدة آمريكا كه از طريق اما نكته ها و نوشته هاي شامل اين مجموعه به صورت الزامي بيانگر نظريات و , بطه با محتويات آن مسؤليت مي پذيرددر را , PACE-A – " تعليم و تربيت در افغانستانانكشافجهت

.و حكومت ايالات متحده آمريكا نمي باشد ) USAID (" اداره انكشافي بين الملي ايالات متحده آمريكا "خواسته هاي بنياد , كميتة نجات بين المللي, پاملرنه : يك نهاد ايتلافي است كه شامل چهار سازمان غير دولتي بين المللي مانند ) PACE-A( "تربيه در افغانستان مشاركت جهت انكشاف تعليم و "

. مي گردد ) CRS( انكشافي آغاخان و خدمات آسايشي كاتوليك

This Training Guide is made possible by the support of the American people through the United States Agency for International Development (USAID). The content is the responsibility of the Partnership for Advancing Community Education in Afghanistan (PACE-A) and do not necessarily reflect the views of USAID or the United States government. PACE-A is a consortium comprised of four international NGOs: CARE International, International Rescue Committee, Aga Khan Foundation and Catholic Relief Services.

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8E Math Activities Training teacher's guide English July 2009