2GEO – METRY When we learn about GEO-METRY we are learning about measuring all the things on the Earth.
3When you were in Kindergarten and First Grade you learned about shapes in our world. There were: circles squares triangles and rectangles.
4There were: trapezoids pentagons hexagons octagons rhombus and ovals.
5Now we are going to look more closely at each shape Now we are going to look more closely at each shape. Each shape has SIDES and ANGLES. TRI stands for 3. So a TRIangle has 3 angles and it also has 3 sides. Each angle point has a special name. It is called the VERTEX.VERTEXA tricycle has 3 wheels! TRI = 3
7This is a square. A square has 4 equal sides and 4 equal angles and 4 equal vertices. What makes a square special is that all the sides must be exactly the same. If they are not the same then we call it a RECTANGLE!
11Rhombus also have 4 sides, 4 angles and 4 vertices but two of the sides are tipped over. A rhombus looks like a square or a rectangle that someone sat on. SQUISH!rhombusRhombus
12Trapezoids also have 4 sides, 4 angles and 4 vertices Trapezoids also have 4 sides, 4 angles and 4 vertices. Two of the sides are parallel to each other. When lines are parallel it means they stay the same distance apart forever! Train tracks are parallel.
14Did you know that they have a special name for all the shapes that have 4 sides, 4 angles and 4 vertices? They are called QUADRILATERALS! QUAD means 4. A quad runner has 4 wheels. All quadrilaterals have 4 sides and 4 angles and 4 vertices.
15All shapes that have 4 sides, 4 angles, and 4 vertices are called QUADRILATERALS. REMEMBER: Any SHAPE with 4 SIDESand 4 ANGLES or 4 VERTICESis called a QUADRILATERAL.
165. A pentagon has 5 sides, 5 angles and 5 vertices. The prefix PENT means 5.Any word with the prefixPENT has somethingto do with5.The Pentagon is located in Washington, D.C.It has 5 sides and 5 angles and 5 vertices.
18Anything with the prefix hex has The hexagon has 6 sides,6 angles and 6 vertices.The prefix HEX means 6.Anything with the prefix hex hassomething to do with6.
19Look at each shape. Circle all vertices. Put a line through each side Look at each shape. Circle all vertices. Put a line through each side. I did the first one for you.TRI = QUAD = PENT = HEX = 6
20But there are many other shapes But there are many other shapes. Shapes with more than 3, or 4, or 5, or even 6 sides. What about an OCTAGON? The prefix OCT means 8. So an octagon has 8 sides, 8 angles and 8 vertices. Can you circle the vertices and put a line through each side?
21Do all octagons have to be so perfect. NO Do all octagons have to be so perfect? NO! Any shape with 8 sides, 8 angles and 8 vertices is an Octagon! Can you find each Octagon?
22The shapes we have looked at are called 2-D or 2 dimensional The shapes we have looked at are called 2-D or 2 dimensional. That means that they are flat. If the shape is not flat than it is 3-D or 3 dimensional. This is a CUBE. A cube is not flat but it has 6 flat sides or faces. Each side has a flat square shape. A cube is not a square but you need 6 squares to make a cube!
23This pattern is called a net This pattern is called a net. If you fold the 6 squares you can make the cube. When we look at a cube We can only see 3 faces, but if you look behind and under you will count 6 faces on a cube.
24Just like the 2-D shapes each 3-D geometric solid has the same parts Just like the 2-D shapes each 3-D geometric solid has the same parts. They each have a flat surface called the face, they each have vertices where the points come together and they each have edges where the faces come together.
25These are cubes. They are geometric solids. They have 6 equal faces These are cubes. They are geometric solids. They have 6 equal faces. They have 8 equal vertices. Count them. One is hiding… They have 12 equal edges. Count them. Three are hiding…
26There are many different 3-D geometric solids There are many different 3-D geometric solids. These all have faces, edges, and vertices. Can you name some of these?
27This is a very fancy house. Do you see the front porch? The roof to the porch isheld up with columns.Columns go up and down. They are VERTICAL.
28In math lines that go up and down are called VERTICAL LINES In math lines that go up and down are called VERTICAL LINES. I like to think of the V in Vertical as the point of the arrow. We are going to use vertical lines to cut a rectangle into equal sections. V
29In math any lines that go side to side are called HORIZONTAL ROWS In math any lines that go side to side are called HORIZONTAL ROWS. Horizontal is a really big word so we just say: ROWS! Rows go from one side of a shape to the other. Remember the word parallel? Rows need to be spaced equally. Rows should be parallel to each other.
30The rectangle was partitioned We are going to use columns l and rows to partition or section off a rectangle. Let’s do one together. Split this rectangle into 2 rows and 3 columns.The rectangle was partitionedinto 6 equal sections.
32Let’s do some more. 3 rows & 5 columns 4 rows & 3 columns rows & 6 columns____ equal sections ____ equal sections ____ equal sections
33Partitioning a rectangle into rows and columns is not the only way to make equal sections in a rectangle. What about cutting the rectangle into equal sections using triangles?We have made 4 equalsections by slicing the rectangle from corner to corner.
34Another way to partition a rectangle into 4 equal parts is to think of it as a rectangular clock. Make your line from 12 o’clock down to 6 o’clock and make another line from 9 o’clock to 3 o’clock.
35Now you try some. Make your line from 12 to 6 and another line from 9 to 3.
36Of course you can always use rows and columns to partition a rectangle into 4 equal parts. Because we made 4 equal parts we can call each part one of four or 1/4th. In this picture 1/4th of the rectangle is red. The number under the line tells us how many parts the rectangle was cut into. The top number tells us how many of those parts are red.
37Can you partition each rectangle using rows and columns? Can you shade in 1 of the 4 equal parts andwrite 1/4 by your rectangle?Remember that the number under the line shows how many pieces you cut it into and the number on top shows how many of those parts are shaded.
38There is one more way to partition a rectangle into 4 equal parts. It is a little tricky!First you are going to cut your rectangle in 2 parts.Anything that is cut into 2 equal parts is cut in HALF.After making your line from12 o’clock to 6 o’clock youwill draw a line from thetop corner to 6 o’clock.Now draw a line from 12 o’clock to the lower right corner.
39Now it is your turn to practice. If you need help look at the examples.
40These are all different ways you can cut or partition a rectangle into 4 equal parts.
41You have probably helped cut a pizza into equal sections You have probably helped cut a pizza into equal sections. Try to cut this pizza into 4 equal slices or sections.12Think of the pizza as a clock.Draw your line from the 12down to the 6. Now draw aline from the 9 to the 3.You just divided your pizzainto 4 equal pieces!936
42Your pizza should have looked like this Your pizza should have looked like this. Now partition this clock into 4 equal sections.
43Now partition or divide each circle into 4 equal sections. If you shade 1 of the 4 sections you have shaded 1/4 orone fourth of the parts. Shade 1/4 of each.What would you write if you shaded 2 of the 4 parts? or ½.4
44Maybe you don’t want to cut your pizza into 4 sections Maybe you don’t want to cut your pizza into 4 sections. Maybe you only need 3 sections. How could you use the clock to make 3 equal sections?
45Now partition or divide each circle into 3 equal sections. If you shade 1 of the 3 sections you have shaded 1/3 orone third of the parts.Shade 1/3 of each. What would you write if you shaded 2 of the 3 parts?3
46When you cut something into 2 equal parts we say you cut it into halves. If you shade 1 section then you shaded one half or ½ of the shape.The number under the line showshow many parts you cut it into.The number above the line showshow many of the parts are shaded.
47When the number on the top of the line is the same as the number under the line then you shaded the whole thing.3/3 = 1 whole2/2 = 1 whole4/4 = 1 whole
48If I cut a pizza into 3 equal pieces and I eat all 3 pieces then I ate the WHOLE thing!
49If I cut a pizza into 4 equal pieces and I eat all 4 pieces then I ate the WHOLE thing!
50You can cut or partition any rectangle by using rows and columns. We have only looked at halves, thirds, and fourths,but you can partition a rectangle into as many parts as you want.Instead of writing down the words rows and columnswe just write down the number of rows first with anX and then the number of columns we want to have.So 2 rows with 5 columns would be written 2 x 5and look like this.2x5
51This is a 2 X 5. But if you flip it over it becomes a 5 X 2 This is a 2 X 5. But if you flip it over it becomes a 5 X 2. These can be written as addition sentences = 10 or = 102X55X2
52It is your turn to write the addition sentences to go with each rectangle below. When you line up objects in rows and columns it is called a rectangular ARRAY. __+__+__+__+__+__=___ __+__+__+__=___4X66X4
53Use an addition sentence to tell how many objects are in each rectangular ARRAY.
54ARRAYS can be fun to make. They can also help you solve math problems ARRAYS can be fun to make. They can also help you solve math problems. Let’s try one together. Quintin has 8 chairs. He wants to arrange them in equal rows. What are some ways that he can arrange the chairs? There are 4 possible arrays to solve this problem.1 X 8 = 8or8 X 1 = 84 X 2 = or X 4 = 8
55These are all the ways you can arrange 16 chairs These are all the ways you can arrange 16 chairs. It is easy to make little squares in your array but if you wanted to you could draw the little chairs.This is a 2 X 8 = 16 array.
56Label and solve each picture array. Rows X Columns = Label and solve each picture array. Rows X Columns = ? ___ X ___ = ___ ____ X ____ = ____ ____ X ____ = ____
57Label and solve each picture array Label and solve each picture array. Write the addition sentences that go with each array.2+ 28= 8
58Paul makes an array with 12 tennis balls as shown below Paul makes an array with 12 tennis balls as shown below. Write two different equations to represent his arrangement.Equation is a fancy math word that means a math sentence with equal = signs.
59Joannie arranges 15 penguins into a rectangular array as shown below Joannie arranges 15 penguins into a rectangular array as shown below. Write two different equations to represent her arrangement.
60Mark arranges 12 ice cream cones into a rectangular array as shown below. Write two different equations to represent his arrangement.
61Keith arranges triangles into a rectangular array as shown below Keith arranges triangles into a rectangular array as shown below. Write two different equations to represent his arrangement.
62Look at each building array Look at each building array. Write two equations to represent each array.
63Barbara draws a rectangle on grid paper Barbara draws a rectangle on grid paper. She needs to count the number of small squares within the rectangle. How many small squares are found in the shaded rectangle? a. 22 b. 30 c. 28 d. 24
64Adam designed a sign for his bedroom door to keep his sister out of his room. The shape of the sign has 4 equal sides and 4 equal angles. What shape is his sign? a. square b. triangle c. sphere d. trapezoid
65Ellsa wants to build a go kart Ellsa wants to build a go kart. As she builds the go kart she notices many different shapes in her design. She grabs the last piece of the go kart and begins to attach it to the hood. What is the name of this shape? a. square b. trapezoid c. rhombus d. rectangle
66Carter is having a birthday party. His mother is baking cupcakes Carter is having a birthday party. His mother is baking cupcakes. He notices that the cupcake pan is divided into smaller parts. How many small sections are within the cupcake pan? a. 10 c. 15 b. 12 d. 16
67Leah likes to practice math at home Leah likes to practice math at home. She has a chalkboard so she can draw different shapes. Today she drew a rectangle and split it into 5 rows and 2 columns. How many small squares did Leah make? a. 8 b. 14 c. 10 d. 6
68Easton is helping his dad make a checker board Easton is helping his dad make a checker board. Eaton paints the black squares in the rectangle and his dad paints the red squares. How many small squares make up the checker board? a. 18 b. 26 c. 30 d. 36
69Naomi and her mom want to make a blanket to give to her baby brother Naomi and her mom want to make a blanket to give to her baby brother. Naomi decides on this pattern. How many small airplanes are within the rectangle of her pattern? a. 4 b. 12 c. 16 d. 20
70Melanie arranges 8 ice cream cones into a rectangular array as shown below. Which equation represents her arrangement? a b = 8 c. 8 – 4 = 4 d = 4
71Ronan is baking brownies with his friend. They partition the pan intoequal shares or sections like thepicture.What do we call these equal parts?halves b. thirdsc. fourths d. whole
72Willow loves working with the geoboards Willow loves working with the geoboards. She uses rubber bands to make different shapes. She even uses rubber bands to partition the geoboard into equal sections. How did she partition her geoboard? a. halves b. thirds c. fourths d. fifths
73Micah likes to eat a sandwich for snack after school every day.He cuts his sandwich into equalpieces as pictured.How can he describe how he cut his whole sandwich?one half b. two halvesc. three thirds d. four fourths
74Lillian made a pie with her mother. She cut the pie into equal pieces as pictured.How can the whole pie be described?one half c. two halvesfour fourths d. three thirds
75Zoe likes to pretend she is a teacher Zoe likes to pretend she is a teacher. She has a whiteboard so she can draw different shapes. Today she drew a rectangle and split it into 3 rows and 6 columns. How many small squares did Zoe make? a. 18 b. 16 c. 14 d. 12
76Zander is baking a round cake to take to school for the bake sale.He partitions the cake into equalshares or sections like the picture.What do we call these equal parts?whole b. halvesc. thirds d. fourths
77Hunter uses partitioned baby plates when he serves dinner to his little brother.What do we call the waythis plate is partitioned?one whole b. one halfc. halves d. thirds
78Evan is having a birthday party. His mom is serving pizza Evan is having a birthday party. His mom is serving pizza. He notices that the pizza is divided into smaller parts. How many small sections are within the round pizza? a. 4 c. 6 b. 8 d. 10
79Ian has been assigned an art project Ian has been assigned an art project. He must create a work of art using only shapes with 5 sides and 5 angles. What is the name of the shape he will be using? a. pentagon b. rhombus c. trapezoid d. triangleCanyou drawhis shapehere?
80Dylan designed a sign for his lemonade stand. The shape of the sign has6 sides and 6 angles. What shape is his sign?rectangle b. pentagonc. hexagon d. trapezoid
81Eva is helping the teacher clean up after math centers. She puts all of the squares, rectangles, and trapezoidsinto one of the math tubs.What is Eva sorting by?size of the faces c. color of the edgesnumber of sides, vertices and angles d. number of sharp corners
82Parker draws a rectangle on grid paper Parker draws a rectangle on grid paper. He needs to count the number of small squares within the rectangle. How many small squares are found in the shaded rectangle? a. 20 b. 34 c. 40 d. 42
83Bennett wants to build a boat out of Legos Bennett wants to build a boat out of Legos. As he builds the boat he notices many different shapes in his design. He grabs the last Lego piece of the boat and begins to attach it. What is the name of this shape? a. triangle b. trapezoid c. hexagon d. rectangle
84Iris buys a box of candy to give to her Mom. The top of the box has 5 sides, 5 vertices, and 5 angles. Which box contains the candy?c.b d.
85Tanaya is cleaning up the math manipulatives after centers Tanaya is cleaning up the math manipulatives after centers. She threw some wrong shapes into the quadrilateral tub. Circle the shapes she should remove? Why? _______________________
86Sienna is sorting shapes during math centers Sienna is sorting shapes during math centers. She pulls out all of the yellow shapes to create a bee hive. What shape is she using? a. pentagon b. octagon c. hexagon d. rhombus
87Elias and his brother make a cake for Father’s Day. They decide to cut the cake into four equal pieces.What is the name of the equal shares or equal parts?fourthshalvesthirdsfifths
88Ryder designs a sign for his clubhouse Ryder designs a sign for his clubhouse. He wants the sign to have 4 sides, 4 angles, and 4 vertices, but he wants the sign to look like someone sat on it. Which shape should he use? Can you draw his shape? a. trapezoid b. rhombus c. square d. rectangle
89Sienna draws a rectangle on grid paper. She needs to count the number of small squares outside of her rectangle.How many of the small squares are NOT shaded?425052100
90Martin is making soup for dinner with toasted cheese sandwiches Martin is making soup for dinner with toasted cheese sandwiches. He cuts the sandwiches into equal shares or equal parts. How can the whole sandwich be described? a. one half b. one third c. two halves d. four fourths
91Katrina always has a snack after dance practice. Today she decided to have a banana and a glass of milk. She slices thebanana into equal shares or equal pieces as shown.How can the whole banana be described?one halftwo halvestwo thirdsthree thirds
92Isaiah loves making shapes on the geoboards. Today he decides to partition the geoboard with rubber bands and makes thegeoboard pattern shown.How did he partition his geoboard?wholehalvesthirdsfourths
93Autumn wants to make a big game board to play hop scotch on the playground. She creates the board and divides it into5 rows and 3 columns.How many small squares make up her board?8101215
94Which equation describes this rectangular array. a Which equation describes this rectangular array? a = 16 b = 16 c. 16 d
95Which cake is partitioned into equal fourths? b.c d.