Middle School Alternate Assessment Math Spring 2012

Sixth Grade KAAP (M-6.4) Identify when two expressions are equivalent. 1.Identify was equivalent means. 2.Many of the misconceptions when dealing with expressions stem from the misunderstanding/reading of the expression. For example, knowing the operations that are being referenced with notation like, x3, 4x, 3(x + 2y) is critical. 4x means 4 times x or x+x+x+x, not forty- something. 3.When evaluating 4x when x = 7, substitution does not result in the expression meaning 47.

Expression Match

6 th Grade KAAP (M-6.5) Find the area of polygons by composing into rectangles or decomposing into other shapes in the context of solving real-world problems It is very important for students to continue to physically manipulate materials and make connections to the symbolic and more abstract aspects of geometry. KAAP (M-6.6) Display numerical data in plots on a number line and histograms. Now students learn to organize data in appropriate representations.

6 th Grade Geometry

1.Use a Geoboard and start with a square that is one unit on each side. 2.Have students use rubber bands to create squares that are 2, 3, 4, and even 5 units on each side. 3.Then, find the area of each square. 4.Do the same with triangles and other quadrilaterals.

Example—6 th Grade Dot Plot X X X X X X X X X X Ages of the students in our class

Example—6 th Grade Ages of the students in our class How old are most students in your class? How do you know?

7 th Grade KAAP (M-7.4) Solve real-world and mathematical problems involving the four operations with rational numbers. 1. Students need to be able to determine which operation to use. 2. A rational number is any number that can be written as a fraction, including integers and whole numbers.

7 th Grade KAAP (M-7.5) Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas, (triangles and quadrilaterals) from a scale drawing. 1. Use various models to demonstrate scale. Matchbox cars are excellent examples.

1.Use the inchworms manipulative. They come in 1 inch, 2 inch, 3 inch, and 4 inch lengths. 2.Have a picture of anything. (You can place it on 1 inch grid paper if needed.) Use the inchworms to measure in inches. 3.Use a scale of 1 inch = 2 feet (or other appropriate scale). 4.Find the actual lengths of the object in the picture.

1 cm = 2 feet

Divide into rectangles to determine area. A= 21 cm 2 B= 5cm 2 C= 18cm 2 Total Area= 45 cm 2

7 th Grade KAAP (M-7.6) Solve real-world or mathematical problems involving volume and surface area of three dimensional objects composed of cubes and right prisms. 1.Define volume and surface area. 2.Use multiple representations of cubes and right prisms.

Activities

7 th Grade Define volume. “Volume measures space. It is the amount of cubic units that takes up a space.” Demonstrate by pouring water into a container. Point out household items that are measured in volume (milk carton, bottle of cola, box of sugar cubes, sandbox, etc.) Have students look through magazines and cut out pictures of items and discuss how to talk about each item’s volume. Stress “cubed”. Note: Volume is NOT weight.

Volume 5cm 3

Activities Fill a box with cubes (wooden, plastic, or sugar cubes). Count the number of cubes it takes to fill up this rectangular prism with cubes. Discuss the volume as “cubed”. Students fill up different boxes with cubes and compare the volumes. APPS: --Geometry: Volume of Solids

Activities Relate to Base 10 Set. Show a 1000s cube. Have students stack hundreds squares on top of each other to make the cube. How many does it take? How many unit cubes does it take to fill up the larger cube? APPS: --Base Ten Number Blocks ($0.99)

Activities Use rectangular baking pans and wet or dry ingredients. Determine how many cups (of water, sugar, flour, etc.) it takes to fill up that pan. A cup is another unit of volume.

Face Part of a shape that is flat.(Or curved) For example, A cube has 6 of these.

Surface Area: the measure of all the sides 1.How many pairs of identical faces does cube have? 2.Calculate the area of each face. 3.Add up the areas to determine total surface area. 1.A cube has 6 identical faces. Each face is a square. 2.Each face of the cube has sides which are 9 inches long. 3.The area of one face is 9 in x 9in = 81 square inches 4.There are 6 faces: 81 x 6 = 486 square inches.

IXL Surface Area, IXL.com

Activities Surface area is the area of all of the sides added together. Take a box and break it apart to show all 6 sides. (This is called a “net”.) Measure or label the length of each side. Find the area of each individual rectangle then add them up to find total surface area. Stress “Covers” and “Square units”. How much do we need to cover the whole box? You could have students wrap a box to find out how much wrapping paper covers the box.

Activities

Draw the net of a cube on grid paper. Students count the blocks to find the area of each part. Add up all the parts to get the total surface area. Do this on cardstock and cut out then fold and tape to make the cube.

Activities Activity 7

Using the Accucut

KAAP (M-8.4) Demonstrate understanding of similarity between two-dimensional figures. KAAP (M-8.5) Demonstrate an understanding that a function is a rule that assigns to each input exactly one output. KAAP (M-8.6) Given a volume formula, solve real- world problems involving cones, cylinders and spheres.

8 th Grade KAAP (M-8.4) Demonstrate understanding of similarity between two-dimensional figures. 1. Define similarity. (shapes that have equal corresponding angles and whose corresponding sides are in proportion to one another.

These triangles are similar.

These ovals are similar.

Real-life Similar Shapes Sunshine Skyway Bridge Tampa, Florida

Real-life Similar Shapes

Which shape does not belong? Cross out the shape that isn’t similar.

8 th Grade KAAP (M-8.5) Demonstrate an understanding that a function is a rule that assigns to each input exactly one output. 1.Make a function machine. 2.Use manipulatives to show input/output.

spider spiders Complete the Function Table.

dog Complete the Function Table.

Answer dog 2 4 6

Rule: ___________ Teacher provides input values and a rule, while student determines output values.

Rule: ____________

Spin a Rule

Complete the Function Table. Can you determine the rule? ______________ At Larry’s Lemonade Stand, 1 cup of lemonade costs $ Complete the function table to show the cost of lemonade. Number of CupsCost 1$ 2$ 3$ 4$

8 th grade KAAP (M-8.6) Given a volume formula, solve real- world problems involving cones, cylinders and spheres.

Troy was getting ready to eat a push-up pop ice cream. The ice cream is 13 centimeters tall and has a radius of 6 centimeters. How many cubic centimeters of ice cream will Troy get to eat?

William bought a can of Pringles that was 12 centimeters tall and had a radius of 4 centimeters. How many cubic centimeters of Pringles are inside the can?

Volume Formula for a Sphere

Emily owns a world globe with a radius of 5 inches. If the globe is hollow, how many cubic inches of air are inside the globe?

Lauren received a rubber ball for her birthday. If the ball had a radius of 10 centimeters, how many cubic centimeters were in the ball?

Volume Formula for a Cone

Find the volume, in square centimeters, of the ice cream cone if the cone is 40 cm tall and has a radius of 4 cm.

Shea wants to fill the hat she wore for her birthday party with candy. If the hat is 9 inches tall and has a radius of 3 inches, calculate the volume in square inches.

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