# Please bring a laptop or tablet next week! Upcoming Assignment Measurement Investigations Patterns & Algebraic Thinking Investigations Break A Few

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1 Please bring a laptop or tablet next week! Upcoming Assignment Measurement Investigations Patterns & Algebraic Thinking Investigations Break A Few More Investigations Literature Circles

2 Final Lesson Plan This should include all supplementary materials (worksheets, assessment tasks, rubrics, etc.). Information regarding class size, time frame, etc. should be filled in. Please keep the formatting consistent. (i.e., Don t have random gray text. Keep fonts & sizes consistent.) Include one or two Standards for Mathematical Practice. Include assessment criteria.

3 Problem-Solving Strategies (p. 46) Look for a pattern. Construct a table. Make an organized list. Act it out. Draw a picture. Use objects. Guess and check. Work backward. Write an equation. Solve a simpler (or similar) problem. Make a model.

4 Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

5 Fixed Perimeter (source) Fixed Area

6 Investigation: Perimeter & Area

7 Fixed Area Working in groups of 2 or 3: Cut a square that measures 8 by 8 from the index card. Each person should cut two squares. Each group should keep one square as is and graph its perimeter. Take one square at a time, cut, reshape, and tape it back together. For each square (original and reshaped), trace the perimeter of your shape on the graph.

8 Using Geoboards to Inves1gate Area Re-create one of these shapes on your Geoboard and find the area of the shape

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10 Pattern Investigations

11 Stages in Learning about Patterns, Functions, and Algebraic Thinking 1. Introducing Patterns 2. Describing Patterns Verbally 3. Introducing Functions 4. Representing Patterns Numerically, Algebraically, and Geometrically 5. Learning the Uses of Variables

12 Pattern Investigation 1. Construct a table and continue the table until you have the number 10 in the column. 2. Describe the pattern. 3. Make a graph and describe the pattern made by the points. 4. If you can, represent the pattern with an equation.

13 Paper Folding For this investigation you will need a piece of paper. Make a table with a column for Folds and a column for Sections. Fold the paper in half once, reopen it, and record the number of sections. Then fold it back in half, and then in half again. Reopen and record the number of sections. Repeat until you ve folded 6 times.

14 Pattern Investigation 1. Continue the table started until you have the number 10 in the column. 2. Describe the pattern. 3. Make a graph and describe the pattern made by the points. 4. If you can, represent the pattern with an equation.

15 Painting Towers Consider a tower that is built in the shape of a cube. If the cube is one unit tall, how many squares do you have to paint (if you paint the top and the sides, but do not paint the bottom)? If the cube is two units tall, how many squares would you have to paint? Record your results in a table with the column headings Height and Squares. If you had a tower that was 99 units high, how many squares would you have to paint?

16 Pattern Investigation 1. Continue the table started until you have the number 10 in the column. 2. Describe the pattern. 3. Make a graph and describe the pattern made by the points. 4. If you can, represent the pattern with an equation.

17 Diagonals Diagonals are line segments that connect non-consecutive vertices of a polygon. Draw a triangle. How many diagonals can you draw? Draw a quadrilateral. How many diagonals can you draw? Record your results in a table with the headings Sides and Diagonals. How many diagonals would a dodecagon have?

18 Pattern Investigation 1. Continue the table started until you have the number 10 in the column. 2. Describe the pattern. 3. Make a graph and describe the pattern made by the points. 4. If you can, represent the pattern with an equation.

19 Handshake Problem Suppose every person in this room shakes hands with every other person in the room. How many handshakes will that be? Create a table with the headings People and Handshakes.

20 Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

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22 A Row of Triangles If you line up one hundred equilateral triangles, what will the perimeter measure?

23 A Row of Squares If you line up one hundred squares, what will the perimeter measure?

24 A Row of Hexagons If you line up one hundred regular hexagons, what will the perimeter measure? Challenge: There s a way to figure out the pattern for a row of any regular polygon. Try it if you re interested!

25 Angles with Pattern Blocks and Hinged Mirrors In groups of four - work on chart paper The size of an angle is a measure of rotation, and degrees are used to measure angles. Part 1: Figure out how many degrees there are in the angles formed by the vertices of each pattern block. Use the following procedure: 1. Place a vertex of a block in the hinged mirror. 2. Close the mirrors so the vertex nestles snugly. 3. Use pattern blocks to build the design. 4. Sketch or trace it. 5. Figure out the degrees in the nestled corner by dividing 360 degrees by the number of blocks, in the design. Label your drawing to show the number of degrees in each angle.

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