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Grade 4 – Unit 8 Lesson Focus Anytime Problems Lesson 1 Draw and describe points, rays, angles, and other geometric figures. Hannah has been asked to baby-sit her sisters from 9:30 in the morning until 2:15 in the afternoon. How many hours is that? Lesson 2 Draw and measure angles. The perimeter of a rectangle is 15 inches. Two of the sides are each 2 ½ inches long. What is the length of each of the other two sides. Lesson 3 Identify, measure, and draw angles in a circle. Lesson 4 Draw and classify triangles by their angles and sides. Marita wrote a 3-digit number. The digit in the tenths place is 5 less than the digit in the ones place. The digit in the hundredths place is the sum of the digits in the tenths and the ones places. What are the possible numbers? Mitch has saved $13.00 so that he can buy a T-shirt. When he goes to the store, he finds a second T-shirt that he wants to get for his brother’s birthday. If each T-shirt costs $8.50, how much more money does Mitch need to buy both T-shirts? Lesson 5 Find unknown angle measures. Karen and her sister Jean are packing for a trip. They can each bring only one suitcase that weighs no more than 40 pounds. Jean finds that her suitcase weighs 52 pounds, but Karen still has room in her suitcase and it only weighs 25 pounds. What can they do? Explain how they might work together to solve this problem. Writing PromptIntervention Explain all the ways you can tell the difference between a right angle, an acute angle, and on obtuse angle. Writing Prompt-On level Writing Prompt-Challenge Explain how you remember what the terms right angle, acute angle, and obtuse angle mean. Draw examples of each kind of angle. Explain how to use a protractor to draw an angle with a measure of 87⁰. Chin said that on his walk he followed a path that made two acute angles, an obtuse angle, and he ended where he started. Can he be correct? Explain. How is measuring an obtuse angle different from measuring an acute angle? Explain how to find an 3 angle that traces a 4 turn in a circle. Why does a 90⁰ turn counterclockwise have the same effect as a 270⁰ turn clockwise? Name another pair of turns that have the same effect. Draw and label a scalene triangle, and isosceles triangle, and an equilateral triangle. Explain why the triangles are scalene, isosceles, or equilateral. Use letters, angles, and sides to describe all the ways to name a triangle. With words and pictures, explain why it is impossible to have a right triangle with an obtuse angle. Explain what operation you would use to solve the equation x + 50⁰ = 125⁰. When an obtuse angle is separated into two smaller angles, what kinds of angles might be formed? Describe the steps in an angle measure problem as if you were telling a friend how to draw the diagram and how to write and solve an equation to find an unknown angle measure. Describe how you measure an angle. Do you turn the angle to be horizontal, or do you turn the protractor to fit the angle? If one angle drawn from the center of a circle measures 130⁰, what is the measure of the other angle that is formed? Explain. Lesson 6 Add and subtract angle measures. Teams in a hockey league receive two points for a win, no points for a loss during the regular game time, and one point if they lose in overtime. If a team has played 6 games this season and has 10 points, how many games have they won? What are the two types of angles that are easiest to use as “whole angles” when writing an equation about angle measures? Explain why. Explain why angles in real world situations are sometimes difficult to measure directly. How does it help to use an equation to find the measure? Write a real world problem about angle measures. Include a diagram, with angle measures noted. You might use the Internet to find angles or do your own measuring in your classroom or at home. Lesson 7 Demonstrate understanding of parallel and perpendicular figures. Use triangles, squares, and circles to make a pattern that matches the pattern A, A, B, B, C, C, A, A, B, B, C, C. If the pattern continues, what shape will the fifteenth figure be? Explain how you can use lined paper or grid paper to check whether two lines are parallel or perpendicular. How many different lines can you draw through one point? How many different lines can you draw through two points? Explain your thinking. The lines drawn on your MathBoard all lie on the same surface. Look around your home or classroom. Do you see any pairs of lines that are not parallel but are not intersecting either? Describe how you could model a pair of these lines using your arms. Lesson 8 Name and classify quadrilaterals based on sides and angles. Decompose quadrilaterals and triangles into other figures. One triangle has 3 angles, each with measure 60⁰. What is the sum of those angle measures? What other kind of figure has that result as its angle measure? Sixteen dogs are at the dog park today. Six of them have blue leashes. Twelve of the dogs have brown collars. Four of the dogs have a blue leash but don’t have a brown collar? Explain why every square is a rhombus, but not every rhombus is a square. Explain why a trapezoid can If a trapezoid has three equal never be a rectangle, a sides, explain why it must be rhombus, a square, or a an isosceles trapezoid. parallelogram. What is the diagonal of a quadrilateral? Use pictures and words to explain. How many diagonals can you draw in a quadrilateral? Sort triangles and quadrilaterals by a number of different rules. Suppose that you cut a string in half. Then cut each half in half. Then you cut each new half in half again. If you cut all the pieces in half two more times, how many pieces of string will you have? What is the pattern? Give an example of a sorting that would have no figures in it. In your own words, explain how a perpendicular drawn in a triangle makes right triangles and explain when those triangles are the same size and shape. Explain why a sorting of figures by right angles is the same as a sorting of the figures by perpendicular sides. Lesson 9 Lesson 10 Suppose you want to make a rhombus from two triangles that are the same size and shape. Thinking of sides and angles, list all the triangles you can use. Draw a picture to help you explain why a sorting of figures by parallel sides never has a triangle figure in it. Lesson 11 Recognize and draw lines of symmetry and determine when figures have line symmetry. Lesson 12 Use the CCSS and Practices in a variety of real world problem solving situations. Chen, Wendy, Lourdes, and Rick have bikes. Each bike is a different color: red, green, black, or white. Wendy’s bike is white. Chen’s bike is not red. Rick’s bike is not green. Lourdes’s bike is not black or red. What color is each person’s bike? Barney made $785 last week at his job. He spent $135 at the grocery store and wants the rest of the money to last for 2 weeks. How much can Barney spend each of the 2 weeks if he spends the same amount each week? What is special about the polygons on the Activity Card? Draw a 5-sided polygon that is special in the same way. How many lines of symmetry does it have? Explain how you determine if a figure has a line of symmetry. Draw half of a figure. Explain how to draw the other half so that the whole figure has line symmetry. Which of the capital letters do not have line symmetry, but can be cut into two matching halves? Explain your thinking. Explain the relationship between a quadrilateral and a polygon. Explain how finding a line of symmetry in a rectangle is different than finding a line of symmetry in a triangle. How is it the same?