Unit 6: Geometry March 10 - 14, 2014 Mrs. Gray

Monday -Content Standard MCC4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles Tier 2 words Tier 3 Words

Essential Question and I can Statements EQ: How are different ideas about geometry connected? I can identify and classify angles and identify them in two-dimensional figures. I can identify differences and similarities among two dimensional figures based on the absence or presence of characteristics such as parallel or perpendicular lines and angles of a specified size.

Students will classify attributes of triangles given by the teacher. Assessment Students will classify attributes of triangles given by the teacher.

Monday – I Do There are many different kinds of triangles. You can classify triangles by the measure of their angles.

Vocabulary Right triangle A right triangle has one right angle. The two sides that form the right angle are perpendicular. Acute triangle An acute triangle has three acute angles. Obtuse triangle An obtuse triangle has one obtuse angle. Vertices and Line Segments A triangle has three vertices and three line segments. Each point is formed by the intersection of two line segments.

Monday – I Do Ex. 1: This sandwich is cut in half. Classify the triangle represented by the half sandwich as right acute or obtuse. Determine if any of the sides are perpendicular. Half of the sandwich had one right angle. The two sides that form the right angle are perpendicular. So, this half of the sandwich is a right triangle.

Monday – I Do Ex. 2: Classify the triangle as right, acute or obtuse. Identify the vertices and line segments of the triangles. The triangle is an obtuse triangle because it has an obtuse angle. There are 3 vertices: Vertices L, M, P. There are 3 line segments:

Monday- We Do Classify the triangles as acute, right or obtuse. Determine how many sides are perpendicular. 1. 2. 3.

Monday – You Do Classify the triangles as acute, right or obtuse. Determine how many sides are perpendicular. 1. 2. 3.

Monday – You Do Chapter 14, Lesson 4 McGraw-Hill Volume 2. pgs. 921-922 Group1 (with teacher) Materials: craft sticks and clay, or pretzel sticks and marshmallows Have groups of students construct examples of each of the following triangles: acute, obtuse, and right. (Craft sticks and pretzels can be broken to make different lengths.) Have students label each type of triangle. McGraw-Hill: 2, 5, 7, 8, 10, 12, 13, 16.

Monday – You Do Chapter 14, Lesson 4 McGraw-Hill Volume 2. pgs. 921-922 Groups 2 and 3 Materials: geoboards, rubber bands, Isometric Dot paper found online in Program Resources Students use rubber bands to create a triangle on their geoboard, and then switch the geoboard with a partner. Students then classify the triangle, draw it on the dot paper, and label its vertices. McGraw-Hill: 3-11 (odd), 12, 13, 15, 16.

Monday – You Do Chapter 14, Lesson 4 McGraw-Hill Volume 2. pgs. 921-922 Group 4 Materials: plain paper, scissors, rulers, pencils, protractor Explore the following using the given materials: Can you draw a triangle that has one 90° angle, one 45° angle, and with the length of the side between those two angles as 5 cm? Yes Classify this triangle. right triangle Can you draw a triangle in which the length of two sides are 4 cm and 7 cm, and has one 30° angle? No Explain. Have students continue to work with angles and sides until they realize that they need to know two angles and one side length to draw a triangle. McGraw- Hill: 3-11 (odd), 12-16

Students will classify attributes of triangles given by the teacher. Assessment Students will classify attributes of triangles given by the teacher.

Tuesday – Content Standard MCC4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles Tier 2 words Tier 3 Words

Essential Question and I can Statements EQ: How are different ideas about geometry connected? I can identify and classify angles and identify them in two-dimensional figures. I can identify differences and similarities among two dimensional figures based on the absence or presence of characteristics such as parallel or perpendicular lines and angles of a specified size.

Assessment Students will answer the following questions: Is a square a rhombus? Is a square a rectangle?

Tuesday – I do All quadrilaterals have 4 sides and 4 angles. There are so many different kinds of quadrilaterals.

Vocabulary Parallelogram A parallelogram has opposite sides equal in length and parallel. In addition, opposite angles have the same size. Rectangle A rectangle has opposite sides equal in length and parallel. It has 4 right angles. Rhombus A rhombus has opposite sides equal in length and parallel. It has 4 equal sides. Square A square has opposite sides equal in length and parallel. It has 4 right angles and 4 equal sides. Trapezoid A trapezoid has exactly on pair of parallel sides.

Tuesday – I Do Ex. 1:The speed limit sign represents a quadrilateral. Classify the angles formed by the quadrilateral. Determine if any of the sides are parallel or perpendicular. There are 4 right angles, 0 acute angles and 0 obtuse angles. The top and bottom sides are parallel. The left and right sides are parallel. Since there are 4 right angles, the sides that form each right angle are perpendicular. So, there are 4 pairs of perpendicular sides.

Tuesday – I Do Ex. 2: Classify the quadrilateral in as many ways as possible. The quadrilateral has opposite sides equal in length and opposite sides parallel. It also has 4 equal sides. So , it is a parallelogram and a rhombus.

Tuesday – We Do Classify the quadrilaterals in as many ways as possible. 1. 2.

Tuesday – You Do Classify the quadrilaterals in as many ways as possible. 1. 2.

Tuesday – You Do Chapter 14, Lesson 5 McGraw-Hill Volume 2. pgs. 927-928 Group 1 (with teacher) Have students walk around the classroom looking for quadrilaterals. Remind them that quadrilaterals are two-dimensional, flat figures. Have students write what they find on paper. Ask them to make a quick sketch, identify the object (such as a window), and write the type of quadrilateral that best describes the shape. Have students return to the group and discuss their findings. McGraw-Hill: 2-10 (even), 14.

Tuesday – You Do Chapter 14, Lesson 5 McGraw-Hill Volume 2. pgs. 927 – 928 Groups 2 and 3 Materials: index cards Have students draw two different examples of each quadrilateral mentioned in the lesson on separate index cards. With a partner, shuffle the cards together. Then have students spread out the index cards facedown. Student 1 chooses a card and classifies the quadrilateral in as many ways as possible. One point is given for every correct classification. If Student 1 forgets any classifications, Student 2 can earn points by naming them. Then switch roles. McGraw- Hill: 2-10 (even), 12-14

Tuesday – You Do Chapter 14, Lesson 5 McGraw-Hill Volume 2. pgs. 927- 928 Group 4 Materials: index cards Ask students to write a logical statement about one or more quadrilaterals on each card. Statements may look like this: I always have four right angles; I am a quadrilateral but not a parallelogram. Then students will identify and draw as many quadrilaterals on the card that fit in each category. When completed, students will regroup and discuss their answers. McGraw- Hill: 4, 6, 8-14

Assessment Students will answer the following questions: Is a square a rhombus? Is a square a rectangle?

Wednesday – Content Standard MCC4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles Tier 2 words Tier 3 Words

Essential Question and I can Statements EQ: How are different ideas about geometry connected? I can identify and classify angles and identify them in two-dimensional figures. I can identify differences and similarities among two dimensional figures based on the absence or presence of characteristics such as parallel or perpendicular lines and angles of a specified size.

Assessment Students will make a model based on the following problem: Julio went on a hike with her family. They started their hike at 2,000 feet above sea level and climbed 4,000. They then descended to 3,000 feet and climbed back up 6,500. How many feet did they hike uphill?

Wednesday – I Do Steps to problem solving: Understand: Review what you know and what you need to know. Plan: Discuss a strategy to solve the problem. With these problems, we will make a model. Solve: Make a model to find the answer. Check your answers to see if they make sense.

Wednesday – I Do Ex. 1: Maya has a square piece of paper. She folds it in half so there are two triangle-shaped parts. She folds it in half again so there are four triangle-shaped pieces. When she unfolds the paper, how many right angles are shown? Step 1: Understand. What do we know? Maya folds her paper 2 times diagonally. Step 2: Plan. I will make a model to find the answer.

Wednesday – I Do When we count, we see that there are 8 right angles. Step 3: Solve. Use a square piece of paper. Follow the same steps that Maya followed. When we count, we see that there are 8 right angles. Step 4: Check. Does our answer make sense? Yes. We folded the paper and found 8 square corners, or right angles.

Wednesday – I Do Ex. 2: Tyrone drew a figure with four sides. One side measures 5 centimeters and another side measures 9 centimeters long. The figure has four right angles. What is the figure. Step 1: Understand. We know that Tyrone drew figure that measured 5 cm on one side and 9 cm on the other. We want to determine the figure. Step 2: Plan. I will design a model to help determine the figure.

Wednesday – I Do Step 3: I measured and drew a figure that had one side 5cm long and the other 9 cm long. The figure is a rectangle. Step 4: Check. Yes, my answer makes sense because I drew the model and determined it creates a rectangle.

Wednesday- We Do Solve the following word problem.

Wednesday – You Do Solve the following word problem.

Wednesday – You Do Chapter 14, Lesson 6 McGraw-Hill Volume 2. pgs. 939-940 Group 1 (with teacher) Materials: Four-Step Problem-Solving Plan graphic organizer Choose one of the exercises from today’s lesson that the students found difficult. Help students break down the problem by walking them through the four-step plan. As they identify what is known and what is needed, help them begin to develop a plan. Work through the problem talking aloud so students understand what they should be thinking. McGraw-Hill: 1, 2, 4, 5

Wednesday – You Do Chapter 14, Lesson 6 McGraw-Hill Volume 2. pgs. 939 – 940 Groups 2 and 3 Have students work in pairs to write a multi-step real-world word problem that will require someone to make a model in order to solve. Use the concept of classifying triangles and quadrilaterals by their attributes, and line symmetry in the content. Trade with another pair of students and solve each other’s problem. McGraw-Hill: 2-6

Wednesday – You Do Chapter 14, Lesson 6 McGraw-Hill Volume 2. pgs. 939-940 Group 4 Have students write a multi-step real-world word problem that will require someone to make a model in order to solve. Use the concept of classifying triangles and quadrilaterals by their attributes, and line symmetry in the content. Trade with another student and solve each other’s problem.   McGraw- Hill: 1-3, 6,7

Assessment Students will make a model based on the following problem: Julio went on a hike with her family. They started their hike at 2,000 feet above sea level and climbed 4,000. They then descended to 3,000 feet and climbed back up 6,500. How many feet did they hike uphill?

Thursday – Content Standard MCC4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Tier 2 words Tier 3 Words

Essential Question and I can Statements EQ: How are different ideas about geometry connected? I can draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. I can identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines in two-dimensional figures.

Assessment Students will sketch a diagram based on the following description: Should be a combined angle composed of two individual angles. One of the individual angles should have a measure of 60 degrees. The combined angle should have a measure of 100 degrees. Students should label each angle with their measures. They should label the unknown angle measure with a variable, and write an equation than can be used to find the measure of the unknown angle. Then they should find the measure of the unknown angle.

Thursday – I Do An angle can be decomposed, or broken, into non-overlapping parts. The angle measure of the whole is the sum of the angle measures of the part.

Thursday – I Do Ex. 1: Rachel and Dean made a sign out of fabric, like the one being shown, to hang in the school gym. The blue piece has a 35 degree angle. The red piece is attached to the longest side of the side of the blue piece. Together, the pieces form a right angle. What is the angle shown on the res piece? One way: Make a model. Draw a 90◦ angle. Mark off a 35◦ angle. Measure the other angle. The other angle has an angle of 55◦

Thursday – I Do Another Way: Use an equation. The 90◦ angle measure is the sum of two parts. One angle is 35◦. Find the unknown angle measure. Let r represent the unknown angle measure. 35 + r = 90. We know that we need to get the variable alone. Using what we know about fact families, I can re-write the equation as: 90 – 35 = r. 55 = r So, the angle shown on the red piece measures 55◦.

Thursday – I Do Ex. 2: Find the combined measure of the angle shown. One of the angles is 20◦. The symbol on the other angle shows that it is a right angle. Therefore, it is 90◦. Let a represent the unknown angle measure. a = 20◦ + 90◦ a = 110◦ So, the combined measure of the angle is 110◦.

Thursday – We Do Find each unknown. 1. 2.

Thursday – You Do Find each unknown. 1. 2.

Thursday – You Do Chapter 14, Lesson 7 McGraw-Hill Volume 2. pgs. 913-914 , 4, 7, 8, 11, 13 Group 1 (with teacher) Materials: protractors, index cards Each student will draw one angle on an index card and write its measure. Shuffle all the cards together and pass out one card to each student. Have two students come together and find the total angle measure of their two cards. Repeat the exercise.

Thursday – You Do Chapter 14, Lesson 7 McGraw-Hill Volume 2. pgs. 913-914 , 4-12 (even), 13 Groups 2 and 3 Materials: protractors, index cards Have students draw two different angles on separate cards. Do not label. Cards are shuffled together. Two cards are given to each student who measures each angle and records it on the card. On a third card the combined angle measure is written. Then the cards of the combined angle measures are shuffled separately from the angle cards. Students will take one card from each pile. They are to determine the unknown angle measure using the information given on the two cards

Thursday – You Do Chapter 14, Lesson 7 McGraw-Hill Volume 2. pgs. 913-914 , 4-8 (even), 10-13 Group 4 Materials: protractors, index cards Have students write riddles with the following two sentence stems. 1. My combined angle measure is _____. One angle measures _____. What is my other angle’s measure? 2. One angle measures _____. The other angle measures _____. What is my combined angle measure? Cards are shuffled together. One card is given to each student. On the back of the card the riddle is solved by drawing and labeling the given angles.

Assessment Students will sketch a diagram based on the following description: Should be a combined angle composed of two individual angles. 2 One of the individual angles should have a measure of 60 degrees. The combined angle should have a measure of 100 degrees. Students should label each angle with their measures. They should label the unknown angle measure with a variable, and write an equation than can be used to find the measure of the unknown angle. Then they should find the measure of the unknown angle.