Lesson 11 Skills Maintenance. Activity 1. Model. The addition problem is = 4. The subtraction problem is 5 9 = 4.

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1 Lesson Skills Maintenance Lesson Planner Vocabular Development -coordinate -coordinate point of origin Skills Maintenance ddition and Subtraction of Positive and Negative Integers Problem Solving: We look more in-depth at coordinate graphs and introduce quadrants. There is formal language used to describe the features of a coordinate graph. s students move into higher levels of math (e.g., algebra), it is critical the learn and use this language correctl. The points on a coordinate graph are identified b their - and -coordinates, or an ordered pair. The origin of the coordinate graph is the center point (0, 0). The - and - aes create four sections called quadrants. Each quadrant contains a series of points with unique characteristics. Quadrants are numbered with Roman numerals. Objective Students will find coordinates in the four quadrants of a graph. Homework Students compare two integers and tell which is bigger b writing a < or > sign, solve a mi of integer addition and subtraction problems, and tell which quadrant each point is in. In Distributed Practice, students practice rational number conversions, as well as decimal number and fraction computations. Name 0 Unit Lesson Date Skills Maintenance ddition and Subtraction of Positive and Negative Integers ctivit The arrow and number line represent both an addition problem and a subtraction problem. Write both.... Model The addition problem is + =. The subtraction problem is = The addition problem is + 9 =. The subtraction problem is 9 = The addition problem is + = 9. The subtraction problem is = The addition problem is + = 9. The subtraction problem is = 9. Skills Maintenance ddition and Subtraction of Positive and Negative Integers (Interactive Tet, page 0) ctivit Students use a number line to write addition and subtraction problems. 9 Unit Lesson

2 Problem Solving: Problem Solving: How do we find coordinates on the graph? (Student Tet, pages 9 9) Connect to Prior Knowledge Begin b reminding students about the basic structure of the coordinate graph. Draw the -ais and -ais on the board or overhead, leaving them unlabeled. sk students to describe the various features of the coordinate graph the learned so far. Listen for: The vertical line (line going up and down) is the -ais. The horizontal line (line going across the page) is the -ais. There is a 0 in the middle. You can put points on the graph. If ou had a grid it would make that easier. Link to Toda s Concept Tell students that we look at some more features of coordinate graphs in toda s lesson. Engagement Strateg: Teacher Modeling how to locate a point on a coordinate graph in one of the following was: : Use the mbook Teacher Edition for Student Tet, page 9. Overhead Projector: Displa Transparenc, and modif as discussed. Board: Draw the coordinate graph from Eample on the board, and modif as discussed. Problem Solving: How do we find coordinates on the graph? We use coordinates to find where the dot goes on the coordinate graph. From now on we will refer to the dots on a graph as points. The point on the graph is described this wa: point = (, ) The coordinates for a point (, ) are made up of two parts. The first part is the -coordinate, and the second part is the -coordinate. In the graph, Point has the coordinates (, ). Eample Locate (, ) on the coordinate graph. = (, ) Go right on the -ais to and then up the -ais to. Vocabular -coordinate -coordinate point of origin Unit Lesson 9 The dots on a coordinate graph are referred to as points. The have coordinates that are the - and -reference points for finding the point. The coordinates are written in parentheses (, ), and the are called ordered pairs. The have two components: () an -coordinate and () a -coordinate. We use these two coordinates to locate the point. Show the coordinate graph and point out the -ais and -ais. In this eample, we are plotting point (, ). Show students how we go over two and up five to reach point. Make sure students see how the coordinates are used to locate the point. 9 Unit Lesson 99

3 Lesson How do we find coordinates on the graph? (continued) Tell students that we also talk about the location of a point b telling what region or quadrant it falls in. There are four sections, or regions, that are created with the intersecting - and - aes. Have students look at the coordinate graph on page 9 of the Student Tet that has the four quadrants labeled. Point out to students that we use Roman numerals to reference the four quadrants. Eplain that Quadrant I is in the upper right, II in the upper left, III in the lower left, and IV in the lower right. If students are not familiar with Roman numerals, be sure ou define them: I =, II =, III =, and IV =. The Roman numeral IV means before. Since V is, then IV is. Tell students that these quadrants are just another wa to think about the location of points on the graph. Have them look at the table. This shows the - and - coordinates of sample points in each quadrant. If ou feel students need practice plotting points on the graph, have them locate each point in each of the quadrants. Watch for: Do students count the correct number horizontall for the -coordinate? Do students count the correct number verticall for the -coordinate? Do students locate the points correctl? 9 Coordinate graphs are divided into four sections, or quadrants. We use Roman numerals to label these quadrants. 9 Unit Lesson II III I Now let s put points in each section, or quadrant, of the graph. Point -coordinate -coordinate Quadrant How We Write It I = (, ) B II B = (, ) C III C = (, ) D IV D = (, ) IV 90 Unit Lesson

4 Have students look at the patterns of positive and negative coordinates located in the various quadrants, as shown in the coordinate graph on Student Tet page 9. For now, just have students make informal observations about the coordinates on the graph. Listen for: Points in Quadrant I have both positive - and -coordinates. Points in Quadrant II have a negative - and a positive -coordinate. Points in Quadrant III have both negative - and -coordinates. Points in Quadrant IV have positive - and negative -coordinates., II (, ) B (, ) C III, (, ) I IV, (, ), D Notice there are - and -coordinates in each corner of the graph to help us see a pattern. For points in Quadrant I, like Point, the coordinates are both positive. For points in Quadrant II, like Point B, the -coordinate is alwas negative and the -coordinate is positive. ll the coordinates in Quadrant III for Point C are negative. For points in Quadrant IV, like Point D, the -coordinate is alwas positive and the -coordinate is negative. The place where the - and -aes cross is (0, 0). This point is called the point of origin. Eplain that in the net unit, we look more formall at what positive and negative coordinates tell us about the location of points without even seeing them plotted on a graph. Point out that the point (0, 0) is where the - and - aes meet. It is called the point of origin. Unit Lesson 9 think of the answer. Then call on a student. Go over the answers with students. 9 Check for Understanding Engagement Strateg: Think, Think Write the following coordinates on the board: (, ) (, ) Tell students that ou will ask them about the location of each. Eplain to students that ou want to know in which quadrant the are found. Tell students that ou will call on one of them for an answer for each ordered pair. Tell them to listen for their names. llow time for students to Unit Lesson 9

5 Lesson What shape is it? (Student Tet, pages 9 00) Point out that in toda s lesson, we see one of the most important uses of the coordinate graph: understanding properties of geometric shapes. Eplain that we can use coordinates to identif the vertices of different shapes. Read through the tet at the top of page 9 of the Student Tet. Show students the square on the coordinate graph in Eample. Point out that the vertices of the square are all labeled with a letter. The letters represent the coordinates of the vertices. What shape is it? One of the important uses of the coordinate graph is to help us understand geometr. We can learn a lot about different shapes b seeing them on a coordinate graph. For one thing, it gives us a wa to assign numbers to the different vertices. Remember, the vertices of a shape are the points where the sides meet. We can use the coordinates of the vertices to tell us more about the properties of the shape. Here is an eample of a square on a coordinate graph. Notice the coordinates of the vertices. Eample What are the coordinates of the vertices of square BCD? B C D 9 9 Unit Lesson 9 Unit Lesson

6 Continue looking at Eample on page 99 of the Student Tet. Eplain that we want to find the coordinates of the square BCD. We can assign numbers to the corners of the square. Point out that this is a wa to observe numeric patterns in shapes along with the visuals that we see in front of us. Notice some of the features of the coordinates. For instance, all the coordinates are positive. This means the shape is in Quadrant I. We do not epect students to make this tpe of conclusion quite et, but the familiarit with the coordinates and the shapes is important developmentall. Be sure to probe for observations so that students can begin to put together these important properties that later become formal proofs. The coordinates are: (, ), B (, ), C (, ), and D (, ). (, ) (, ) B C D (, ) (, ) The coordinate graph gives us more was to describe the shape. We could discuss its location (in Quadrant I). We could talk about the signs of the coordinates of the vertices (all are positive). We could compare the different numbers in the coordinates (the are all s and s, in different orders and combinations). There are man new things to look at when we put the shape on a graph. Sometimes, we can even predict what the shape is if we are given its coordinates without its picture. Let s see if we can guess what shape is represented in the net eample. 99 Unit Lesson 99 Unit Lesson 9

7 Lesson What shape is it? (continued) Net have students look at Eample on page 00 of the Student Tet. In this eample, we ask students to predict the shape. Because there are three coordinates, students should realize that the figure is a triangle. Point out that the distance of the coordinates from one to another also indicate that it is an equilateral triangle, although it is earl to epect this tpe of observation. Check for Understanding Engagement Strateg: Think Tank Write the following coordinates on the board: (, ) (, ) (, ) (, ) 00 Eample Identif the shape with these vertices. Use a graph to check our answer. (, ) B (, ) C (, ) There are onl three sets of coordinates. That means it is a triangle. 00 Unit Lesson B C The three vertices are the clue that told us there are three sides. Triangles are shapes with three sides. s we get better at recognizing shapes b their coordinates, we would also notice that it is an equilateral triangle. This can be determined b looking at the coordinates and the distances between them. We will work more with coordinates and shapes in later lessons, where we will learn some of the important patterns. Problem-Solving ctivit Turn to Interactive Tet, page 0. Reinforce Understanding Use the mbook Stud Guide to review lesson concepts. Distribute pieces of graph paper to the class. Tell students to draw a coordinate graph and plot each of the points. Then have them connect the vertices to make a shape. Have students identif the shape. Have students write their names and answers on the pieces of graph paper. When students finish, collect the papers in a container. Draw out an answer, and share it with the class. If the answer is correct, congratulate the student. If it is incorrect, have a volunteer share the correct answer. 9 Unit Lesson

8 Problem-Solving ctivit Name Date Problem-Solving ctivit (Interactive Tet, pages 0 0) Have students turn to pages 0 0 in the Interactive Tet, and complete the activities. First students plot points on the graph and label them. Then students identif points on a coordinate graph b giving their coordinate pairs. Monitor students work as the complete the activities. Watch for: Can students locate points given their coordinates? Can students identif the coordinates of points when the graph contains points in all four quadrants? Reinforce Understanding Remind students that the can review lesson concepts b accessing the online mbook Stud Guide. Problem-Solving ctivit On the coordinate graph, find the location of each of the given coordinate pairs. Place a dot at the location, and label it with its letter and the - and -coordinates. (, ) C (, ) B (, ) E (, 0) F (, ) D (, ) Name Model Find the location of (, ). Place a dot at the location and label it. Find the location of (, ). Place a dot at the location and label it B.. Find the location of (, ). Place a dot at the location and label it C.. Find the location of (, ). Place a dot at the location and label it D.. Find the location of (, 0). Place a dot at the location and label it E.. Find the location of (, ). Place a dot at the location and label it F. Lesson Problem-Solving ctivit Problem-Solving ctivit Date Give the coordinate pair (, ) that describes the location of each point on the coordinate graph. (, ) B E G F C D Unit Lesson 0 Unit Model (, ). B (, ). C (, ). D (, ). E (, ). F (, ). G (, ) Reinforce Understanding Use the mbook Stud Guide to review lesson concepts. 0 Unit Lesson Unit Lesson 9

9 Lesson Homework Homework Go over the instructions on page 0 of the Student Tet for each part of the homework. ctivit Students compare two integers and tell which is bigger b writing < or > between the two numbers on their paper. ctivit Students solve a mi of integer addition and subtraction problems. ctivit Students tell which quadrant each point is in. The can plot them if the like, or the can refer to the diagram on page 9 to see what the signs of the coordinates are that fall in the four different quadrants. ctivit Distributed Practice Students practice rational number conversions, as well as decimal number and fraction computations, to become more proficient in these skills. ctivit Write > or < to show which is the larger number.. 0 <. > 0. < 0. > 0. 0 >. 9 < ctivit Solve the addition and subtraction problems with positive and negative numbers. For the subtraction problems, remember to add the opposite ctivit Tell which quadrant ou would find each point in on a coordinate graph. nswer I, II, III, or IV.. (, ) I. (, ) II II I. (, ) III. (, ) I. (, ) IV. (, ) II III IV. (, ) IV. (, ) III ctivit Distributed Practice Solve.. Convert % to a fraction.. Convert 0. to a percent. % 00. Convert to a decimal number Unit Lesson 0 9 Unit Lesson