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STUDY LINK 5 1 Angles 145 160 230–232 Name Date Time Copyright © Wright Group/McGraw-Hill 1. Measure each angle to the nearest degree. Write the measure next to the angle. C B A D G E F H KI J L 2. a. Which angle above is an acute angle? b. A right angle? c. An obtuse angle? d. Which angles above are reflex angles? 3. a. Measure each angle in triangle ADBat the right. b. Find the sum of the 3 angle measures. ° c. Use Problem 3b to calculate the sum of the interior angle measures in quadrangle ABCD. ° A DC B Try This 4. Find the measure of KLM. Then draw an angle that is 60% of the measure of KLMon the reverse side of this paper. Label it as NOP. L M KLESSON 5 1 Name Date Time 146 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill Making an Angle Measurer
LESSON 51 Name Date Time Constructing a Hexagon 147 Copyright © Wright Group/McGraw-Hill Follow the directions below to draw hexagon ABCDEF. Line segment AFat the bottom of the page is one of the sides of the hexagon. The completed drawing should be a convex hexagon. Use your Geometry Template and a pencil with a sharp point. 1. Draw a 130angle with its vertex at point A. One side of the angle is A F. Draw a point on the other side that is 5 centimeters from point A. Label this point B. 2. Draw a 115angle with its vertex at point B.One side of the angle is A B. Draw a point on the other side that is 1 1 2inches from point B.Label it point C. 3. Draw a 145angle with its vertex at point C.One side of the angle is B C. Draw a point on the other side that is 6.5 centimeters from point C.Label it point D. 4. Draw a 90angle with its vertex at point D.One side of the angle is C D. Draw a point on the other side that is 2 3 4inches from point D. Label it point E.Then draw E F to complete the hexagon. 5. What is the measure of E? of F? 6. What is the length of E F to the nearest 1 8inch? 7. What is the sum of the measures of the angles of your hexagon? The closer this sum is to 720°, the more accurate your drawing is. B AF 130° 5 cm A F
STUDY LINK 52 Angle Relationships Copyright © Wright Group/McGraw-Hill 148 163 233 Name Date Time Find the following angle measures. Do not use a protractor. 1. 2. 3. 45°ca t 50°15° x 60°y mymxmc ma mt 4. mqmrms 5. mamb mcmd memf mgmh mi 6. mwma mtmc mh 70° 60°s q r chg i 80° 60°40° bf d e a 105° 75° a t c h w Practice 7. 3 4of 16 8. 3 5of 50 9. 1 3of 330
LESSON 52 Name Date Time Angle Measures: Triangles and Quadrangles 149 Copyright © Wright Group/McGraw-Hill Cut out any or all of the triangles and quadrangles on this page. B C A tear tear tear BC A tear tear tear B C A tear tear tear A B C tear tear tear DE G F tear tear tear tear D E G F tear tear tear tear DE GF tear tear tear tear DE GF tear tear tear tear
LESSON 52 Name Date Time Finding Sums of Angle Measures 150 Copyright © Wright Group/McGraw-Hill 1. Cut out one of the triangles on Math Masters, page 149. Carefully cut or tear off each angle. Use point Pat the right to position the angles so they touch but do not overlap. The shaded regions should form a semicircle. Use tape or glue to hold the angles in place. 2. Notice that the combined shaded regions form an angle. How many degrees does this angle measure? 3. Compare your results with those of other students. What do your triangles seem to have in common? 4. Complete the following statement. The sum of the measures of the angles of any triangle is ° . A B C P 5. Cut out one of the quadrangles on Math Masters, page 149. Carefully cut or tear off each angle. Use point Qat the right to position the angles so they touch but do not overlap. The shaded regions should form a circle. Use tape or glue to hold the angles in place. 6. Notice that the combined shaded regions form a figure. How many degrees are in this figure? 7. Compare your results with those of other students. What do your quadrangles seem to have in common? 8. Complete the following statement. The sum of the measures of the angles of any quadrangle is . ° E F G D Q
LESSON 52 Name Date Time Applying Angle Relationships 151 Copyright © Wright Group/McGraw-Hill 1. Extend each side of the regular pentagon in both directions to form a star. The first extension has been done for you. Then use what you know about angle relationships to find and label the measures of each interior angle in your completed star. 108 2. Describe the angle relationships you used to determine the measures of the interior angles.
LESSON 53 Name Date Time Graphing Votes 152 Copyright © Wright Group/McGraw-Hill Percent of Degree Measure of Sector Candidate Votes Received (to nearest degree) Connie 28% 0.28 º 360100.8101 Josh º 360 Manuel º 360 Total 100% 360
LESSON 53 Name Date Time Pet Survey 153 Copyright © Wright Group/McGraw-Hill Fraction Decimal Percent Degree Measure Kind Number of Total Equivalent of Total of Sector of Pet of Pets Number (to nearest Number of Pets thousandth) of Pets Dog 8 28 4 0.333 33 1 3% º 360 Cat 6 º 360 Guinea pig 3º 360 or hamster Bird 3 º 360 Other 4 º 360 120 1 3
STUDY LINK 53 Circle Graphs Copyright © Wright Group/McGraw-Hill 154 Name Date Time 1. The table below shows a breakdown, by age group, of adults who listen to classical music. a. Calculate the degree measure of each sector to the nearest degree. b. Use a protractor to make a circle graph. Do notuse the Percent Circle. Write a title for the graph. AgePercent of Degree Listeners Measure 18–24 11% 25–34 18% 35–44 24% 45–54 20% 55–64 11% 6516% Source: USA Today,Snapshot 2. On average, about 8 million adults listen to classical music on the radio each day. a. Estimate how many adults between the ages of 35 and 44 listen to classical music on the radio each day. About (unit) b. Estimate how many adults at least 45 years old listen to classical music on the radio each day. About (unit) Practice Order each set of numbers from least to greatest. 3. 7, 0.07, 7, 0.7, 0 4. 0.25, 0.75, 0.2, 4 5, 4 4, 0.06, 0.18, 11 0 49 147
LESSON 53 Name Date Time Fractions of 360 155 Copyright © Wright Group/McGraw-Hill Shade each fractional part. Then record the number of degrees in each shaded region. 1. Shade 1 2of the circle. 2. Shade 1 4of the circle. 1 2of 360° 1 4of 360° 3. Shade 1 6of the circle. 4. Shade 1 3of the circle. 1 6of 360° 1 3of 360° 5. Shade 11 2of the circle. 6. Shade 3 4of the circle. 11 2of 360° 3 4of 360° 0 360° 350340 320310 290280 260250 230220 200190 170160 140130 110100 8070 5040 2010 330 300 270 240 210 180 150 120 90 60 30 0 360° 350340 320310 290280 260250 230220 200190 170160 140130 110100 8070 5040 2010 330 300 270 240 210 180 150 120 90 60 30 0 360° 350340 320310 290280 260250 230220 200190 170160 140130 110100 8070 5040 2010 330 300 270 240 210 180 150 120 90 60 30 0 360° 350340 320310 290280 260250 230220 200190 170160 140130 110100 8070 5040 2010 330 300 270 240 210 180 150 120 90 60 30 0 360° 350340 320310 290280 260250 230220 200190 170160 140130 110100 8070 5040 2010 330 300 270 240 210 180 150 120 90 60 30 0 360° 350340 320310 290280 260250 230220 200190 170160 140130 110100 8070 5040 2010 330 300 270 240 210 180 150 120 90 60 30
LESSON 53 Name Date Time Sums of Angle Measures in Polygons 156 Copyright © Wright Group/McGraw-Hill A diagonalis a line segment that connects two vertices of a polygon and is nota side. You can draw diagonals from one vertex to separate polygons into triangles. 1. Draw diagonals from the given vertex to separate each polygon into triangles. Then complete the table. 2. a. Study your completed table. Use any patterns you notice to write a formula to find the sum of the angle measures in any polygon (n-gon). Formula b. Use the formula to find the sums of the angle measures in a heptagon. ° nonagon. ° dodecagon. ° 1,800 1,260 900 (n2) º 180 Number of Number of Sum of Angle Measures Polygon Sides (n)Triangles Example:Quadrangle 4 2 2 º 180360 Pentagon 53 º Hexagon 64 º Octagon 86 º Decagon 10 8 º 8 6 4 3 diagonal 180540 180 180 180720 1,080 1,440
STUDY LINK 54 More Polygons on a Coordinate Grid 157 166 169 234 Name Date Time Copyright © Wright Group/McGraw-Hill For each polygon described below, some vertices are plotted on the grid. Either one vertex or two vertices are missing. Plot and label the missing vertex or vertices on the grid. (There may be more than one place you can plot a point.) Write an ordered number pair for each vertex you plot. Draw the polygon. 1. Right triangle ABCVertex C:(,) 2. Parallelogram DEFGVertex F:( , ) Vertex G:(,) 3. Scalene triangle HIJVertex J:(,) 4. Kite KLMNVertex M:(,) 5. Square PQRSVertex Q:(,) –1 –2 –3 –4 –5 –7 –8 –6 123456781 2 4 3 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –80 –9 –109 10 9 10 x –9 –10 D E H I L K N P S R A B y
LESSON 54 Name Date Time X and O—Tic-Tac-Toe 158 Copyright © Wright Group/McGraw-Hill Materials4 each of number cards 0–10 (from the Everything Math Deck, if available) Coordinate Grid (Math Masters,p. 417) Players2 Object of the game To get 4 Xs or Os in a row, column, or diagonal on the coordinate grid. Directions 1. Shuffle the cards and place the deck facedown on the playing surface. 2. In each round: Player 1 draws 2 cards from the deck and uses the cards in any order to form an ordered pair. The player marks this ordered pair on the grid with an X and places the 2 cards in the discard pile. Player 2 draws the next 2 cards from the deck and follows the same procedure, except that he or she uses an O to mark the ordered pair. Players take turns drawing cards to form ordered pairs and marking the ordered pairs on the coordinate grid. If the 2 possible points that the player can make have already been marked, the player loses his or her turn. 3. The winner is the first player to get 4 Xs or 4 Os in a row, column, or diagonal.
LESSON 54 Name Date Time Plotting Triangles and Quadrangles 159 Copyright © Wright Group/McGraw-Hill Plot each of the described triangles and quadrangles on Math Masters, page 417. Record the coordinates of each vertex in the table below. Description Coordinates of Each Vertex Example:Square with side measuring 3 units (6,6); (6,3); (9,3); (9,6) 1.A rhombus that is not a square, which has at least one vertex with a negative x-coordinate and a positive y-coordinate 2.An isosceles triangle that has an area of 2 square units 3.A rectangle that has a perimeter of 16 units 4.A right scalene triangle that has each vertex in a different quadrant 5.A kite that has one vertex at the origin 6.A parallelogram that has an area of 18 square units and one side on the y-axis 7.An obtuse scalene triangle that has at least two vertices with a negative x-coordinate and a negative y-coordinate 8.Write your own description.
STUDY LINK 55 Transforming Patterns Copyright © Wright Group/McGraw-Hill 160 180 181 Name Date Time A pattern can be translated, reflected, or rotated to create many different designs. Consider the pattern at the right. The following examples show how the pattern can be transformed to create different designs: 1. Translate the pattern at the right across 2 grid squares. Then translate the resulting pattern (the given pattern and its translation) down 2 grid squares. 2. Rotate the given pattern clockwise 90 around point X.Repeat 2 more times. 3. Reflect the given pattern over line JK. Reflect the resulting pattern (the given pattern and its reflection) over line LM. A B C D TranslationsRotationsReflections 4. 26 5. 35 6. 70 7. 43 Practice X J K L M
LESSON 55 Name Date Time Degrees and Directions of Rotation 161 Copyright © Wright Group/McGraw-Hill When a figure is rotated, it is turned a certain number of degrees around a particular point. A figure can be rotated clockwise or counterclockwise. Position a trapezoid pattern block on the center point of the angle measurer as shown at the right. Then rotate the pattern block as indicated and trace it in its new position. Example:Rotate 90clockwise. For each problem below, rotate and then trace the pattern block in its new position. 1. Rotate 90counterclockwise. 2. Rotate 270clockwise. 12 6 11 5 10 4 1 72 83 9 degrees 12 6 11 5 10 4 1 72 83 9 degrees 12 6 11 5 10 4 1 72 83 9 degrees
LESSON 55 Name Date Time Scaling Transformations 162 Copyright © Wright Group/McGraw-Hill Some scaling transformations produce a figure that is the same shape as the original figure but not necessarily the same size. Enlargements and reductions are types of scaling transformations. Enlargement:Follow the steps to draw a triangle D E F with angles that are congruent to triangle DEFand sides that are twice as long as triangle DEF. Step 1Draw rays from Pthrough each vertex. The first rayP Dhas been drawn for you. Step 2Measure the distance from point Pto vertex D. Then locate the point on P Dthat is 2 times that distance. Label it D . Step 3Use the same method from Step 2 to locate point F on P Fand point E onP E. Step 4Connect points D , E , andF . Reduction: Change Steps 2 and 3 to draw a triangle D E F with angles that are congruent to triangle DEFand sides that are half as long as triangle DEF. P D FE
STUDY LINK 56 Congruent Figures and Copying 163 178 Name Date Time Copyright © Wright Group/McGraw-Hill Column 1 below shows paths with the Start points marked. Complete each path in Column 2 so that it is congruent to the path in Column 1. Use the Start points marked in Column 2. In Problems 2 and 3, the copy will not be in the same position as the original path. (Hint:If you have trouble, try tracing the path in Column 1 and then slide, flip, or rotate it so that its starting point matches the starting point in Column 2.) Example:These two paths are congruent, but they are not in the same position. Start Start Start Start Start Start Start Start 1. Column 1 Column 2 2. 3.
LESSON 56 Name Date Time Quadrangles and Congruence 164 Copyright © Wright Group/McGraw-Hill 16 15 14 13 12 11 9 5 4 3 2 1 Cut out the 16 quadrangles and the 6 set labels. All Right Angles A All Sides Congruent A Adjacent Sides Congruent C All Pairs Opposite Sides Congruent B At Least 2 Acute Angles B At Least 1 Right Angle C 6 7 8 10
LESSON 56 Name Date Time Quadrangles and Congruence continued 165 Copyright © Wright Group/McGraw-Hill Cut out the quadrangles and set labels from Math Masters,page 164. Place the two A, B, or C set labels in the placeholders above the rings and sort the quadrangles accordingly.
STUDY LINK 57 Angle Relationships Copyright © Wright Group/McGraw-Hill 166 163 233 Name Date Time Write the measures of the angles indicated in Problems 1–6. Do not use a protractor. 1. mr ms mt 3. ma mb mc 5. Angles xand yhave the same measure. mx my mz x y z 60° a c b 2. JKLis a straight angle. mNKO 4. Angles aand thave the same measure. ma mc mt 6. mp p 36° a t c21° 135° M J K L ON 15° 93° 62° 133° r st Practice 7. 0.09 º 0.03 8. 0.15 º 0.8 9. 0.07 º 0.07 10. 0.75 º 0.3
LESSON 57 Name Date Time Circle Constructions 167 Copyright © Wright Group/McGraw-Hill Use the directions and the pictures below to make one or both of the constructions. You may need to make several versions of the construction before you are satisfied with your work. Cut out your best constructions and tape or glue them to another sheet of paper. Construction #1 Step 1Draw a small point that will be the center of the circle. Press the compass anchor firmly on the center of the circle. Step 2Hold the compass at the top and rotate the pencil around the anchor. The pencil must go all the way around to make a circle. You may find it easier to firmly hold the compass in place and carefully turn the paper under the compass. Step 3Without changing the opening of the compass, draw another circle that passes through the center of the first circle. Mark the center of the second circle. Step 4Repeat Step 3 to draw a third circle that passes through the center of each of the first two circles. Construction #2 Follow the steps to make the three circles from Construction #1. Then draw more circles to create the construction shown at the right.
LESSON 57 Name Date Time Octagon Construction 168 Copyright © Wright Group/McGraw-Hill Use the directions and the pictures to construct an octagon. Step 1Draw a circle with a compass. Label the center of the circle A. Then draw a diameter through A. Label the two points where the diameter intersects the circle Sand T. Step 2Use the length of ST to set the compass opening. Then place the anchor of your compass on Sand draw an arc below the circle and another arc above the circle. Without changing the compass opening, place the compass anchor on Tand draw another set of arcs above and below the circle. Label the points where the arcs intersect as Dand E. Draw a line through Dand E. Label the points where DE intersects the circle as Mand N. Step 3Set the compass opening so that it is equal to the length of SM . Then place the compass anchor on Sand draw an arc; reposition the anchor on Mand draw another arc. Label the point where the arcs intersect as G. Draw a line through Gand A. Label the points where GA intersects the circle as Hand I. Step 4Repeat Step 3, using the length of MT to set the compass opening. Label the points of intersection as X, Y,and Z. Step 5Connect the points on the circle to form an octagon. A ST A G HD M N E S IT A G HD MX Y N E Z S IT
STUDY LINK 58 Isometry Transformations on a Grid 169 180 181 234 Name Date Time Copyright © Wright Group/McGraw-Hill 1. Graph and label the following points on the coordinate grid. Connect the points to form quadrangle ABCD. A:(2,1)B:(6,2) C:(8,4)D:(5,7) 2. Translate each vertex of ABCD(in Problem 1) 0 units to the left or right and 8 units down. Plot and connect the new points.Label them A , B , C , and D . Record the coordinates of the image. 3. Reflect quadrangle ABCDacross the y-axis. Plot and connect the new points. Label them A , B , C , and D . Record the coordinates of the image. 4. Rotate quadrangle A B C D 90° clockwise around point (0,0). Plot and connect the new points. Label them A , B , C , and D . Record the coordinates of the rotated image. –1 –2 –3 –4 –5 –7 –8 –6 12345678x y 1 2 4 3 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –80 Try This Practice 5. 300 0.001 6. 143 10 3 7. 35.9 1,01 00
LESSON 58 Name Date Time Inscribing a Circle in a Triangle 170 Copyright © Wright Group/McGraw-Hill Follow the steps to inscribe a circle in triangle ABC. Step 1Construct the bisectors of Aand B. Then label the intersection of the angle bisectors as P. Step 2Construct a line segment through point P,perpendicular to AB . Label the point at which the line segment intersects AB as Q. Step 3Center the compass anchor on Pand the pencil point on Q. Draw a circle through Q. The circle will be tangent to all three sides of the triangle.B C A
LESSON 58 Name Date Time Constructing Perpendicular Bisectors 171 Copyright © Wright Group/McGraw-Hill 1. Draw a large triangle. Construct perpendicular bisectors for each side of the triangle. What observations can you make? 2. Use a protractor and a ruler to draw a large square. Draw a diagonal. Then construct the perpendicular bisector of the diagonal. What observations can you make?
1. Use a ruler and a straightedge to draw 2 parallel lines. Then draw another line that crosses both parallel lines. 2. Measure the 8 angles in your figure. Write each measure inside the angle. 3. What patterns do you notice in your angle measures? STUDY LINK 59 Parallel Lines and a Transversal Copyright © Wright Group/McGraw-Hill 172 163 230 231 Name Date Time Practice Remember:1,000 milliliters (mL) 1 liter (L) 4. 500 mL L 5. 2.5 L mL 6. 1,300 mL L 7. 0.95 L mL 8. 3,250 mL L 9. 0.045 L mL
LESSON 59 Name Date Time Angle Relationships and Algebra 173 Copyright © Wright Group/McGraw-Hill Apply your knowledge of angle relationships to find the missing values and angle measures. Do not use a protractor. 1. x° 2. Lines land mare parallel. y° mp° mr° mq° ms° 3. 4. Turn this page over. Using only a straightedge and a compass, design a problem that uses angle relationships. Create an answer key for your problem. Then ask a classmate to solve your problem. 150 2x 10 100°y 40° 2y° n spq rl m 50° 70° 70° a x 30°c2x 70° x° ma° mc°
STUDY LINK 5 10 Parallelogram Problems Copyright © Wright Group/McGraw-Hill 174 163 169 233 Name Date Time All of the figures on this page are parallelograms. Do not use a ruler or a protractor to solve Problems 1, 2, or 3. 1. a. The measure ofX° . Explain how you know. b. The measure of Y° . Explain how you know. 2. Alexi said that the only way to find the length of sides COand OAis to measure them with a ruler. Explain why he is incorrect. 3. What is the measure of MAR? . Explain how you know. 4. Draw a parallelogram in which all sides have the same length and all angles have the same measure. What is another name for this parallelogram? 5. Draw a parallelogram in which all sides have the same length and no angle measures 90°. What is another name for this parallelogram? 130° Y X Z W CO TA 10 cm 30 cm 70° 40° M KR A
LESSON 510 Name Date Time Using Quadrangles to Classify Quadrangles 175 Copyright © Wright Group/McGraw-Hill Read each statement. Then decide if the statement is always, sometimes,or nevertrue. If you write sometimes,identify a case for which the statement is true. 1. A square is a rectangle. 2. A rhombus is a trapezoid. 3. A square is a parallelogram. 4. A rhombus is a parallelogram. 5. A kite is a parallelogram. 6. A rhombus is a rectangle. 7. A square is a rhombus. 8. A trapezoid is a parallelogram. Fill in the blank using always, sometimes,or never.If you write sometimes,identify a case for which the statement is true. 9. A rectangle has consecutive sides that are congruent. 10. The diagonals of a rhombus are congruent. Example:A rectangle is a square. sometimes A rectangle is a square when its 4 sides are the same length.
STUDY LINK 511 Unit 6: Family Letter Copyright © Wright Group/McGraw-Hill 176 Name Date Time Number Systems and Algebra Concepts InFourthandFifth Grade Everyday Mathematics,your child worked with addition and subtraction of positive and negative numbers. In this unit, students use multiplication patterns to help them establish the rules for multiplying and dividing with positive and negative numbers. They also develop and use an algorithm for the division of fractions. In the rest of the unit, your child will explore beginning algebra concepts. First, the class reviews how to determine whether a number sentence is true or false. This involves understanding what to do with numbers that are grouped within parentheses and knowing in what order to calculate if the groupings of numbers are not made explicit by parentheses. Students then solve simple equations by trial and error to reinforce what it means to solve an equation—to replace a variable with a number that will make the number sentence true. Next, they solve pan-balance problems, first introduced in Fifth Grade Everyday Mathematics,to develop a more systematic approach to solving equations. For example, to find out how many marbles weigh as much as 1 orange in the top balance at the right, you can first remove 1 orange from each pan and then remove half the remaining oranges from the left side and half the marbles from the right side. The pans will still balance. Students learn that each step in the solution of a pan-balance problem can be represented by an equation, thus leading to the solution of the original equation. You might ask your child to demonstrate how pan-balance problems work. Finally, your child will learn how to solve inequalities— number sentences comparing two quantities that are not equal. Please keep this Family Letter for reference as your child works through Unit 6.
177 Copyright © Wright Group/McGraw-Hill Vocabulary Important terms in Unit 6: cover-up method An informal method for finding the solution of an open sentence by covering up a part of the sentence containing a variable. Division of Fractions Property A property of dividing that says division by a fraction is the same as multiplication by the reciprocalof the fraction. Another name for this property is the “invert and multiply rule.” For example: 585 1 8 5 8 15 3 515 5 3 7 3525 1 2 3 5 1 25 3 5 6 In symbols: For aand nonzero b, c,andd, ba dc bad c Ifb1, then baaand the property is applied as in the first two examples above. equivalent equations Equations with the same solution. For example, 2 x4 and 6 x8 are equivalent equations with solution 2. inequality A number sentence with a relation symbolother than , such as , ,,,, or . integer A number in the set {..., 4,3,2,1, 0, 1, 2, 3, 4, ...}. A whole number or its opposite, where 0 is its own opposite. Multiplication Property of1 A property of multiplication that says multiplying any number by 1 gives the opposite of the number. For example, 1 55 and –1 3 (3) 3. Some calculators apply this property with a [/] key that toggles between a positive and negative value in the display. open sentence A number sentence with one or more variables. An open sentence is neither true nor false. For example, 9 __15, ? 24 10, and 7xyare open sentences. opposite of a number n A number that is the same distance from zero on the number line as n,but on the opposite side of zero. In symbols, the opposite of a number nis –n,and, in Everyday Mathematics,OPP(n). If nis a negative number, –n is a positive number. For example, the opposite of –55. The sum of a number nand its opposite is zero;n–n0. order of operations Rules that tell the order in which operations in an expression should be carried out. The conventional order of operations is: 1.Do the operations inside grouping symbols. Work from the innermost set of grouping symbols outward. Inside grouping symbols, follow Rules 2– 4. 2.Calculate all the expressions with exponents. 3.Multiply and divide in order from left to right. 4.Add and subtract in order from left to right. For example: 5 2(3 4 – 2)/5 5 2(12 – 2)/5 5210/5 2510/5 252 27 reciprocals Two numbers whose product is 1. For example, 5 and 1 5,3 5 and 5 3, and 0. 2 and 5 are all pairs of multiplicative inverses. trial-and-error method A method for finding the solution of an equation by trying a sequence of test numbers. 0354 1 1 2 32 4 5 Unit 6: Family Letter cont. STUDY LINK 511
Copyright © Wright Group/McGraw-Hill 178 Do-Anytime Activities To work with your child on concepts taught in this unit, try these interesting and engaging activities: 1.If your child helps with dinner, ask him or her to identify uses of positive and negative numbers in the kitchen. For example, negative numbers might be used to describe the temperature in the freezer. Positive numbers are used to measure liquid and dry ingredients. For a quick game, you might imagine a vertical number line with the countertop as 0; everything above is referenced by a positive number, and everything below is referenced by a negative number. Give your child directions for getting out items by using phrases such as this: “the 2 mixing bowl”; that is, the bowl on the second shelf below the counter. 2.If your child needs extra practice adding and subtracting positive and negative numbers, ask him or her to bring home the directions for the Credits/Debits Game. Play a few rounds for review. 3.After your child has completed Lesson 6, ask him or her to explain to you what the following memory device means: Please Excuse My Dear Aunt Sally.It represents the rule for the order of operations: parentheses, exponents, multiplication, division, addition, subtraction. Your family might enjoy inventing another memory device that uses the same initial letters; for example, Please Excuse My Devious Annoying Sibling; Perhaps Everything Might Drop Again Soon,and so on. In Unit 6, your child will work on his or her understanding of algebra concepts by playing games like the ones described below. Algebra ElectionSeeStudent Reference Book, pages 304 and 305. Two teams of two players will need 32 Algebra Electioncards, an Electoral Vote map, 1 six-sided die, 4 pennies or other small counters, and a calculator. This game provides practice with solving equations. Credits/Debits Game (Advanced Version)SeeStudent Reference Book, page 308. Two players use a complete deck of number cards and a recording sheet to play the advanced version of the Credits/Debits Game. This game provides practice with adding and subtracting positive and negative integers. Top-ItSeeStudent Reference Book, pages 337 and 338. Top-It with Positive and Negative Numbersprovides practice finding sums and differences of positive and negative numbers. One or more players need 4 each of number cards 0–9 and a calculator to play thisTop-Itgame. Building Skills Through Games Unit 6: Family Letter cont. STUDY LINK 511
179 Copyright © Wright Group/McGraw-Hill As You Help Your Child with Homework As your child brings assignments home, you might want to go over the instructions together, clarifying them as necessary. The answers listed below will guide you through some of the Unit 6 Study Links. Study Link 6 1 2.✓3.✓5.✓7. 11 9 9. 27 6 11. 3 4 13.12 1 2lb14.38 1 4in. 15.67 1 2in. 3 16.8117.218.67 Study Link 6 2 1. 4 5 3.15.17. 95 8 9.1010.1411.1712.13.56 13.589.3614.13 Study Link 6 3 1. a.46(19) 27c.56.8 1.8 2. a.29c.2 1 5 e.3 1 4 g.18.2 3. a.(2)c.2 1 4 e.3.7g. 17 6 4.25.116.87.6 Study Link 6 4 1.603.65.57.6 9.1,15011.5413.215. 5 9 17.219. a.36b.77 Study Link 6 6 1.213. 2 31 2 5.727.1 9.2811.312.2313.6, 1 14.2, 115.4, 4 Study Link 6 7 1. a.17 27; 3 15 100; (5 4)2020; 1212 b.Sample answer: A number sentence must contain a relation symbol. 568 does not include one. 2. a.trueb.falsec.falsed.true 3. a.(286)931b.20 (409)11 c.(36/6) / 2 12d.4(84)164. a.601450; falseb.90330; true c.217 40; trued. 36 1 210; true 5.0.926.3.517.251.515 Study Link 6 8 1. a.b19b.n24c.y3d.m 1 5 2. a. 6x10;x60b.2007n;n193 c.b482,928;b61 3.Sample answers: a.(311)(129)b.21814 4.545.3.66.121 Study Link 6 9 1.12.1 1 2 3.54.1 6.Answers vary.7.108. 1 4 9. 2 3 10. 1 2 Study Link 6 10 1.k45; 3k1215; 20k121517k 2.Multiply by 2; M 23.Add 5m; A 5m Subtract 3q; S 3qDivide by 2; D 2 Add 5; A 5 Subtract 6; S 6 Study Link 6 11 1.k123.x15.r2 Study Link 6 12 1. a.1537b.x575 c. 9 91314 2. a.200(45)10 b.162 2(53)12 3. a.46b.18c.0d.8 4. a.x1b.y6.5 5. a.Sample answers: 3,2 1 2,2 6.$0.25; $0.217.1; 1.288.800; 781 Unit 6: Family Letter cont. STUDY LINK 511