Lesson 31 † Pairs Of Lines † Angles

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ReteachingName31Lesson 31 Pairs of Lines AnglesPairs of Lines When lines cross, they intersect. Lines that go in the same directions and do not intersect are calledparallel lines. Lines that intersect to form square corners are perpendicular. Intersecting lines that do not form square corners are oblique.Types of LinesParallel LinesParallel SegmentsIntersecting PerpendicularHorizontal Vertical Oblique Horizontal Vertical ObliqueLinesSegmentsIntersecting ObliqueLinesSegmentsAngles Angles form when lines, line segments, or rays intersect. A vertex is where 2 sides of an angle meet.sideanglevertex Angles can be right, acute, obtuse, or straight.Straight angleRightangleThe square corner fitsthe corner of your paper.AcuteangleLess than a right angle(a cute little angle)ObtuseangleMore than a right angleMakes a straight line,line segment, or rayPractice:1. Draw two vertical lines.2. Draw two intersecting oblique linesegments.3. Draw two horizontal line segments.4. Draw two perpendicular lines.Draw an example of each angle.5. right angle346. obtuse angle7. acute angle Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Saxon Math Intermediate 5

ReteachingName32Lesson 32 Polygons Polygons are closed, flat shapes formed fromstraight line segments. Congruent figures have the same shape and size.Their angles and sides match. Similar figures have the same shape and matchingangles but do not have to be the same size.Practice:1. Draw a triangle with an obtuse angle.2. Which shape is not a polygon?ABCD3. Draw two similar, but not congruent rectangles.4. Can a triangle have more than one right angle?Saxon Math Intermediate 5 Harcourt Achieve Inc. and Stephen Hake. All rights reserved.35

ReteachingName33Lesson 33 Rounding Numbers and Estimating To make arithmetic easier, we can round a number. We “round up” or “rounddown” to the number that is closest in value to the given number. To round a number to the nearest ten, we look at the ones place. If the ones placeis less than 5, we round down. If the tens place is equal to or greater than 5, weround up.Example:Round these numbers to the nearest ten:122 is less than 5, so we round down to 10.177 is greater than 5, so we round up to 20. Rounding numbers can help us estimate the answer to a problem. Estimatedanswers are close to, but not equal to, the exact answer.Example:Estimate 12 17.Think 10 20 200. We can estimate that 12 17 is about 200. One way to see which number to round a given number to is by using anumber line.Example:Round 78 to the nearest ten.78 is closer to 80 than 70.78 rounds up to 80.70757880Practice:Round each number to the nearest ten.1. 542. 673. 124. 855. 236. 71Estimate each calculation by rounding two-digit factors to the nearest ten beforemultiplying.367. 23 9 8. 4 51 9. 7 67 10. 96 4 Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Saxon Math Intermediate 5

ReteachingName34Lesson 34 Division with Zeros in the Quotient Use the division algorithm (divide, multiply, subtract, “bring down”). Place a digit above each digit. Use zero as a placeholder when the next digit in the dividend cannot be divided. Any number “left over” becomes the remainder.Examples:106 R37) 745 R3745 R3045 R3005 R345 R342 R33 R30 33 R37)234 R3034 R3234 R3214 R324 R321 R33 R3Practice:Divide. Remember to write the dollar sign in money problems.R1. 2) 192. 5)3287. 8) 710010. 2) 8.94Saxon Math Intermediate 56. 6) 3.72RR8. 4)321011. 9)8605R5. 5) 4.25R3. 3)2174. 7) 609RR9. 3)625R12. 7)2850 Harcourt Achieve Inc. and Stephen Hake. All rights reserved.37

ReteachingName35Lesson 35 Word Problems About Comparing, and Elapsed Time Place the greater number on top.LargerLater Smaller EarlierDifferenceDifference Watch for these keywords in elapsed-time ssPractice:Write an equation and solve the problem. Remember to write the units.1. A kickball team has 6 players. They need 18 players. How many more playersdoes the team need?2. The Empire State Building is 1250 feet tall. If the Sears Tower is 1450 feet tall,how many feet less is the Empire State Building?3. Halley’s comet appeared in the sky in 1985. The comet will be visible again in2061. How many years are there between the times the comet is visible?38 Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Saxon Math Intermediate 5

ReteachingName36Lesson 36 Classifying Triangles Three types of angles are acute angles, right angles, and obtuse angles.AcuteangleRightangleObtuseangle Triangles can be classified by their angles, their sides, or both.Classifying TrianglesBy SidesTypeBy AnglesCharacteristicExampleTypeCharacteristic ExampleEquilateraltriangleThree sides of equal lengthAllAcutetriangle acute anglesIsoscelestriangleAt least two sides of equallengthRighttriangleScalene triangleThree sides of unequal lengthOneObtusetriangle obtuse angleOneright angleExamples:isosceles andacuteisosceles andrightisosceles andobtusePractice:Classify each triangle by its sides.1.2.3.Classify each triangle by its angles.4.Saxon Math Intermediate 55.6. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.39

ReteachingName37Lesson 37 Drawing Pictures of Fractions There are many ways to divide figures into equal fractional parts.These show 12. Remember, not all fractional parts are equal parts.This does not show equal halves, but it might show 13 and 23. To divide a circle in half:1. Put a point in the center.2. Draw a line segment through the center. To divide a circle in thirds:1. Put a point in the center.2. Draw a “Y” from the center.Practice:1. Shade 15 of the rectangle.2. Shade 23 of the circle.3. The shaded portion of the first square represents the fraction 39.Use the second square to show another way to shade 39.4. The shaded portion of the first circle represents the fraction 14.Use the second circle to show a way to shade 34.40 Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Saxon Math Intermediate 5

ReteachingName38Lesson 38 Fractions and Mixed Numbers on a Number LineBA1234 To identify a fraction or mixed number on a number line:1. Count the parts between the whole numbers. (4 parts, so fourths)2. Name the arrow as a fraction. (A: 24, B: 34 )3. Don’t forget the whole number. (A: 1 24 , B: 3 34 )Practice:Name the fraction or mixed number marked by each arrow on these number lines.1. A AB2. B 33. C 45C4. D 06D12Three fractions are graphed on the number line below. Refer to the number line tocompare the fractions in problems 5–7.1 1 24 3 52 33 4015.411226.53217.2538. Place the following numbers on the number line below. 1 12, 1 34, 2 140Saxon Math Intermediate 512 Harcourt Achieve Inc. and Stephen Hake. All rights reserved.341

ReteachingName39Lesson 39 Comparing Fractions by Drawing Pictures One way to compare fractions is to draw and shade congruent polygons torepresent the fractions. Then we see which polygon is more shaded.Example:12 13Practice:Compare each pair of fractions. Draw pictures to illustrate the fractions.4211.2233.534412.3134.4748 Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Saxon Math Intermediate 5

ReteachingName40Lesson 40 Writing Quotients with Mixed Numbers To draw pictures that show mixed numbers:1. Divide the circles into the parts shown in the denominator.2. Shade the whole number and the parts shown in the numerator.Example:Whole number and a fraction213 Some division problems will need the remainder shown as a fraction. Write the remainder over the divisor.4Example:R12)914 22) 9 1remainderdivisorPractice:Write a mixed number to name the number illustrated.1.2.Shade the circles to represent each mixed number.3. two and three fourths4. three and one third5. Kimberly, Maxine, Toby, and Jabari will share five sandwiches. How manysandwiches are there for each person?1for Jabari41for Kimberly4Show the remainder as a fraction.1for Toby4Saxon Math Intermediate 51for Maxine44) 5 Harcourt Achieve Inc. and Stephen Hake. All rights reserved.43

Types of Lines Horizontal Vertical Oblique Horizontal Vertical Oblique Lines Segments Lines Segments Parallel Lines Intersecting Perpendicular Intersecting ObliqueParallel Segments Angles † Angles form when lines, line segments, or rays intersect. † A vertex is where 2 sides of an angle meet. vertex side angle † Angles can be right, acute .

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