# Triangles, Rectangles, Squares, and Circles

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1 Triangles, Rectangles, Squares, and Circles Triangle sides Rectangle 4 sides Lesson Square length a rectangle with 4 equal sides width Measures of a circle: Radius = 1 diameter Diameter = 2 radius 2 Radius Diameter To draw circles, we can use a tool called a compass. Here are two types of compasses: cm in Draw a triangle with no sides that are the same length. 2. Draw a rectangle that is about three times as long as it is wide.. Use a compass to draw a circle with a diameter of 2 inches. 4. Draw a square that has sides 2 inches long. Saxon Math Intermediate 4 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 2

3 Lines, Segments, Rays, and Angles Lesson 2 2 A line extends in opposite directions with no end. Arrowheads show that it continues in both directions. A line segment is part of a line. It has endpoints, not arrowheads. line segment A ray begins at a point and continues in one direction without end. It has one arrowhead. Parallel lines or segments never cross. When lines or segments cross, we say they intersect. Intersecting lines or segments that form square corners are perpendicular. ray Parallel Lines Parallel Segments Types of Lines Intersecting Perpendicular Intersecting Oblique Horizontal Vertical Oblique Horizontal Vertical Oblique Lines Segments Lines Segments Angles are formed where lines or segments intersect or where two or more rays or segments begin. Types of Angles Obtuse Acute Right Straight 1. Draw two segments that intersect and are perpendicular. 2. Draw a ray.. Describe something in the real world that can represent a pair of parallel lines. Saxon Math Intermediate 4 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 25

4 Inverse Operations When we know one addition fact, we know three other facts. Example: If we know n + 1 = Lesson then we also know 1 + n = n = 1 1 = n Notice that one of the facts shows us how to find the missing addend from the original problem. 1 = n So, n = 2 Addition and subtraction are inverse operations because one operation undoes or reverses the other. Write a subtraction fact for each addition fact r m z d Write an addition fact for each subtraction fact q t a w + 00 For each number sentence, write a fact to show how to find the missing number. Then solve t = a + 12 = y = 9 t = a = y = Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 4

5 Subtraction Word Problems Subtraction problems follow a pattern: Some Some went away = Some left Another way to express the pattern is: Original amount Some part = Difference Lesson If the original amount (top number) is missing, add the difference to the part. Some Some went away Some left 0m apples 12 apples 2 apples m = 5 apples If the subtracted part is missing, subtract the difference from the original amount. Some Some went away Some left 45 apples 0m apples 28 apples m = 17 apples If the difference is missing, subtract the part from the original amount. Some Some went away Some left 67 apples 04 apples 0m apples 67 4 m = apples 1. At the start line, 5 cyclists had water. Some cyclists dropped their bottles during the race. At the finish, only 28 cyclists had bottles. How many cyclists dropped bottles? 5 had bottles 0w dropped bottles 28 now have bottles 67 4 w = dropped bottles 2. A flock of geese started flying north. Then 55 geese landed at a pond. Now 28 geese are flying together. How many geese were flying north before some landed? 0y geese started 55 landed 28 now flying 67 4 y = geese started. Thom had \$40. He spent \$24. Then how much money did Thom have? Saxon Math Intermediate 4 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 27

6 Drawing Pictures of Fractions Lesson To draw a picture of a fraction: 1. Draw the figure. 2. Divide into equal parts.. Shade the correct number of parts. Examples: 2 Rectangle equal parts 2 parts shaded Other examples: To divide a circle into equal thirds: Draw a dot in the center. These are not equal parts: 2. Make a Y from the dot. 1. Shade one fourth of the square. 2. Shade two thirds of the circle.. Shade two fifths of the rectangle. 4. Shade three fourths of the circle. 5. Is one fifth of this circle shaded? Why or why not? 28 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 4

7 Multiplication as Repeated Addition More Elapsed-Time Problems Multiplication as Repeated Addition Multiplication can represent the addition of identical numbers. Example: = 6 5 Lesson Elapsed Time Picture a clock face divided into 4 equal parts. Each part represents 15 minutes. The difference between a time on the clock and the time directly across from it is always 0 minutes. Every twelve hours is the same hour only the a.m. or p.m. will change. Every twenty-four hours is the same time of day, but it is the next day of the week. Write the following repeated addition problems as multiplication problems = = Write the following multiplication problems as repeated addition problems Look at a clock or use a student clock to answer problems 6 7. Remember to write a.m. or p.m. 6. If it is morning, what time will it be in hours and 45 minutes? Start time: 10:45 Count forward 45 minutes. Count forward hours. 7. If it is evening, what time was it 7 hours and 15 minutes ago? Start time: 8:15 Count backward 15 minutes. Count backward 7 hours. Saxon Math Intermediate 4 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 29

8 Multiplication Table Lesson Numbers we multiply together are called factors. The answer to a multiplication problem is called a product. A multiplication table shows the products of different pairs of factors. To use the multiplication table to find a product, we first find one factor in a row. Then we find the other in a column. The product is the number where the row and column meet. The Commutative Property of Multiplication states that changing the order of factors does not change the product. a b = b a The Property of Zero for Multiplication states that any number times zero equals zero. a 0 = 0 The Identity Property of Multiplication states that any number times one equals the number. a 1 = a Properties of Multiplication Commutative Property Identity Property m n = n m 1 n = n Zero Property 0 n = 0 Use the multiplication table to find each product Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 4

9 Multiplication Facts ( 0s, 1s, 2s, 5s) Lesson Zero any number = 0. (Property of Zero for Multiplication) One any number = the same number. (Identity Property of Multiplication) Two any number = double the number. Five any number = a number that ends in 0 or in 5. Complete the multiplication facts below = =. 0 4 = = = 6. 2 = = = = = = = = = = = = = = = = Saxon Math Intermediate 4 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 1

10 Subtracting Three-Digit Numbers with Regrouping Lesson 0 0 Work from right to left. When the digit in the top number is smaller than the digit in the bottom number, we regroup from the next place to the left. When regrouping, it helps to cross-out the digit and rewrite the new number above the column. When subtracting dollars and cents, remember to line up the decimal points and to write the dollar sign in money problems. Example: \$5.17 \$5.17 \$5.17 \$.28 \$.28 \$ \$ \$6.4 \$6.4 \$6.4 \$4.56 \$4.56 \$ \$1.87 Subtract. Remember to write the dollar sign in money problems. 1. \$ \$277 \$6.74 \$ Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 4

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