Word Problems About Combining Some and some more problems have an addition formula. Formula Problem Some miles + Some more + miles Total 15 miles Find a missing total by adding. Find a missing addend by subtracting. Remember to check your answer. Lesson 11 11 Find the missing number and check the answer. Remember to write the dollar sign in money problems. 1. Quentin wants to buy a new pair of shoes for the choir performance. Shoes cost $3. Quentin has $2. How much money does he need to buy the shoes? 2. Nicolette s mother asked her how many times she had watched her favorite movie. Nicolette said she had watched it 1 times last month, but she had watched 2 times in all. How many times, before last month, had Nicolette watched the movie? 3. Write a word problem about combining for the equation to the right. Then answer the question in your word problem. $3 + $5 = b 12 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 5
Lines Number Lines Tally Marks Lines A point, a line, a line segment, and a ray are shown below: Lesson 12 12 Point Line Line segment Ray Lines, rays, and segments can be horizontal, vertical, or oblique. Horizontal line Vertical line Oblique lines Number Lines A number line represents numbers in order. Integers are separated by unit intervals. Unit interval 5 3 2 1 0 1 2 3 5 Tally Marks Tally marks can be used to quickly record data of things we count by ones. We then use a cross hatch to mark sets of five, so it s easier to read large numbers of tally marks. Four Five Six 1. Which of these represents a line segment? A B C 2. Show the number 21 using tally marks. 3. Draw a pair of oblique line segments. Saxon Math Intermediate 5 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 13
Multiplication as Repeated Addition Adding and Subtracting Dollars and Cents Multiplication as Repeated Addition Multiplication is repeated addition of the same number. 5 6 = 5 + 5 + 5 + 5 + 5 + 5 Lesson 13 13 Adding and Subtracting Dollars and Cents When adding or subtracting dollars and cents, line up the decimal points. Example: $2.5 + $.15 + $0.60 = 1 $2.5 $.15 + $0.60 $.2 Write a multiplication problem for each of these addition problems. 1. + + + + = 2. 13 + 13 + 13 = 3. Write a multiplication problem that shows how to find the number of Xs. X X X X X X X X X X X X X X X X X X X X X X X X X X X X Find each sum or difference. Remember to write the dollar sign.. $.1 + $1.12 5. $6.3 $3.55 6. $11.2 + $10.6. $5.60 $3. 1 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 5
Missing Numbers in Subtraction Lesson 1 1 To find missing numbers in subtraction: If the top number is missing, add. a a 11 If the bottom number is missing, subtract. 15 n 15 n 6 To check your work, put the number you found back into the original problem, and perform the subtraction. Find each missing number. Check your answers. 1. Bottom number missing, subtract. 2. Top number missing, add. 1 b n 2 3. 16 x. n 5 13 5. Write a subtraction problem with the top number missing. Solve and show how to check. 6. Write a subtraction problem with the bottom number missing. Solve and show how to check. Saxon Math Intermediate 5 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 15
Making a Multiplication Table Lesson 15 15 If you know one fact family, you know four facts. 3 = 12 3 = 12 12 3 = 12 = 3 Factors are numbers that are multiplied together to get a product (the answer). The Commutative Property of Multiplication says that the order of the numbers does not matter. 5 = 20 5 = 20 The Property of Zero for Multiplication says any number times zero equals zero. 2 0 = 0 The Identity Property of Multiplication says that any number times one equals itself. 2 1 = 2 Practice reciting the four facts for each triangle by covering one number in the triangle at a time. 12 1 21 2 3 3 3 3 6 3 3 16 2 2 32 36 6 36 2 5 6 6 6 6 6 56 63 6 2 1 Find each product. 1. 3 = 2. = 3. 6 3 =. 10 0 = 5. 10 = 6. 6 =. The answer to a multiplication problem is called the. The numbers we multiply together are called. 16 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 5
Word Problems About Separating Lesson 16 16 In word problems about separating, the missing number can be the top number, the bottom number, or the difference. If the top number is missing, add. Some Some went away What is left m $13 $20 $20 $13 $33 If the bottom number is missing, subtract. Some Some went away What is left $33 m $13 $33 $13 $20 If the difference is missing, subtract as usual. Some Some went away What is left $33 $13 m $33 $13 $20 1. 600 students started a painting club for the city. In the sixth month there were 313 members. How many members dropped out of the club? 2. Edwin paid $65.00 for 5 tickets to the school play. He had $12.00 left. How much did Edwin have before he bought the tickets? 3. An adventure team has members. 1 of the members went camping, while the others went rafting. How many members went rafting? Saxon Math Intermediate 5 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 1
Multiplying by One-Digit Numbers Lesson 1 1 Learn to carry using mental math. If the carry number is more than 5, write it down instead. Example: 3 3 5 = 15 05 Write 5 in the ones column. 5 Carry the 1 mentally. 3 5 = 20 05 Add the carried 1 to the product (20 + 1 = 21). 215 Write the 21. When multiplying money amounts that have decimals, show two decimal places in the answer for cents. 1. 3 5 2. 0 3. $0.5. 320 5. $6.2 6. 0 6. $35. 50. $2.3 3 1 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 5
Three Factors and Missing Factors We can multiply factors in any order. 3 5 3 5 3 5 Lesson 1 1 15 = 60 12 5 = 60 3 20 = 60 To find missing factors, first recall any multiplication facts that might use the same numbers. 1. 5 3 = 2. 10 6 2 = 3. 2 3 =. 5 3 1 = Find each missing factor. 5. m = 2 6. 5 b = 5 m = b =. 5 = n 2. 2 = p n = p = Saxon Math Intermediate 5 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 1
Relationship between Multiplication and Division Lesson 1 1 If you know one fact family, you know two multiplication facts and two division facts: 35 5 5 35 5 35 5 ) 35 5 ) 35 Find the missing number in each triangle (fact family). 1. 3 ) 1 1 2. ) 20 20 3 3. 6 ) 36 36. 10 ) 0 0 6 10 5. ) 63 63 6. ) 2 2. ) 56 56. 5 ) 55 55 5 20 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 5
Three Ways to Show Division Below are three ways to show division: _ divisor ) dividend dividend divisor dividend divisor Box Sign Bar The answer to a division problem is called the quotient. Say the dividend first. Lesson 20 20 1. Show 15 divided by 3 in three different forms: ) 2. Use three different division forms to show 32 divided by. ) Use words to show how each division problem is read. 3. ) 2 divided by.. 2 6 divided by. 5. 2 divided by. Rewrite each division problem with a division box. 6. 5 6. 0 ) ). Identify the quotient, dividend, and divisor in this equation: 2 3 = quotient dividend divisor Saxon Math Intermediate 5 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 21