Saxon 6/5 math pdf download

In each case the sum is zero. Notice also that 1 times any number is that number. The fact that one times a number equals the number might seem obvious, but it is also very powerful. This fact is called the identity property of multiplication. It is used in every math course you will take from now until the end of high school.

Using Activity Master 9, make a multiplication table with 11 columns and 11 rows. Be sure to line up the numbers carefully. Use your multiplication table to answer the Lesson Practice problems below. Write that number as your answer. Find each product: e. The answer to a multiplication problem is called the product. What do we call the numbers that are multiplied together?

Draw a number line marked with integers from —3 to How many unit segments are there from 3 to 8? Kobe was the ninth person in line.

How many people 7 were in front of him? Mary used tally marks to count the number of trucks, cars, and motorcycles that drove by her house. Thirteen cars drove by her house. Write two addition facts and two subtraction facts for the 8 fact family 1, 9, and For problems 5 and 6, write an equation and find the answer.

Hint: Problem 6 has three addends. During the first four weeks of school, Gretta read two books totaling pages. If the first book was pages long, how long was the second book? Chang read three books. The first was pages, the second pages, and the third pages. What was the total number of pages in the three books? Write the smallest three-digit even number that has the 2 digits 1, 2, and 3. Try to answer the comparison without adding or multiplying. What term is missing in this counting sequence?

Lesson 15 71 Use digits to write eight hundred eighty dollars and 5 eight cents. A dozen is How many is half of half a dozen? Write a multiplication problem 13 that shows how to find the number of circles in this pattern. Two integers are indicated by arrows on this number line.

Write the two integers, using a comparison symbol to show which number is greater and which is less. In this lesson we will consider stories about separating.

Stories about separating have a subtraction pattern. Below are examples of stories about separating. After losing pounds, Jumbo still weighed pounds. How much did Jumbo weigh before he lost the weight? Four hundred runners started the race, but many dropped out along the way. If runners finished the race, then how many dropped out of the race? Then he spent some of his money, so some went away. He still had some money left. We write the equation using a subtraction pattern.

The answer is sensible because Jack has less money than he started with. The answer is correct. Example 2 After losing pounds, Jumbo still weighed pounds.

Before, Jumbo weighed Then Jumbo lost Jumbo still weighed W pounds — pounds pounds To find the first number of a subtraction problem, we add. Is it sensible? Is the arithmetic correct? We can check the arithmetic by using the answer in the original equation.

Before losing weight, Jumbo weighed pounds. Some dropped out Since we expect the number of runners who dropped out to be less than the number who started, our answer is reasonable. There were runners who dropped out of the race. Then answer the question. Five hundred runners started the race. Only finished the race. How many runners dropped out of the race? How much money did Jamal have before he paid the rent?

The 26 members of the posse split into two groups. Fourteen members rode into the mountains, while the rest rode down to the river. How many members rode down to the river? For the following equation, write a story problem about separating. Then answer the question in your story problem.

By how many dollars did the price increase? Use an addition pattern to solve the problem. For the fact family 6, 8, and 14, write two addition facts 8 and two subtraction facts. For problems 5—7, write an equation and find the answer. Pink ink spots were here, and pink ink spots were there. Four hundred spots here, six hundred spots there, how many ink spots were everywhere?

The custodian put away 24 chairs, leaving 52 chairs in the room. How many chairs were in the room before the custodian put some away? Use a subtraction pattern to solve the problem. Then how much money did Jill have left? C 13 Think of two one-digit odd numbers. Multiply them. Is the product odd or even? Which of these is a horizontal line? Use digits and a comparison symbol to write this 4 comparison: Eight hundred forty is greater than eight hundred fourteen.

What number is missing in this counting sequence? The letter y stands for what number in this equation? What word is used to describe a line that goes straight up 12 and down?

How many cents is half a dollar? How many cents is half 2 of half a dollar? Write a multiplication problem 13 that shows how to find the number of small squares in this rectangle. Use this information to 16 write a story problem about separating.

Quarters are put into rolls of 40 quarters. Dimes are put into rolls of 50 dimes. One roll of quarters has the same value as how many rolls of dimes? How much would three tickets cost? To find the answer by adding, we add the price of three tickets.

First we multiply the 4 ones by 3. This makes 12 ones, which is the same as 1 ten and 2 ones. We write the 2 ones below the line and the 1 ten above the tens column. Then we add the 1 ten to make 7 tens. We see that the total is 3 dimes and 12 pennies. Since 12 pennies is more than a dime, we trade ten pennies for a dime.

The result is 4 dimes and 2 pennies. However, we will use this problem to practice the pencil-and-paper algorithm for multiplication. First we multiply 5 pennies by 6, which makes 30 pennies. Then we add the 3 dimes to make 15 dimes. Finally, we insert the decimal point two places from the right-hand end and write the dollar sign. We multiply 5 ones by 6 and get Next we multiply 2 tens by 6, making 12 tens, and add the 3 tens to get 15 tens.

Then we multiply 3 hundreds by 6 and add the 1 hundred. How much would four tickets cost? Solution We may find the answer by adding or by multiplying. At that price, how much would four tires cost? Show how to find the total cost by adding and by multiplying. Nathan had five quarters in his pocket. Altogether, how much did the milk cost? Find the answer by multiplying. Draw a vertical line segment.

Cedric read 3 books. Each book had pages. How many pages did Cedric read? Find the answer once by adding and again by multiplying. The spider spun its web for 6 hours the first night and for 11 some more hours the second night.

If the spider spent a total of 14 hours spinning its web those two nights, how many hours did the spider spend the second night? How much money did Carmela have before she bought the notebook? Altogether, how much did the pens cost? Think of two one-digit even numbers. Use digits and a comparison symbol to write this 7 comparison: Five hundred four thousand is less than five hundred fourteen thousand.

Which digit in shows the number of hundreds? These tally marks represent what number? Is the th term of this counting sequence odd or even? Use the commutative property to 15 change the order of factors.

Then multiply. Show your work. Copy the problem and fill in the missing digits. Remember that numbers multiplied together are called factors.

In the problem below we see three factors. Then we multiply the product we get by the third factor. First we multiply 9 by 8 to get Then we multiply 72 by 7 to get Sometimes, changing the order of the factors can make a problem easier.

We may choose an order of factors that makes the problem easier. In this problem we choose to multiply 6 and 5 first; then we multiply the resulting product by 3. If we multiply 5 by 7 first, then we must multiply 35 by But if we multiply 5 by 12 first, then we would multiply 7 by 60 next. The second way is easier and can be done mentally. We rearrange the factors to show the order in which we choose to multiply. Solution We may count all the blocks, or we may multiply three numbers.

We can see that the top layer has 2 rows of 3 blocks. Since there are two layers, we multiply the number in each layer by 2. Missing Now we will practice finding missing factors in multiplication numbers in problems. In this type of problem we are given one factor and a multiplication product. Now we are ready to find the missing factors. There are many ways to do this. We could also use a multiplication table.

We see that the missing factors are 6, 8, and Show which numbers you chose to multiply first. How many blocks were used to build this figure? Write a multiplication problem that provides the answer. Lesson 18 Find each missing factor: f. Draw a horizontal line and a vertical line. Then write the words horizontal and vertical to label each line. How many pounds did Reggie lose?

In one class there are 33 students. Fourteen of the students are boys. How many girls are in the class? In another class there are 17 boys and 14 girls. How many students are in the class? Altogether, how much money did the folders cost? Think of a one-digit odd number and a one-digit even number. Use digits and symbols to write this comparison: 4, 15 Eight times eight is greater than nine times seven. For the fact family 7, 8, and 15, write two addition facts 8 and two subtraction facts.

Write a multiplication fact that 13 shows the number of squares in this rectangle. Write a three-factor multiplication 18 fact that shows the number of blocks in this figure.

What are the next three integers in this counting sequence? When Kurt turned two years old, he was 3 feet tall. If the rule works for Kurt, about how tall will he be as an adult?

A division problem is like a miniature multiplication table. The two factors are outside the box. One factor is in front, and the other is on top. In the problem below, the factor on top is missing. We need to find the number that goes above the box. Multiplication and division are inverse operations. One operation undoes the other.

If we start with 5 and multiply by 6, we get a product of If we then divide 30 by 6, the result is 5, the number we started with. The division by 6 undid the multiplication by 6. Using the commutative property and inverse operations, we find that the three numbers that form a multiplication fact also form division facts. Example 4 Write two multiplication facts and two division facts for the fact family 5, 6, and Write two multiplication facts and two division facts for the fact family 3, 8, and By how many dollars had the dress been marked down?

Room 15 collected aluminum cans. Room 16 collected cans. Room 17 collected cans. How many cans did the three rooms collect in all? There are 5 rows of desks with 6 desks in each row. For the fact family 7, 8, and 56, write two multiplication facts and two division facts.

R T 14 — Use digits and symbols to write this comparison: 4, 15 Eight times six is less than seven times seven. Ed cut a inch long piece of licorice in half.

How long 2 was each half? Write a multiplication fact that 13 shows how many squares cover this rectangle. Write a three-factor multiplication 18 fact that shows how many blocks form this figure.

The Mississippi River begins in Minnesota. From there it 7 flows miles to the Gulf of Mexico. The Missouri River is miles long and begins in Montana. The Colorado River is the longest river in the U. It starts in the Rocky Mountains and flows miles to the Gulf of California. Write the names of the three rivers in order from shortest to longest. In the second we use a division sign. In the third we use a division bar. To solve longer division problems, we usually use the first form.

In later math courses we will use the third form more often. We should be able to read and solve division problems in each form and to change from one form to another. Three numbers are involved in every division problem: 1. The location of these numbers in each form is shown below.

To show division with a division bar, we write the dividend on top. Lesson 20 93 Example 4 In the following equation, which number is the divisor, which number is the dividend, and which number is the quotient? The answer is the quotient, 8. Draw a horizontal number line marked with even integers from —6 to 6. Write two multiplication facts and two division facts for the fact family 4, 9, and Jim reads 40 pages per day.

How many pages does Jim read in 4 days? There are students at Gidley School. If there are girls, how many boys are there?

Write an equation and find the answer. What is the sum of five hundred twenty-six and six hundred eighty-four? Compare: 15 3 4, 20 Try multiplying. What was the total cost of the five notebooks? Z R 14 — Use digits and symbols to write this comparison: 4 Ten times two is greater than ten plus two. Lesson 20 95 What are the next three terms in this counting sequence? In this equation, which number is the divisor?

Write a multiplication equation 13 that shows the number of squares in this rectangle. We use two numbers to write a fraction.

The bottom number, the denominator, shows the number of equal parts in the whole. The top number, the numerator, shows how many of the equal parts are counted. The denominator of the fraction shows the number of equal groups. We divide the total by the denominator to find the number in each group. Example 1 Half of the 18 students in the class are girls. We find the number in each group by dividing by 2. This means there are 9 girls in the class.

Example 2 a How many cents is one fourth of a dollar? Solution The word fourth means that the whole dollar is divided into four equal parts. Since four quarters equals a dollar, one fourth of a dollar equals a quarter, which is twenty-five cents.

Three fourths of a dollar three quarters equals seventy-five cents. Example 3 One tenth of the 30 students earned an A on the test. How many students earned an A? So 3 students earned an A. Use this information to answer problems 1—4: There were 20 pumpkins in the garden.

One fourth of the pumpkins were too small, one tenth were too large, and one half were just the right size. The rest of the pumpkins were not yet ripe. How many pumpkins were too small? How many pumpkins were too large? How many pumpkins were just the right size? How many pumpkins were not yet ripe? He could carry a pack F his weight for two miles without resting.

Sam weighs 80 pounds. How heavy a pack could Sam carry for 2 miles without resting? How heavy a pack could Sam carry for only half a mile without resting? If you wish to color-code the manipulatives, photocopy each master on a different color of construction paper, or, before cutting, have students color both sides of the fraction circles using different colors for different masters. Following the activity, each student may store the fraction manipulatives in an envelope or plastic bag for use in later lessons.

Preparation: Distribute materials. Have students separate the fraction manipulatives by cutting out the circles and cutting apart the fraction slices along the lines. Use your fraction manipulatives to help with each exercise below. Show that two quarters equals one half. Two quarters of a circle is what percent of a whole circle? How many tenths equal one half? Investigation 2 99 Is one quarter plus two tenths more or less than one half? One fourth of a circle plus two tenths of a circle is what percent of a whole circle?

One half of a circle plus four tenths of a circle is what percent of a whole circle? Two half circles can be put together to form a whole circle.

Use your fraction manipulatives to find other ways to form a whole circle. Write an equation for each way you find. One fourth of a circle plus one tenth of a circle is what percent of a whole circle?

Two fourths of a circle plus two tenths of a circle is what percent of a whole circle? What percent of a circle is one half plus one fourth plus one tenth? What fraction piece covers one half of a half circle? List all the uppercase and lowercase letters that enclose at least one area. Stories about equal groups have a multiplication pattern. Altogether, how many students are in the four classes? The coach separated the 48 players into 6 teams with the same number of players on each team.

How many players were on each team? Monifa raked up 28 bags of leaves. On each trip she could carry away 4 bags. How many trips did it take Monifa to carry away all the bags? The answer is 3. These numbers are related by multiplication.

The total number in all groups is the product. If the total is missing, we multiply to find the missing number. Example 1 At Lincoln School there are 4 classes of fifth graders with 30 students in each class.

Altogether, how many students are in the 4 classes? Solution This story is about equal groups. We are given the number of groups 4 classes and the number in each group 30 students. We write an equation. There are many more students in four classes than in one class, so is reasonable. There are students in all 4 classes. Example 2 The coach separated 48 players into 6 teams with the same number of players on each team.

The groups are teams. We are given the number of groups 6 teams and the total number of players 48 players. We are asked to find the number of players on each team. The answer is reasonable because 6 teams of 8 players is 48 players in all. Example 3 Monifa raked up 28 bags of leaves. Solution The objects are bags, and the groups are trips. The missing number is the number of trips.

We show two ways to write the equation. On the shelf were 4 cartons of eggs. There were 12 eggs in each carton. How many eggs were in all four cartons?

Thirty desks are arranged in 6 equal rows. How many desks are in each row? Twenty-one books are stacked in piles with 7 books in each pile. How many piles are there? If 56 zebus were separated into 7 equal herds, then how many zebus would be in each herd? The coach separated the PE class into 8 teams with the same number of players on each team.

If there are 56 students in the class, how many are on each team? Use a multiplication pattern. Tony opened a bottle containing 32 ounces of milk and poured 8 ounces of milk into a bowl of cereal. How many ounces of milk remained in the bottle? The set of drums costs eight hundred dollars. The band has earned four hundred eighty-seven dollars. How much more must the band earn in order to buy the drums? Draw an oblique line. Write two multiplication facts and two division facts for the fact family 6, 7, and If a dozen items are divided into two equal groups, how 21 many will be in each group?

Use words to show how this problem is read: 20 10 2 What number is the dividend in this equation? Below is a story problem about equal groups. Saxon math programs produce confident students who are not only able to correctly compute, but also to apply concepts to new situations.

These materials gently develop concepts, and the practice of those concepts is extended over a considerable period of time. This is called "incremental development and continual review.

Both facets are then practiced together until another one is introduced. This feature is combined with continual review in every lesson throughout the year. Topics are never dropped but are increased in complexity and practiced every day, providing the time required for concepts to become totally familiar. The Facts Practice Workbook helps reinforce students' recall of basic facts and eliminates the need for costly and time-consuming photocopying.

Get Saxon Math 6 5 Books now! Download or read online Saxon Math written by Stephen Hake, published by Unknown which was released on Get Saxon Math Books now! Download or read online Resources in education written by Anonim, published by Unknown which was released on Get Resources in education Books now!

Download or read online The Educational Times and Journal of the College of Preceptors written by Anonim, published by Unknown which was released on Download or read online The Education Outlook written by Anonim, published by Unknown which was released on Get The Education Outlook Books now!

Download or read online The Spectator written by Anonim, published by Unknown which was released on