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1.8: Multiply Whole Numbers (Part 2)

1.8: Multiply Whole Numbers (Part 2)


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Translate Word Phrases to Math Notation

Earlier in this section, we translated math notation into words. Now we’ll reverse the process and translate word phrases into math notation. Some of the words that indicate multiplication are given in Table (PageIndex{3}).

Table (PageIndex{3})
OperationWord PhraseExampleExpression
Multiplicationtimes3 times 83 × 8, 3 • 8, (3)(8),
productthe product of 3 and 8(3)8, or 3(8)
twicetwice 42 • 4

Example (PageIndex{12}): Translate and simplify

Translate and simplify: the product of (12) and (27).

Solution

The word product tells us to multiply. The words of (12) and (27) tell us the two factors.

the product of 12 and 27
Translate.12 • 27
Multiply.324

exercise (PageIndex{23})

Translate and simplify the product of (13) and (28).

Answer

(13 · 28); (364)

exercise (PageIndex{24})

Translate and simplify the product of (47) and (14).

Answer

(47 · 14); (658)

Example (PageIndex{13}): translate and simplify

Translate and simplify: twice two hundred eleven.

Solution

The word twice tells us to multiply by (2).

twice two hundred eleven
Translate.2(211)
Multiply.422

exercise (PageIndex{25})

Translate and simplify: twice one hundred sixty-seven.

Answer

(2(167)); (334)

exercise (PageIndex{26})

Translate and simplify: twice two hundred fifty-eight.

Answer

(2(258)); (516)

Multiply Whole Numbers in Applications

We will use the same strategy we used previously to solve applications of multiplication. First, we need to determine what we are looking for. Then we write a phrase that gives the information to find it. We then translate the phrase into math notation and simplify to get the answer. Finally, we write a sentence to answer the question.

Example (PageIndex{14}): multiply

Humberto bought (4) sheets of stamps. Each sheet had (20) stamps. How many stamps did Humberto buy?

Solution

We are asked to find the total number of stamps.

Write a phrase for the total.the product of 4 and 20
Translate to math notation.4 • 20
Multiply.
Write a sentence to answer the question.Humberto bought 80 stamps.

exercise (PageIndex{27})

Valia donated water for the snack bar at her son’s baseball game. She brought (6) cases of water bottles. Each case had (24) water bottles. How many water bottles did Valia donate?

Answer

Valia donated (144) water bottles.

exercise (PageIndex{28})

Vanessa brought (8) packs of hot dogs to a family reunion. Each pack has (10) hot dogs. How many hot dogs did Vanessa bring?

Answer

Vanessa bought (80) hot dogs.

Example (PageIndex{15}): multiply

When Rena cooks rice, she uses twice as much water as rice. How much water does she need to cook (4) cups of rice?

Solution

We are asked to find how much water Rena needs.

Write as a phrase.twice as much as 4 cups
Translate to math notation.2 • 4
Multiply to simplify.8
Write a sentence to answer the question.Rena needs 8 cups of water for cups of rice.

exercise (PageIndex{29})

Erin is planning her flower garden. She wants to plant twice as many dahlias as sunflowers. If she plants (14) sunflowers, how many dahlias does she need?

Answer

Erin needs (28) dahlias.

exercise (PageIndex{30})

A college choir has twice as many women as men. There are (18) men in the choir. How many women are in the choir?

Answer

There are (36) women in the choir.

Example (PageIndex{16}): multiply

Van is planning to build a patio. He will have (8) rows of tiles, with (14) tiles in each row. How many tiles does he need for the patio?

Solution

We are asked to find the total number of tiles.

Write as a phrase.the product of 8 and 14
Translate to math notation.8 • 14
Multiply to simplify.
Write a sentence to answer the question.Van needs 112 tiles for his patio.

exercise (PageIndex{31})

Jane is tiling her living room floor. She will need (16) rows of tile, with (20) tiles in each row. How many tiles does she need for the living room floor?

Answer

Jane needs (320) tiles.

exercise (PageIndex{32})

Yousef is putting shingles on his garage roof. He will need (24) rows of shingles, with (45) shingles in each row. How many shingles does he need for the garage roof?

Answer

Yousef needs (1,080) tiles.

If we want to know the size of a wall that needs to be painted or a floor that needs to be carpeted, we will need to find its area. The area is a measure of the amount of surface that is covered by the shape. Area is measured in square units. We often use square inches, square feet, square centimeters, or square miles to measure area. A square centimeter is a square that is one centimeter (cm.) on a side. A square inch is a square that is one inch on each side, and so on.

Figure (PageIndex{2})

For a rectangular figure, the area is the product of the length and the width. Figure (PageIndex{3}) shows a rectangular rug with a length of (2) feet and a width of (3) feet. Each square is (1) foot wide by (1) foot long, or (1) square foot. The rug is made of (6) squares. The area of the rug is (6) square feet.

Figure (PageIndex{3}): The area of a rectangle is the product of its length and its width, or 6 square feet.

Example (PageIndex{17}): area

Jen’s kitchen ceiling is a rectangle that measures (9) feet long by (12) feet wide. What is the area of Jen’s kitchen ceiling?

Solution

We are asked to find the area of the kitchen ceiling.

Write as a phrase.the product of 9 and 12
Translate to math notation.9 • 12
Multiply to simplify.
Write a sentence to answer the question.The area of Jen's kitchen ceiling is 108 square feet.

exercise (PageIndex{33})

Zoila bought a rectangular rug. The rug is (8) feet long by (5) feet wide. What is the area of the rug?

Answer

The area of the rug is (40) square feet.

exercise (PageIndex{34})

Rene’s driveway is a rectangle (45) feet long by (20) feet wide. What is the area of the driveway?

Answer

The area of the driveway is (900) square feet

Key Concepts

OperationNotationExpressionRead asResult
  • Multiplication Property of Zero
    • The product of any number and (0) is (0).
  • Identity Property of Multiplication
    • The product of any number and (1) is the number.
  • Commutative Property of Multiplication
    • Changing the order of the factors does not change their product.
  • Multiply two whole numbers to find the product.
    • Write the numbers so each place value lines up vertically.
    • Multiply the digits in each place value.
    • Work from right to left, starting with the ones place in the bottom number.
    • Multiply the bottom number by the ones digit in the top number, then by the tens digit, and so on.
    • If a product in a place value is more than (9), carry to the next place value.
    • Write the partial products, lining up the digits in the place values with the numbers above. Repeat for the tens place in the bottom number, the hundreds place, and so on.
    • Insert a zero as a placeholder with each additional partial product.
    • Add the partial products.

Glossary

product

The product is the result of multiplying two or more numbers.

Practice Makes Perfect

Use Multiplication Notation

In the following exercises, translate from math notation to words.

  1. 4 × 7
  2. 8 × 6
  3. 5 • 12
  4. 3 • 9
  5. (10)(25)
  6. (20)(15)
  7. 42(33)
  8. 39(64)

Model Multiplication of Whole Numbers

In the following exercises, model the multiplication.

  1. 3 × 6
  2. 4 × 5
  3. 5 × 9
  4. 3 × 9

Multiply Whole Numbers

In the following exercises, fill in the missing values in each chart.

In the following exercises, multiply.

  1. 0 • 15
  2. 0 • 41
  3. (99)0
  4. (77)0
  5. 1 • 43
  6. 1 • 34
  7. (28)1
  8. (65)1
  9. 1(240,055)
  10. 1(189,206)
  11. (a) 7 • 6 (b) 6 • 7
  12. (a) 8 × 9 (b) 9 × 8
  13. (79)(5)
  14. (58)(4)
  15. 275 • 6
  16. 638 • 5
  17. 3,421 × 7
  18. 9,143 × 3
  19. 52(38)
  20. 37(45)
  21. 96 • 73
  22. 89 • 56
  23. 27 × 85
  24. 53 × 98
  25. 23 • 10
  26. 19 • 10
  27. (100)(36)
  28. (100)(25)
  29. 1,000(88)
  30. 1,000(46)
  31. 50 × 1,000,000
  32. 30 × 1,000,000
  33. 247 × 139
  34. 156 × 328
  35. 586(721)
  36. 472(855)
  37. 915 • 879
  38. 968 • 926
  39. (104)(256)
  40. (103)(497)
  41. 348(705)
  42. 485(602)
  43. 2,719 × 543
  44. 3,581 × 724

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.

  1. the product of 18 and 33
  2. the product of 15 and 22
  3. fifty-one times sixty-seven
  4. forty-eight times seventy-one
  5. twice 249
  6. twice 589
  7. ten times three hundred seventy-five
  8. ten times two hundred fifty-five

Mixed Practice

In the following exercises, simplify.

  1. 38 × 37
  2. 86 × 29
  3. 415 − 267
  4. 341 − 285
  5. 6,251 + 4,749
  6. 3,816 + 8,184
  7. (56)(204)
  8. (77)(801)
  9. 947 • 0
  10. 947 + 0
  11. 15,382 + 1
  12. 15,382 • 1

In the following exercises, translate and simplify.

  1. the difference of 50 and 18
  2. the difference of 90 and 66
  3. twice 35
  4. twice 140
  5. 20 more than 980
  6. 65 more than 325
  7. the product of 12 and 875
  8. the product of 15 and 905
  9. subtract 74 from 89
  10. subtract 45 from 99
  11. the sum of 3,075 and 950
  12. the sum of 6,308 and 724
  13. 366 less than 814
  14. 388 less than 925

Multiply Whole Numbers in Applications

In the following exercises, solve.

  1. Party supplies Tim brought 9 six-packs of soda to a club party. How many cans of soda did Tim bring?
  2. Sewing Kanisha is making a quilt. She bought 6 cards of buttons. Each card had four buttons on it. How many buttons did Kanisha buy?
  3. Field trip Seven school busses let off their students in front of a museum in Washington, DC. Each school bus had 44 students. How many students were there?
  4. Gardening Kathryn bought 8 flats of impatiens for her flower bed. Each flat has 24 flowers. How many flowers did Kathryn buy?
  5. Charity Rey donated 15 twelve-packs of t-shirts to a homeless shelter. How many t-shirts did he donate?
  6. School There are 28 classrooms at Anna C. Scott elementary school. Each classroom has 26 student desks. What is the total number of student desks?
  7. Recipe Stephanie is making punch for a party. The recipe calls for twice as much fruit juice as club soda. If she uses 10 cups of club soda, how much fruit juice should she use?
  8. Gardening Hiroko is putting in a vegetable garden. He wants to have twice as many lettuce plants as tomato plants. If he buys 12 tomato plants, how many lettuce plants should he get?
  9. Government The United States Senate has twice as many senators as there are states in the United States. There are 50 states. How many senators are there in the United States Senate?
  10. Recipe Andrea is making potato salad for a buffet luncheon. The recipe says the number of servings of potato salad will be twice the number of pounds of potatoes. If she buys 30 pounds of potatoes, how many servings of potato salad will there be?
  11. Painting Jane is painting one wall of her living room. The wall is rectangular, 13 feet wide by 9 feet high. What is the area of the wall?
  12. Home décor Shawnte bought a rug for the hall of her apartment. The rug is 3 feet wide by 18 feet long. What is the area of the rug?
  13. Room size The meeting room in a senior center is rectangular, with length 42 feet and width 34 feet. What is the area of the meeting room?
  14. Gardening June has a vegetable garden in her yard. The garden is rectangular, with length 23 feet and width 28 feet. What is the area of the garden?
  15. NCAA basketball According to NCAA regulations, the dimensions of a rectangular basketball court must be 94 feet by 50 feet. What is the area of the basketball court?
  16. NCAA football According to NCAA regulations, the dimensions of a rectangular football field must be 360 feet by 160 feet. What is the area of the football field?

Everyday Math

  1. Stock market Javier owns 300 shares of stock in one company. On Tuesday, the stock price rose $12 per share. How much money did Javier’s portfolio gain?
  2. Salary Carlton got a $200 raise in each paycheck. He gets paid 24 times a year. How much higher is his new annual salary?

Writing Exercises

  1. How confident do you feel about your knowledge of the multiplication facts? If you are not fully confident, what will you do to improve your skills?
  2. How have you used models to help you learn the multiplication facts?

Self Check

(a) After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

(b) On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?


4th Grade Fractions – Part 2

The Common Core Standards for 4th graders have several fraction standards. The following refer to the third of the 4th Grade Fraction standards. The third standard is broken into 4 different skills. It is important that 4th graders are fluent in these concepts and skills in order to move to the more complicated skills for middle school math.

STANDARD: CCSS.Math.Content.4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

  • PART A of STANDARD: CCSS.Math.Content.4.NF.B.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

This section of the third 4th grade fraction expects that a child understands that refers to two of the ‘s of a whole. So to add to would be the addition of two of the ‘s to one of the ‘s so the sum would be ‘s.

Additionally, would result in one of the ‘s of a whole subtracted by one of the ‘s would be .

Where many math students are taught that to solve an addition or subtraction problem ‘just add or subtract the numerator when the denominator is the same’, the Common Core expects that students have a deep understanding of why the process works, not just to memorize the ‘procedure’. For this reason, it is important that children have applied understanding in a real-world concept.

  • PART B of STANDARD: CCSS.Math.Content.4.NF.B.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 3/8 = 1/8 + 2/8 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

So, using the illustrations above representing 2 wholes and ths, children should be able to recognize that it is equal to + + . This is an important concept as children begin to move toward the next standards where they will need to add and subtract mixed numbers.

  • PART C of STANDARD: CCSS.Math.Content.4.NF.B.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

This standard expects that children will recognize that mixed numbers can be deconstructed into fractions with common denominators. An example would be:

added to resulting in 5 added to to equal 6.

  • PART D of STANDARD: CCSS.Math.Content.4.NF.B.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

This standard expects children to be able to apply the addition and subtraction in real-world type problems. The children should be able to construct models, if necessary, to help to solve the problem. An example of an appropriate problem might be:

The Smith family ate dinner at a local pizza restaurant and were expecting to be joined by the Taylor family. After the order was placed, the Taylor family had an emergency and were unable to join the Smiths. After eating their dinner, the Smith’s took pizzas home to eat later. Jon and Samantha Smith each ate for lunch the next day. How much pizza was left for the family dinner that night?

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How to use Simple Number Sense Activities to Boost Part Whole Thinking

THIS POST CONTAINS AFFILIATE LINKS. THIS MEANS, THAT AT NO ADDITIONAL COST TO YOU, I WILL EARN A COMMISSION IF YOU CHOOSE TO MAKE A PURCHASE. I HAVE PERSONALLY USED THESE RESOURCES AND WOULD NOT RECOMMEND THEM IF I DID NOT APPRECIATE THE QUALITY OF THE RESOURCE PRIOR TO RECOMMENDATION.

That moment when one of your first graders tells you, in October, that 24 + 34 is 58 “because 20 and 30 is 50 and 4 and 4 is 8 so it must be 58!” You haven’t done any number sense activities around 2-digit addition but you KNOW that student “has number sense”. They must just have a mind for math.

One of the most recognizable tenents of number sense is flexible thinking. The good news is that, like anything else, this is not a “you have it or you don’t” proposition for your students. You can BUILD this flexible part-whole thinking in your students. And if you read to the end of this post, I have a set of free number sense activities to help you do just that!

Part-Whole Thinking in Kindergarten

In kindergarten, we see this type of thinking built when we ask students to decompose numbers to 10. Students are playing simple shake and spill games to practice number combinations for numbers up to ten…. and with extra attention to partners of 10!

Later in the kindergarten year, your students decompose teen numbers into a ten and “some” ones. These activities build both number sense AND a foundation for place value understanding!

Part-Whole Thinking in 1st Grade

In first grade, your students are applying their understanding of part-whole thinking to solve addition and subtraction facts. For example, students who are using the “make a ten” strategy to add numbers together will be decomposing an addend to make partners of ten and composing a ten and some ones to create a teen number.

Yes. ALL of those kindergarten part-whole activities are synthesized together and applied to first grade standards.

Do you have a first-grade student who is struggling with these number sense activities? Go back and check their fluency with number decomposition for all numbers to 10 and allow your students to play simple activities like Shake & Spill or Break a Rod to become fluent in decompositions to ten.

While your students are applying the decompositions they learned in kindergarten, you are also studying place value to prepare your students for second grade. 1st Grade students are composing and decomposing so that they understand 2-digit numbers as tens and ones.

Part-Whole Thinking in 2nd Grade

Are you starting to see a pattern? In first grade your students worked to understand 2-digit numbers by composing and decomposing tens and ones. In second grade, your students are now applying this understanding so that they can flexibly add and subtract numbers to 100 using strategies based on place value.

Have students who are struggling? By 2nd grade, your students have had more opportunity for gaps. At this point, you will need to go back and check your students’ decompositions for numbers to 10 along with your students understanding of 2-digit numbers as tens and ones.

Those SAME number sense activities you used for 1st graders can apply here as well! Allow your students to play shake and spill but, this time, write 󈫺” on each of the chips your students are spilling out so that they can practice composing and decomposing decade numbers.

Part-Whole Thinking in Third Grade

Part-Whole thinking becomes more complex in third grade as you add on additional topics of study. In third grade, your students are becoming flexible “part-whole-thinkers” relative to factors of numbers to 100 as well as unit fractions.

The main aim in 3rd grade is much like the goals of kindergarten- become fluent in terms of composing and decomposing equal groups and become fluent in terms of composing and decomposing fractions with unit fractions.

Your students will ALSO start to apply their understanding of decompositions of equal groups in order to use the distributive property to multiply.

Part-Whole Thinking in 4th Grade

In third grade, you laid a foundation for multiplication and work with fractions. In fourth grade, you will apply these understandings further.

In terms of multiplication, your students are applying their place value understanding (from back in 1st and 2nd grade!) to multiply larger numbers using strategies such as the area model.

Your students are also applying understanding of unit fractions to perform fraction operations such as addition and subtraction.

Part-Whole Thinking in 5th Grade

In 5th grade, your students are expected to compose and decompose whole numbers, fractions, and decimals in order to flexibly apply all 4 operations.

If you have students who are struggling to think flexibly in 5th grade you have a lot of ground to cover in order to “drill back” to find where the breakdown occurred. The most simple way to accomplish this task is to begin your number sense activities with WHOLE NUMBERS.

  • Determine whether or not your students are fluent with decompositions of numbers to 10
  • Move to learn if your students are fluent decomposing 2, 3, 4, 5 or 6 digit numbers into unit form.
  • Ask your students to perform SIMPLE whole number calculations mentally such as 󈬚 + 23” in order to determine whether or not your students are comfortable breaking a number apart to solve. Yes. You may have 5th-grade students who fall out at this point. Go back and solidify their understanding at THIS LEVEL. Trying to move ahead will do your students no service if you skip this foundation.
  • Continue layering on one skill at a time using increasingly complex numbers until your students are working at the 5th-grade level.

Number Sense Activities for Part-Whole Thinking

Word Problems- State a simple open-ended word problem for your students that asks your student to break a whole into parts. (Ex: I have 24 flowers in my garden laid out in rows of 3. Some rows are made of tulips and some rows are made of daisies. Draw a picture that shows 3 different ways my garden might look and find the total number of daisies and tulips in my garden in each drawing).


Mathematics Grade 3 Practice Questions

1. C: You can think of 6 4 as six groups of four objects. If you buy 6 binders for $4 each, then the total amount of money you spend is $4 + $4 + $4 + $4 + $4 + $4, which is six groups of $4.

2. A: You can think of 24 / 8 as equally dividing 24 objects into eight groups. If 24 slices of pizza are divided between 8 people, then you have to divide the slices into eight groups.

3. B: There are 32 crayons that are evenly divided among 8 students. Therefore, you can find number of crayons each student gets by dividing 32 by 8. The result is 4 crayons each.

4. B: Use trial-and-error to find a number that you can multiply by 4 to get 20. Since 4 1 means four groups of one object, 4 1 = 4. Try using other numbers for missing number.

4 2 = 8
4 3 = 12
4 4 = 16
4 5 = 20

Therefore, the missing number is 5.

Numbers and Operations in Base Ten

5. C: To round to the nearest ten, first look at the digit in the tens place, which is a 3. Thus, if you round 437 down, the 3 will stay the same, and the answer will be 430. Conversely, if you round it up, the 3 will go up to a 4, and the answer will be 440. Finally, look at the number after the 3, which is a 7. Since it is greater than 5, you should round up. Therefore, the answer is 440.

6. B: Set up the addition vertically, making sure to line up the digits by place value.

Numbers and Operations Fractions

7. A: A fraction 1/b can be represented as a whole partitioned (or divided) into b equal parts. For example, if a figure is divided into 2 equal parts, then each part represents 1/2 of the whole. Notice that the rectangle in the problem is divided into 5 equal parts and one of those parts is shaded. Therefore, it represents the fraction 1/5.

8. B: If you partition (or divide) the space between 0 and 1 on a number line into b equal parts, then each part has size 1/b, and the first division to the right of zero represents the point 1/b. For example, if you divide the space between 0 and 1 on a number line into three equal parts, then each part has size 1/3 and the first endpoint represents the point 1/3.

Therefore, to find 1/4, divide the space between 0 and 1 on a number line into four equal parts. The first endpoint represents 1/4.

Measurement and Data

9. D: To calculate when her lunch break finishes, add 30 minutes to the time it starts, 12:15. Since we know that 15 + 30 = 45, the correct answer is 12:45.

10. D: Since each penny has a mass of about 3 grams, you can find the total mass of 6 pennies by adding 3 + 3 + 3 + 3 + 3 + 3. In other words, you have to multiply 3 6. Thus, the total mass is 18 grams.


1.8: Multiply Whole Numbers (Part 2)

Before you understand Ascending Order of Decimals: You must know:

Arranging decimals in ascending order means that arranging decimals in increasing order i.e. we start with the smallest decimals and then next larger decimal but & so on till we reach the largest decimal which is written at the last place.

Follow the following steps for arranging decimals in ascending order:

These Steps are repeated in similar ways till we are left with only one decimal, whose whole number part is the largest among whole number parts of all the given decimals and it would be written at the last place of the order.

Example - Let's try arranging the following series of decimals in ascending order:
181.98, 64.78, 345.75, 9.72, 0.05, 1.8

Solution: This proceeds in the following steps:

Ascending Order Series = 0.05

It is larger than the 0, which is the whole number part of decimal 0.05, but smaller than whole number part of remaining decimals.

So 1.8 is written next to decimals 0.05 in the ascending order and we get series:

Ascending Order Series = 0.05, 1.8

9 is the whole number part of decimal 9.72

It is larger than the 1, which is the whole number part of decimal 1.8, but smaller than whole number part of remaining decimals.

So 9.72 is written next to 1.8 in the ascending order and we get series:

Ascending Order Series = 0.05, 1.8, 9.72

It is larger than the 9, which is the whole number part of decimal 9.72, but smaller than whole number part of remaining decimals.

So 64.78 is written next to 9.72 in the ascending order and we get series:

Ascending Order Series = 0.05, 1.8, 9.72, 64.78

It is larger than the 64, which is the whole number part of decimal 64.78, but smaller than whole number part of remaining decimals.

So 181.98 is written next to 64.78 in the ascending order and we get series:

Ascending Order Series = 0.05, 1.8, 9.72, 64.78, 181.98

Since decimal 345.75, whose whole number part is 345 and the largest among whole numbers part of all the given decimals, so 345.75 would be written at the last place of the ascending order and we get complete series:


Algebra Sleuth: Proof that 1 = 2?

Challenge your high school student to find the flaw in this short mathematical proof that one is equal to two. This activity provides a good review of basic math principals and the structure of mathematical proofs. It&rsquos also a good reminder that knowing math principals is good protection against getting tricked.

What You Need:

What You Do:

  1. Show your teen the proof.
  2. Ask her to tell you which step is invalid. She should determine both which number is wrong, and why.
  3. Help her keep going until she understands the answer.

The Proof that 2 = 1

2) a 2 = ab 2) Multiply both sides by a

3) a 2 -b 2 = ab-b 2 3) Subtract b 2 from both sides

4) (a+b)(a-b) = b(a-b) 4) Factor both sides

5) (a+b) = b 5) Divide both sides by (a-b)

6) a+a = a 6) Substitute a for b

8) 2 = 1 8) Divide both sides by a

Solution:

Part one: Step five is wrong. The rules of mathematics do not allow us to divide by zero.

Since a and b are equal, (a-b) = 0. Therefore, we cannot divide by (a-b)!

Note: To explain why you can't divide something by zero, ask your student how she would divide a pizza into 0 pieces. Impossible! The fewest number of pieces she could make would be one piece&mdashthe whole pizza!


1.8: Multiply Whole Numbers (Part 2)

Before you understand Descending Order of Decimals: You must know:

Arranging decimals in descending order means that arranging decimals in decreasing order i.e. we start with the largest decimals and then next 2nd largest decimal & so on till we reach the smallest decimal which is written at the last place.

Follow the following steps for arranging decimals in descending order:

These Steps are repeated in similar ways till we are left with only one decimal, whose whole number part is the smallest among whole number parts of all the given decimals and it would be written at the last place of the order.

Example - Let's try arranging the following series of decimals in descending order:
181.98, 64.78, 345.75, 9.72, 0.05, 1.8

Solution: This proceeds in the following steps:

And it is smaller than the 345, which is the whole number part of decimal 345.75, but larger than whole number part of remaining decimals.

So 181.98 is written next to decimals 345.75 in the descending order and we get series:

Descending Order Series = 345.75, 181.98

And it is smaller than the 181, which is the whole number part of decimal 18.98, but larger than whole number part of remaining decimals.

So 64.78 is written next to 181.98 in the descending order and we get series:

Descending Order Series = 345.75, 181.98, 64.78

And it is smaller than the 64, which is the whole number part of decimal 64.78, but larger than whole number part of remaining decimals.

So 9.72 is written next to 64.78 in the descending order and we get series:

Descending Order Series = 345.75, 181.98, 64.78, 9.72

And it is smaller than the 9, which is the whole number part of decimal 9.72, but larger than whole number part of remaining decimals.

So 1.8 is written next to 9.72 in the descending order and we get series:

Descending Order Series = 345.75, 181.98, 64.78, 9.72, 1.8

Since decimal 0.05, whose whole number part is 0 and the smallest among whole numbers part of all the given decimals, so 0.05 would be written at the last place of the descending order and we get complete series:


Dubmire Primary Academy

Class Dojo can be used for communication between teachers and parents during school time.

Home-learning

Monday 5th July 2021

Name
05.07.2021 Maths Slides.pdf Download
05.7.2021 - Maths Worksheet.pdf Download
5.7.21 - Homophones worksheet.pdf Download
5.7.21 - Homophones.pdf Download
5.7.21 - Slavery.pdf Download
Arithmetic Test for Daily Maths Meeting.pdf Download

Friday 2nd July 2021

Name
02.07.2021 Maths Slides.pdf Download
02.7.21 - Maths Worksheet.pdf Download
2.7.21 - Suffixes slides.pdf Download
2.7.21 - Suffixes worksheet.pdf Download
Music Lesson.pdf Download

Thursday 1st July 2021

Name
01.07.2021 Maths Slides.pdf Download
01.7.2021 - Maths Worksheet.pdf Download
1.7.21 - answering questions worksheet.pdf Download
1.7.21 - DMM.pdf Download
1.7.21 - Plastic Pollution text.pdf Download
1.7.21 - Reading Comprehension slides.pdf Download
R.E. lesson Monkey King Worksheet.pdf Download
RE Lesson The Monkey King Story#.pdf Download

Wednesday 30th June 2021

Name
30.06.2021 Maths Slides.pdf Download
30.6.21 - answering questions worksheet.pdf Download
30.6.21 - DMM.pdf Download
30.6.21 - Hansel and Gretel text.pdf Download
30.6.21 - Maths Worksheet.pdf Download
30.6.21 - RE - Loy Krathong.pdf Download
30.6.21 - Reading Comprehension slides.pdf Download

Tuesday 29th June 2021

Name
29.06.2021 Maths Slides.pdf Download
29.6.21 - answering questions worksheet.pdf Download
29.6.21 - Difference and discrimination.pdf Download
29.6.21 - DMM.pdf Download
29.6.21 - Maths Worksheet.pdf Download
29.6.21 - Reading Comprehension.pdf Download
29.6.21 - Three Billy Goats Gruff text.pdf Download
29.6.21 -Are-you-the-same-or-different-activity-sheet-english.pdf Download

Monday 28th June 2021

Name
28.06.2021 Maths Slides.pdf Download
28.6.21 - George Washington Carver.pdf Download
28.6.21 - Maths Worksheet.pdf Download
28.6.21 - The Tortoise and the Hare Reading Comprehension.pdf Download
T-T-28174-Significant-Individuals-Fact-File-Template.pdf Download

Homework in Year 2

Name
Homework Friday 25th June 2021.pdf Download
Homework Friday 18th June 2021.pdf Download
Homework Friday 11th June 2021.pdf Download
Homework Friday 28th May 2021.pdf Download
Homework Friday 21st May 2021.pdf Download
Homework Friday 14th May 2021.pdf Download
Homework Friday 7th May 2021.pdf Download
Homework Friday 30th April 2021.pdf Download
Homework Friday 23rd April 2021.pdf Download
Homework Friday 16th April 2021.pdf Download

Due to the recent announcement made by Boris Johnson, the school building is only open to children of key workers. Therefore, we are returning to remote learning.

Each day, children will meet via Zoom with Miss Oyston and Mrs. Clarke to complete a short teaching task (see timetable sent on Class Story on Dojo).

You will find all resources and worksheets that we will be using in school to support your child at home here.

Friday 5th March 2021

Name
05.03.2021 English Slides.pdf Download
05.03.2021 Spelling Task.pdf Download
5.3.21 - Maths worksheet - Finding three-quarters.pdf Download
5.3.21 - Division wheels.pdf Download
5.3.21 - Maths slides - Finding three-quarters.pdf Download

Thursday 4th March 2021

Name
03.03.2021 English Slides.pdf Download
04.03.2021 Spelling Task.pdf Download
4.3.21 - Maths worksheet - Fractions of quantities.pdf Download
4.3.21 - Maths slides - Fractions of quantities.pdf Download
4.3.21 - Multiplication wheels.pdf Download

Wednesday 3rd March 2021

Name
01.03.2021 Science Clues.pdf Download
01.03.2021 Science Recording Sheet.pdf Download
01.03.2021 Science Slides.pdf Download
03.03.2021 Reading Task.pdf Download
3.3.21 - Maths worksheet - Shading Fractions.pdf Download
3.3.21 - Daily Maths slides.pdf Download
3.3.21 - Maths slides - shading fractions.pdf Download

Tuesday 2nd March 2021

Name
02.03.2021 English Slides.pdf Download
02.03.2021 Reading Task.pdf Download
2.3.21 - Maths worksheet - Solving problems - money V2.pdf Download
2.3.21 - Daily Maths slides.pdf Download
2.3.21 - Maths slides - Solving problems - money.pdf Download

Monday 1st March 2021

Name
01.03.2021 English Slides.pdf Download
01.03.2021 English Worksheet.pdf Download
01.03.2021 Reading Task.pdf Download
04.03.2021 History Slides.pdf Download
1.3.21 - Maths worksheet - Finding change - money.pdf Download
1.3.21 - Daily Maths slides.pdf Download
1.3.21 - Maths slides - Finding change - money.pdf Download

Friday 26th February 2021

Name
26.02.2021 English Slides.pdf Download
26.02.2021 English Worksheet.pdf Download
26.02.2021 Spelling Task.pdf Download
26.2.21 - Maths worksheet - Finding the difference - money.pdf Download
26.2.21 - Arithmetic 10.pdf Download
26.2.21 - Maths slides - Findinf the difference - money.pdf Download

Thursday 25th February 2021

Name
25.02.2021 English Slides.pdf Download
25.02.2021 English Worksheet.pdf Download
25.02.2021 History Slides.pdf Download
25.02.2021 History Worksheet.pdf Download
25.02.2021 Spelling Task.pdf Download
25.2.21 - Maths worksheet - Finding totals - money.pdf Download
25.2.21 - Arithmetic 9.pdf Download
25.2.21 - Maths slides - Finding totals with money.pdf Download

Wednesday 24th February 2021

Name
24.02.2021 English Slides.pdf Download
24.02.2021 English Worksheet.pdf Download
24.02.2021 Florence Nightingale Text - only print pages 1-3.pdf Download
24.02.2021 R.E. Slides and Task.pdf Download
24.02.2021 Reading Task.pdf Download
24.2.21 - Maths worksheet - Making same amounts - money.pdf Download
24.2.21 - Daily Maths Slides.pdf Download
24.2.21 - Maths slides - Making same amount.pdf Download

Tuesday 23rd February 2021

Name
23.02.2021 English Slides.pdf Download
23.02.2021 English Worksheet.pdf Download
23.02.20210 Reading Task.pdf Download
23.2.21 - Maths worksheet - Making amounts - money.pdf Download
23.2.21 - Daily Maths Slides.pdf Download
23.2.21 - Maths slides - Making amounts.pdf Download

Monday 22nd February 2021

Name
22.02.2021 English Slides.pdf Download
22.02.2021 English Worksheet.pdf Download
22.02.2021 Reading Task.pdf Download
22.02.2021 Science Slides.pdf Download
22.2.21 - Maths worksheet - Dividing by 10.pdf Download
22.2.21 - Daily Maths Slides.pdf Download
22.2.21 - Maths Slides - Dividing by 10.pdf Download

Friday 12th February 2021

Name
12.02.2021 English Slides.pdf Download
12.02.2021 English Worksheet.pdf Download
12.02.2021 Spelling Task.pdf Download
12.2.21 - Maths worksheet - Dividing by 5.pdf Download
12.2.21 - Arithmetic 8.pdf Download
12.2.21 - Maths Slides - Dividing by 5.pdf Download

Thursday 11th February 2021

Name
11.02.2021 English Slides.pdf Download
11.02.2021 History Body Template.pdf Download
11.02.2021 History Slides.pdf Download
11.02.2021 Spelling Task.pdf Download
11.2.21 - Maths worksheet - Dividing by 2.pdf Download
11.2.21 - Arithmetic 7.pdf Download
11.2.21 - Maths slides - Dividing by 2.pdf Download

Wednesday 10th February 2021

Name
10.02.2021 English Slides.pdf Download
10.02.2021 RE Slides and Worksheet.pdf Download
10.2.21 - Maths worksheet - 10 times table.pdf Download
10.2.21 - Daily Maths Slides.pdf Download
10.2.21 - Maths Slides - 10 times table.pdf Download
10.2.21 - Reading task.pdf Download

Tuesday 9th February 2021

Name
09.02.2021 English Slides.pdf Download
9.2.21 - Maths worksheet - 5 times table.pdf Download
9.2.21 - Daily Maths slides.pdf Download
9.2.21 - Maths Slides - 5 times table.pdf Download
9.2.21 - Reading task.pdf Download
Safer Internet Day 2021 - activity.pdf Download

Monday 8th February 2021

Name
08.02.2021 English Slides.pdf Download
08.02.2021 Science Slides.pdf Download
8.2.21 - Maths worksheet - 2 times table.pdf Download
8.2.21 - Daily Maths slides.pdf Download
8.2.21 - Maths slides - 2 times tables.pdf Download
8.2.21 - Reading task.pdf Download

Friday 5th February 2021

Name
05.02.2021 English Worksheet.pdf Download
05.02.2021 Spelling Task.pdf Download
05.02.21 English Slides.pdf Download
5.2.21 - Maths worksheet - Subtracting 2-digit numbers part 2.pdf Download
5.2.21 - Arithmetic 6.pdf Download
5.2.21 - Maths slides - Subtracting 2 digit numbers part 2.pdf Download

Thursday 4th February 2021

Name
04.02.2021 English Slides.pdf Download
04.02.2021 English Worksheet.pdf Download
04.02.2021 History Slides.pdf Download
04.02.2021 Spelling Task.pdf Download
4.2.21 - Maths worksheet - Adding 2-digit numbers part 2.pdf Download
4.2.21 - Arithmetic 5.pdf Download
4.2.21 - Maths slides - adding 2 digit numbers part 2.pdf Download

Wednesday 3rd February 2021

Name
03.02.2021 English Slides.pdf Download
03.02.2021 RE Slides.pdf Download
03.02.21 English Worksheet.pdf Download
3.2.21 - Daily Maths slides.pdf Download
3.2.21 - maths slides - subtracting 2 digit numbrers.pdf Download
3.2.21 -maths worksheet - subtracting 2-digit numbers.pdf Download

Tuesday 2nd February 2021

Name
02.02.21 English Slides.pdf Download
02.02.21 English Worksheet.pdf Download
2.2.21 - Daily Maths slides.pdf Download
2.2.21 - Slides - adding 2 digit numbers part 2.pdf Download
2.2.21 - worksheet - adding 2-digit numbers part 2.pdf Download

Monday 1st February 2021

Name
01.02.2021 Science Slides.pdf Download
01.02.2021 Science Worksheet.pdf Download
01.02.21 English Slides.pdf Download
01.02.21 English Worksheet.pdf Download
1.2.21 - Daily Maths slides.pdf Download
1.2.21 - slides - adding 2 digit numbers.pdf Download
1.2.21 - worksheet - adding 2-digit numbers.pdf Download

Friday 29th January 2021

Name
15.01.21 Art Worksheet.pdf Download
29.01.21 - Art Slides.pdf Download
29.01.21 English Slides.pdf Download
29.01.21 Images of the Queen.pdf Download
29.01.21 Spelling Task.pdf Download
29.1.21 - Arithmetic test 4.pdf Download
29.1.21 - slides - 10 more and 10 less.pdf Download
29.1.21 - worksheet - 10 more and 10 less V2.pdf Download

Thursday 28th January 2021

Name
28.01.21 - History Slides.pdf Download
28.01.21 English Slides.pdf Download
28.01.21 English Worksheet.pdf Download
28.01.21 Spelling Task.pdf Download
28.1.21 - Arithmetic test 3.pdf Download
28.1.21 - Slides - Counting in 3's.pdf Download
28.1.21 - worksheet - counting in 3's.pdf Download

Wednesday 27th January 2021

Name
27.01.21 English Slides.pdf Download
27.01.21 English Worksheet.pdf Download
27.01.21 RE Slides.pdf Download
27.01.21 Reading Task.pdf Download
27.1.21 - Daily Maths slides.pdf Download
27.1.21 - Slides - Ordering numbers.pdf Download
27.1.21 - worksheet - ordering numbers up to 100.pdf Download

Tuesday 26th January 2021

Name
26.01.21 English Worksheet.pdf Download
26.01.21 English Slides.pdf Download
26.01.21 Reading Task.pdf Download
26.1.21 - Daily Maths slides.pdf Download
26.1.21 - slides - Comparing numbers.pdf Download
26.1.21 - worksheet - Comparing numbers.pdf Download

Monday 25th January 2021

Name
25.01.21 English Slides.pdf Download
25.01.21 English Worksheet.pdf Download
25.01.21 Reading Task.pdf Download
25.01.21 Science Slides.pdf Download
25.01.21 Science Worksheet.pdf Download
25.1.21 - Daily Maths slides.pdf Download
25.1.21 - slides - Partitioning numbers part 3.pdf Download
25.1.21 - worksheet - Partitioning numbers part 3.pdf Download

Friday 22nd January 2021

Name
22.01.21 Art Worksheet.pdf Download
22.01.21 English Slides.pdf Download
22.01.21 Spelling Task.pdf Download
22.01.21- Art Slides.pdf Download
22.1.21 - Arithmetic test 2.pdf Download
22.1.21 - slides - partitioning part 2.pdf Download
22.1.21 - worksheet - Partitioning numbers part 2.pdf Download

Thursday 21st January 2021

Name
21.01.21 English Slides.pdf Download
21.01.21 History Slides.pdf Download
21.01.21 Spelling Task.pdf Download
21.1.21 - Arithmetic test 1.pdf Download
21.1.21 - Maths slides - partitioning 2-digit numbers.pdf Download
21.1.21 - Maths worksheet - Partitioning 2-digit numbers.pdf Download

Wednesday 20th January 2021

Name
20.01.21 English writing checklist.pdf Download
20.01.21 English Slides.pdf Download
20.01.21 R.E. slides.pdf Download
20.01.21 R.E. worksheet.pdf Download
20.01.21 Reading Task.pdf Download
20.1.21 - Daily Maths slides.pdf Download
20.1.21 - slides - representing numbers to 100.pdf Download
20.1.21 - worksheet - Representing numbers to 100.pdf Download

Tuesday 19th January 2021

Name
19.01.21 English Slides.pdf Download
19.01.21 English Worksheet.pdf Download
19.01.21 Reading Task.pdf Download
19.1.21 - Daily Maths slides.pdf Download
19.1.21 - slides - Counting to 100.pdf Download
19.1.21 - worksheet - Counting to 100.pdf Download

Monday 18th January 2021

Name
18.01.21 English Slides.pdf Download
18.01.21 English Worksheet.pdf Download
18.01.21 Reading Task.pdf Download
18.01.21 Science Slides.pdf Download
18.01.21 Science Worksheet.pdf Download
18.1.21 - Daily Maths slides.pdf Download
18.1.21 - slides - Interpreting pictograms.pdf Download
18.1.21 - worksheet - Interpreting Pictograms.pdf Download

Friday 15th January 2021

Name
15.01.21 Art Slides.pdf Download
15.01.21 Art Worksheet.pdf Download
15.01.21 English Slides.pdf Download
15.01.21 English Worksheet.pdf Download
15.01.21 Spelling Task.pdf Download
15.1.21 - Daily Maths slides.pdf Download
15.1.21 - Pictogram slides.pdf Download
15.1.21 - worksheet - Pictograms.pdf Download

Thursday 14th January 2021

Name
14.01.21 English Slides.pdf Download
14.01.21 English Worksheet.pdf Download
14.01.21 History Slides.pdf Download
14.01.21 Spelling Task.pdf Download
14.1.21 - Daily Maths slides.pdf Download
14.1.21 - Tally Charts slides.pdf Download
14.1.21 - worksheet - Tally Charts.pdf Download

Wednesday 13th January 2021

Name
13.01.21 English Slides.pdf Download
13.01.21 English Worksheet.pdf Download
13.01.21 R.E. Slides and Task.pdf Download
13.01.21 Reading Task.pdf Download
13.1.21 - Daily maths slides.pdf Download
13.1.21 - slides for describing movement and turns.pdf Download
13.1.21 - worksheet - Describing movement and turns.pdf Download

Tuesday 12th January 2021

Name
12.01.21 English Slides.pdf Download
12.01.21 English Worksheet.pdf Download
12.01.21 Reading Task.pdf Download
12.1.21 - Daily maths slides.pdf Download
12.1.21 - Describing turns slides.pdf Download
12.1.21 - worksheet - Describing turns.pdf Download
Queen's Throne booklet parents and carers guide.pdf Download
Queen's Throne booklet.pdf Download

Monday 11th January 2021

Name
11.01.21 English Slides.pdf Download
11.01.21 Reading Task.pdf Download
11.01.21 Science Slides.pdf Download
11.1.21 - Daily maths slides.pdf Download
11.1.21 - Describing movement slides.pdf Download
11.1.21 - worksheet - Describing movement.pdf Download

Friday 8th January 2021

Name
08.01.2021 Art Slides.pdf Download
08.01.2021 English Slides.pdf Download
08.01.2021 Spelling Activity.pdf Download
8.1.21 - Daily Maths Slides.pdf Download
8.1.21 - Maths slides - sorting 3-D shapes.pdf Download
8.1.21 - worksheet - Sorting 3-D shapes.pdf Download

Thursday 7th January 2021

Name
07.01.2021 Chapter to read and questions to answer.pdf Download
07.01.2021 English Slides.pdf Download
07.02.21 History Slides.pdf Download
7.1.2021 Reading Task.pdf Download
7.1.21 - Daily Maths Slides.pdf Download
7.1.21 - Maths slides.pdf Download
7.1.21 - maths worksheet - Properties of 3-D shapes.pdf Download

Wednesday 6th January 2021

Name
06.01.2021 English Slides.pdf Download
6.1.2021 Reading Task.pdf Download
6.1.21 - Daily Maths Slides.pdf Download
6.1.21 - Maths slides.pdf Download
6.1.21 - worksheet - Patterns using 2-D shapes.pdf Download

Here are a range of interactive English websites you can access at home.

This site has a range of games which allows the children to practise their Spelling, Punctuation and Grammar work.

This provides games and activities which are linked to children's weekly spellings on their homework sheet.

The children will need to use the username and password which is stuck in the front of their homework book.

Here are a range of interactive Maths websites you can access at home.

Children will love playing games linked to the multiplication and division facts for the 2, 5 and 10 times tables. Each week we will set a particular times table for the children to practise.

The children will need to use the username and password which is stuck in the front of their homework book.

Here are a range of interactive Science websites you can access at home.

Our topic in Science this term is " Materials ".

We have looked at the materials in the classroom and discussed what these materials are used for.

Can you explore the materials in your home and explain how and why they are used?


(4.NBT.6)Dividing Whole Numbers Part 2: 4th Grade Common Core Worksheets

You are purchasing Common Core math practice sheets aligned to assessment tasks. There is a practice sheet for every day of the week and a test for Friday.

There are two sheets for each day that can be copied front and back to save paper. The front sheet focuses on the weekly target skill and the back side of the sheet is a review of previously taught skills.

This particular set of sheets focuses on:

4.NBT.6 Dividing Whole Numbers by 1-Digit Divisors: with remainders.

The Monday sheet gives directions for them to use the Partial Quotient Method. Two examples have been given on the Monday sheet.

I did not specify on the Tuesday through Friday sheet which method to use. I did this in case you wanted your students to use another method other than the Partial Quotient Method.

The students will also have to write an equation once they find the quotient. For example, if the problem is 158 divided by 8, they will be asked to write the equation 8 x 19 + 6 = 158 when they have solved the problem.

The back side of the paper is a REVIEW of the following skills:

4.OA.2 Multiplicative Comparisons with word problems

4.OA.1 Interpret a multiplication equation as a comparison

4.NBT.1/4.NBT.2/4.NBT.3 / 4.NBT.4 Place Value, comparing numbers, rounding, finding the difference

The last two sheets in the set are designed to be an assessment and are aligned to the other practice sheets in the set.


Invite Jesus into Your Heart and Receive the Gift and Confident Hope of Eternal Life…

I’ll leave you with another blessing…

Now may the God of peace make you holy in every way, and may your whole spirit and soul and body be kept blameless until our Lord Jesus Christ comes again.

1 Thessalonians 5:23 NLT

Here’s the blessing in Hebrew, but I suggest you watch the whole video as it’s an important update on what’s going on in Israel, Iran and the Middle East which is part of the End Times.


Watch the video: Πολλαπλασιασμός Μικτών Ε - ΣΤ τάξη (May 2022).