# 4 rows of 6 4 x 6 = rows of 4 6 x 4 = 24

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1 Arrays 8/8/16 Array a rectangular arrangement of equal rows 4 4 rows of 6 4 x 6 = rows of 4 6 x 4 = 24 4 Dimension the number of rows and columns in an array Multiplication the operation of repeated addition of the same number page 1 1

2 Factors 8/9/16 Factor each dimension on an array Factors of , 2, 3, 4, 6, 12 4 page 2 2

3 Prime, Composite, and Square Numbers 8/10/16 Prime Number a number with exactly 2 factors: one and itself Example: 13 is a prime number factors: 1, x 13 or 13 x 1 Composite Number a number with more than 2 factors Example: 8 is a composite number factors: 1, 2, 4, x 8 and 2 x Square Number a number that can represented by a square array Example: 16 is a square number 4 x 4 = 16 4 page 3 4 3

4 Products and Factor Pairs 8/11/16 Product the number of squares in an array; the answer to a multiplication problem 3 3 x 4 = 12 factor x factor = product 4 Factor Pair the dimensions of an array written as an expression 3 x 4 page 4 4

5 Multiplicative Comparison 8/12/16 diamondback rattlesnake 1 1 x 6 = 6 feet 6 reticulated python 4 4 x 6 = 24 feet The python is 24 feet long. 6 page 5 5

6 Array Story 8/15/2016 Write a story that represents 3 x 5 John has \$5 in his wallet. George has 3 times as much money as John. How much money does George have? 3 3 rows of \$5 = \$15 5 George has \$15 page 6 6

7 More Multiplicative Comparisons 8/16/2016 Which statement BEST represents the number sentence below? 28 = 4 x 7 A. The number 4 is 7 times as many as 28 B. The number 28 is 4 times less than 7 C. The number 28 is 4 times as many as 7 D. The number 7 is 4 times as many as 28 factor a whole number that divides another number evenly, with nothing left over multiple the number that you say when you skip count page 7 7

8 Another Array Story 8/17/2016 Write a story that represents 5 x 8. Nicole has 8 followers on Facebook. TerriAnne has 5 times as many followers as Nicole. How many followers does TerriAnne have on Facebook? x 8 = 40 followers page 8 8

9 Prime or Composite 8/19/2016 Tell whether the following numbers are prime or composite. How do you know? 11 prime because it has only 2 factors: 1 x composite because it has more than two factors: 1 x 18 and 2 x 9 List all the prime numbers less than Circle each of the composite numbers Draw a box around the numbers that have only prime digits

10 Factors of Multiples of 100 8/22/16 Factors of 100 1, 2, 4, 5, 8, 10, 20, 25, 50, 100 Factors of 200 1, 2, 4, 5, 8, 10, 20, 25, 50, 100, 200 If 4 x 25 = 100, then 8 x 25 = 200 If 5 x 20 = 100, then 5 x 40 = 200 If 10 x 10 = 100, then 20 x 10 = 200 If 2 x 50 = 100, then 4 x 50 = 200 page 10 10

11 Factors of Related Numbers 8/23/16 If 25 is a factor of 100, then 25 is also a factor of 300 because 300 is a multiple of 100. (100 x 3) If 4 is a factor of 8, then 4 is also a factor of 72 because 72 is a multiple of 8. (8 x 9) If 4 is a factor of 16, then 4 is also a factor of 48 because 48 is a multiple of 16. (16 x 3) page 11 11

12 How Many Arrays? 8/24/16 How many arrays can be made with the following numbers? 4 1 x 4 2 x x 7 1 x x x 12 1 x 24 3 x 8 6 x x 54 2 x 27 3 x 18 6 x 9 page 12 12

13 Data and Line Plots 8/26/16 data collected statistics or information on a topic line plot a useful way to organize data on a number line bar graph a useful way to organize data using scales and bars Data: 35, 33, 36, 37, 35, 33, 37, 37, 33, 37 Line Plot: page 13 13

14 Using Data 8/31/16 Thirteen high school students were asked how many hours they study each week. The results are recorded below. What's the difference between the longest time studying and the shortest time? counting up from 2½ to 5 equals 5 halves. Five halves equals 2½ hours. If all the 3½ hour times were combined, what would the total time studying be? counting three 3s plus three halves equals 10½ hours. page 14 14

15 More Using Data 9/2/16 Seven girls measured the lengths of their hair. The results are listed below. Mary 4½ in., Jane 5 in., Martha 3½ in., Barbara 4½ in., Susan 4½ in., Sally 3½ in., and Faith 4½ in. Use this data to make a line plot. 3 3½ 4 4 ½ 5 Hair Length page 15 15

16 Breaking Numbers Apart 9/14/16 Mr. Jones bought 14 dozen bagels for a birthday party. How many bagels is that all together? 14 x 12 = (10 x 12) + (4 x 12) = = 168 bagels x 12 4 x = 168 bagels x 12 4 x = 168 bagels page 16 16

17 Making Big Arrays 9/15/ x 9 9 x 4 4 x 9 = x 4 4 x 5 (4 x 4) + (4 x 5) = 36 5 x = x 9 2 x 9 (2 x 9) + (2 x 9) = = x 6 6 x 4 4 x 3 3 x 4 (4 x 6) + (4 x 3) = = 36 page 17 17

18 Solving Multiplication Problems 9/19/16 How many wheels are on 27 cars? x 10 4 x x 27 = (4 x 20) + (4 x 7) = = 108 wheels Luke has 16 marbles. Jill has 7 times as many marbles. How many marbles does Jill have? x 10 7 x x 16 = (7 x 10) + (7 x 6) = = 112 page 18 18

19 Division Stories 9/22/16 Use a multiplication tower: The 6th multiple is 108, so it would take 6 trips to carry 108 coins. If the number of total coins was page th multiple 19

20 Measurements Length Equivalents (U.S. Standard System) 1 foot = 12 inches 1 yard = 3 feet 1 yard = 36 inches Length Equivalents (Metric System) 1 centimeter = 10 millimeters 1 meter= 100 centimeters 1 meter = 1,000 millimeters 20

21 Units of Linear Measurement 10/19 U.S. Standard inch distance between the first and second joint of your pointer finger foot 12 inches, a little longer than your foot yard 3 feet, about the width of a door mile 5,280 feet, 1,760 yards, about the distance between Lakewood and Publix Metric millimeter the thickness of a dime centimeter 10 millimeters, about the width of your pinky finger meter 1,000 millimeters, 100 centimeters, about the width of a door kilometer 1,000 meters, about the distance between Lakewood and Pierce Road page 20 21

22 Weight and Capacity Weight 1 pound (lb) = 16 ounces (oz) 1 ton = 2,000 pounds 1,000 milligrams (mg) = 1 gram (g) 1,000 grams (g) = 1 kilogram (kg) Capacity 1 gallon (gal) = 4 quarts (qt) 1 quart (qt) = 2 pints (pt) 1 pint (pt) = 2 cups (c) 1 cup (c) = 8 ounces (oz) (not to be confused with weight ounces) 1 tablespoon (tbs) = 3 teaspoons (tsp) 1,000 milliliters (ml) = 1 liter (L) 1 liter (L) = 1,000 milliliters (ml) 22

23 Area Model Multiplication 1. Break your expression apart by its place value. 2. Draw out the box to solve the equation. 3. Multiply. 4. Add Example) Find the product of 18 x 7. 23

24 Area Model 2 digit by 2 digit Follow the same steps! Ask yourself "What number is beside this box? What number is above this box?" Example: Find the product of 17 x

25 Telling Time 1/4 of an hour = 15 minutes 1/2 of an hour = 30 minutes 3/4 of an hour = 45 minutes 25

26 How many minutes is 2 1/2 hours? 60 min min min. = 150 min. How many minutes is 3 1/4 hours? 60 min min min min.= 195 min. How many minutes is 1 3/4 hours? 60 min min.= 105 min. Example) Miss Edwards left for her beach trip at 9:30 A.M. It took her 2 1/2 hours to get there. What time did she get to the beach? 12:00 P.M. 26

27 Introduction to Polygons Polygons have straight line segments for sides which only cross (intersect) at the point (vertice). Polygons: 1. Never have lines that cross. 2. Never have gaps in their lines. 3. Never have curved edges. Polygons Not Polygons Polygons are named according to the number of sides they have. Ex) Triangle (Tri means 3.) 27

28 Other Geometric Symbols Point Line Segment Line Parallel Lines Intersecting Lines Perpendicular Lines parallelogram a quadrilateral with opposite sides parallel trapezoid quadrilateral with one set of parallel sides 28

29 Angles Right angles = 90 degrees Acute angles= less than 90 degrees Obtuse angles = more than 90 degree but less than 180 degrees. Straight angles = 180 degrees. Example) What could the measurement for this angle be? a. 170 b. 20 c. 110 d

30 Angles Cont. acute right obtuse straight less than 90 o 90 o greater than 90 o 180 o right angles acute angles obtuse angles right angles acute angles obtuse angles right angles acute angles obtuse angles right angles acute angles obtuse angles page 23 right angles acute angles obtuse angles 30

31 trapezoid quadrilateral with at least one pair of parallel sides parallelogram quadrilateral with two pairs of parallel sides rhombus quadrilateral with two pairs of parallel sides all four sides are the same length rectangle quadrilateral with two pairs of parallel sides has 4 right angles square quadrilateral with two pairs of parallel sides has 4 right angles all four sides are the same length 31

32 Measuring angles with a protractor What is the measure of the smallest angle? How many degrees are in 1/4 of a circle? How many degrees are in 1/2 or 2/4 of a circle? How many degrees are in 3/4 of a circle? How many degrees are in 4/4 or 1 whole circle? 32

33 Symmetry An object has symmetry (is symmetrical) when one half is the mirror image of the other half. Directions: Draw lines of symmetry through each of the shapes. 33

34 Area and Perimeter Perimeter Definition: The distance around the outside How to find it: Add up all the sides. Example: 8 11 Real World Use: Building a House Definition: The space inside of a shape Area How to find it: Multiply the length times the width 8 ft. Example: 56 sq. ft. 7 ft. Real World use: finding the square feet in the inside of the classroom 34

35 Area Examples 9 cm. 11 cm.? 5 ft. 7 ft.? 3 in. 3 in.? 2 cm. 4 cm.? 35

36 Area Word Problems Example) A book had a length of 5 inches and a width of 12 inches. What is the area of the book? Example) Susie was cutting some fabric for her friend. The fabric had a width of 6 inches and an area of 42 square inches. What is the length of the fabric? Example) Joey had a rug that was 5 feet long and 6 feet wide. Rebecca had a rug that was 4 feet long and 6 feet wide? Whose rug had the largest area? Show your work! 36

37 Working With Place Value to Add Expanded form Breaking apart a number by its place value Ex) 427 Four hundred + twenty + seven Ex) Add the following numbers using expanded form = =

38 Working With Place Value to Subtract Ex) Subtract the following numbers using expanded form = * You have to take the same amount from both sides of the line!

39 Example Word Problems 1) The weights in the gym are 150 pounds, 200 pounds, 55 pounds, and 45 pounds. How heavy are all the weights combined? 2) Miss Edwards was on a TV Game Show. She won \$5,500 total. During round one, she won \$1,500. During Round 2 she won \$2,000. How much did she win on round 3? 3) At Lakewood Elementary, there are 650 students. 37 students are absent. How many students came to school? 39

40 Place Value Ten thousands, thousands, hundreds, tens, ones Ex) 570 The 7 in the tens place represents the number 70. Place Value Forms number form Base 10 form Expanded Form Word Form 40

41 Continuing with Expanded Form & Condensed Form Example) What number is expressed by the sentence below? (6 x 10,000) + (2 x 1,000) + (1 x 100) + (6 x 10) + (1 x 1)= Example) How many tens are in the following numbers? 600 tens 70 tens 5,000 tens Example) Write out the name in word form for this number 4,205. Example) What number is represented by this name? 6,456 Example) Write the number that has 3 thousands, 1 hundred, 6 tens, and 5 ones. 41

42 Introduction to Fractions Fractions are numbers that look different! Numerator the top number in a fraction that tells us how many pieces of a whole we need to consider Denominator the bottom number in a fraction that tells us how many parts the whole has been divided into Example) 1/5 1 out of the 5 pieces is yellow. Equivalent fractions fractions that are equal Example) 1/2=2/4 42

43 Equivalent Fractions Remember that fractions are spoiled rotten brats! What you do to the top (numerator), you also have to do to the bottom (denominator). Example) Example) 43

44 Equivalent Fractions Practice Which fraction is equivalent to the number of shaded boxes above? A. 1/2 B. 1/3 C. 6/8 D. 4/4 What is the fraction represented by the shaded circles? A. 2/3 B. 5/6 C. 2/6 D. 1/3 44

45 Decimals Continued decimal a different kind of number meaning 10 A quantity that is less that is between whole numbers is known as a decimal or a fraction. Example) 1, 1.5, 2, 2.3, 3, 3.4 1, 1 1/2, 2, 2 3/4, 3, 3 1/4 The numbers to the left of the decimal point are whole numbers. The numbers to the right of the decimal point are parts of whole numbers. Example)

46 Beginning with Decimals Decimal Place Value hundreds tens ones. tenths hundredths thousandths Examples) 1/ one tenth 5/ five tenths 1/ one hundredth 5/ five hundredths 46

47 Greater Than, Less Than, Equal To Fractions and Decimals Fractions) Fill in the blank with <, >, =. 1/3 1/2 2/2 3/4 1/3 2/6 Decimals) Fill in the blank with <, >, =

48 Adding Fractions When you are adding fractions with like denominators, you add the numerator, but the denominator stays the same. Example) 1/4 + 2/4 = 3/4 Example) 1/8 + 5/8 = Example) Miss Edwards has a candy bar. She is sharing it with her friend Ellie. Ellie gets 1/8 and Miss Edwards gets 3/8. How much did they eat altogether? Show a picture to explain your thinking. 48

49 Subtracting Fractions When you are subtracting fractions with like denominators, you subtract the numerator, but the denominator stays the same. Example) 4/4 2/4 = 2/4 Example) 7/8 5/8 = Example) Charles has 6/8 of a pizza left from his birthday party. He can't eat it all, so he shares 2/8 of the pizza with his brother Jake. How much pizza does Charles have left after sharing with Jake? Draw a picture to explain your thinking. 49

50 Adding and Subtracting Mixed Numbers When you are adding and subtracting mixed numbers, add or subtract the fractions first. Then, focus on the wholes. Example) 5 1/4 +3 3/4 Example) 7 6/8 2 5/8 Example) Mrs. Julia is baking a pie. She needs 4 1/4 cups of sugar and 2 2/4 cups of milk. How many cups of ingredients does she need altogether? 50

51 Fractions Greater Than 1 Steps to change a fraction greater than 1 to a mixed number: 1. Divide the numerator by the denominator. 2. Find the whole number. The whole number is the number of times the denominator divides into the numerator. 3. Make the remainder the new numerator. Example) 4/3= 1 1/3 Example) 7/2= 3 1/2 Example) 10 people have 1/4 of a pie. How much pie do they have total? Express your answer as a mixed number, and use a picture to explain your thinking. 51

52 Multiplying Fractions by a Whole Number When you are multiplying fractions by a whole number, you make the whole number the numerator and its denominator 1. Multiply the numerators and the denominators. Example) 3 x 1/4 = 3/1 x 1/4= 3/4 Example) 7 x 5/8 = 7/1 x 5/8= 35/8= 4 3/8 Example) Miss Edwards needs 4 batches of muffins for the bake sale. Each batch requires 3/4 cups of flour. How much flour does she need? Show a picture to explain your thinking. 52

53 53

54 Unit Fractions A unit fraction is a fraction where the numerator is 1 and the denominator is either 1 or a number greater than 1. Examples of unit fractions: 1/2, 1/4, 1/5, 1/6 Complete the multiplication equation below using a unit fraction and a whole number. x = 4/9 x = 6/7 x = 8/7 54

55 55

56 Using Number Lines with Time A train left Massachusetts at 10:26 A.M. and arrived in Albany at 5:13 P.M. How long did it take the train to travel from Massachusetts to Albany? 56

57 57

58 Rounding Step 1: Find the rounding place and underline it. Example) Round to the nearest tens place. 527 Step 2: Look at the digit (number) next door and put a box around it. Example) 527 Step 3: Ask "4 or Less?" or "5 or more?" Ex) 527 rounds to 530 Step 4: 4 or less, let it rest! Step 5: 5 or more, raise the score! Step 6: Everything after the rounded number changes to a 0. 58

59 Partial Quotients Joanna has 265 story books. She has already read most of them, so she is keeping some and splitting the rest between her 3 friends. If there are any left over, she is going to donate them to the school library. How many story books will each person have? Will there be any books left over? 59

60 60

61 Patterns Ex) Miss Edwards is collecting canned goods for the food bank. On the first day, she collects 10 cans. Each day, She adds 6 more to her collection. How many cans will she have on day 7? Miss Edwards is having a party. Her seating chart looks like this. How many tables would she need to seat 12 people? 61

62 Patterns Continued Ex) Mr. Johnson is counting using the rule n+6. Complete the pattern below using this same rule. 18, 24, 30,,,,, Ex) What will be the 15th shape in the pattern below? 62

63 Attachments Friction Lab.docx

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