Math Grade 5 Flip Chart

Copyright © NewPath Learning. All rights reserved. www.newpathlearning.com Charts Charts Grade Grade Curriculum Mastery Flip Charts Combine Essential Math Skills with Hands-On Review! ® 33-5001 555 \|xiBAHBDy01218kzU Sturdy, Free-Standing Design, Perfect for Learning Centers! Reverse Side Features Questions, Math Problems, Vocabulary Review & more!

Phone: 800-507-0966 • Fax: 800-507-0967 www.newpathlearning.com NewPath Learning® products are developed by teachers using research-based principles and are classroom tested. The company’s product line consists of an array of proprietary curriculum review games, workbooks, posters and other print materials. All products are supplemented with web-based activities, assessments and content to provide an engaging means of educating students on key, curriculum-based topics correlated to applicable state and national education standards. Copyright © 2009 NewPath Learning. All Rights Reserved. Printed in the United States of America. Curriculum Mastery® and NewPath Learning® are registered trademarks of NewPath Learning LLC. Math Curriculum Mastery® Flip Charts provide comprehensive coverage of key standards-based curriculum in an illustrated format that is visually appealing, engaging and easy to use. Curriculum Mastery® Flip Charts can be used with the entire classroom, with small groups or by students working independently. Each Math Curriculum Mastery® Flip Chart Set features • 10 double-sided laminated charts covering grade-level specific curriculum content on one side plus write-on/wipe-off charts on reverse side for student use or for small-group instruction. • Built-in sturdy free-standing easel for easy display • Spiral bound for ease of use • Activity Guide with black-line masters of the charts for students to fill-in, key vocabulary terms, corresponding quiz questions for each chart, along with answers Ideal for • Learning centers • In class instruction for interactive presentations and demonstrations • Hands-on student use • Stand alone reference for review of key science concepts • Teaching resource to supplement any program HOW TO USE Classroom Use Each Curriculum Mastery® Flip Chart can be used to graphically introduce or review a topic of interest. Side 1 of each Flip Chart provides graphical representation of key concepts in a concise, grade appropriate reading level for instructing students. The reverse Side 2 of each Flip Chart allows teachers or students to fill in the answers and summarize key concepts. Note: Be sure to use an appropriate dry-erase marker and to test it on a small section of the chart prior to using it. The Activity Guide included provides a black-line master of each Flip Chart which students can use to fill in before, during, or after instruction. On the reverse side of each black-line master are questions corresponding to each Flip Chart topic which can be used as further review or as a means of assessment. While the activities in the guide can be used in conjunction with the Flip Charts, they can also be used individually for review or as a form of assessment or in conjunction with any other related assignment. Learning Centers Each Flip Chart provides students with a quick illustrated view of grade-appropriate curriculum concepts. Students may use these Flip Charts in small group settings along with the corresponding activity pages contained in the guide to learn or review concepts already covered in class. Students may also use these charts as reference while playing the NewPath’s Curriculum Mastery® Games. Independent student use Students can use the hands-on Flip Charts to practice and learn independently by first studying Side 1 of the chart and then using Side 2 of the chart or the corresponding graphical activities contained in the guide to fill in the answers and assess their understanding. Reference/Teaching resource Curriculum Mastery® Charts are a great visual supplement to any curriculum or they can be used in conjunction with NewPath’s Curriculum Mastery® Games. Chart # 1: Chart # 2: Chart # 3: Chart # 4: Chart # 5: Chart # 6: Chart # 7: Chart # 8: Chart # 9: Chart #10: Collecting & Displaying Data Multiplying & Dividing Decimals Measurement: Time & Temperature Multiplying & Dividing Fractions Ratio, Proportion & Percent Operations with Mixed Numbers Introduction to Algebra Probability Concepts Congruence, Transformations & Symmetry Lines, Angles & Circles

Tables Collecting data • You can collect data (information) from other people using polls and surveys. • Scientists collect data from experiments. • Tables and graphs help us organize and interpret collected information. The mean is the average of a set of numbers. To find the mean, add all the numbers in the set and divide the sum by the number of items in the set. The median is the middle number when the data are in numerical order. The mode is the number that occurs most often in a set of data. Bike Color No. of Gears Price Ranger Outdoor Tourist Starburst Mountain Silver 5 10 $240 $295 $325 12 $375 $225 15 6 Blue Red Black White Types of Bikes Sold at the Bike Shop Mean Median Mode 20 ÷ 5 = 4 The mean is 4 The median is 6 The mode is 5 2, 3, 3, 6, 8, 10, 12 3, 5, 5, 5, 6, 6, 8, 9 middle number Frequency Table A frequency table shows the totals of the tally marks. A bar graph is one way of showing data that can be counted. Each segment in a circle graph represents a fraction of a set of data. A line graph presents a set of data collected over time using line segments. Months Months Number of bikes sold Number of Bikes A stem-and-leaf plot shows data arranged by place value. 3 + 5 + 2 + 6 + 4 Line Graph Circle Graph Bar Graph Stem–and–Leaf Plot Ranger Bike Tally Total Outdoor Tourist Starburst Mountain RangerOutdoorT ourist Starburst Mountain 0 1 2 3 4 5 6 7 8 9 10 Total 20 10 2 1 4 3 10 20 30 40 50 60 10 20 30 40 50 60 January F ebruaryM ar ch M ay A pril June July A ugust 15, 20, 28, 31, 35, 46, 49, 52 (arranged from least to greatest) Stem (tens digit) Leaf (ones digit) Mountain (10 bikes) 5 08 15 69 2 1 2 3 4 5 Outdoor (4 bikes) Ranger (3 bikes) Starburst Tourist(1 bike) To find the number of gears of the Starburst bike, look across the Starburst row until it meets the Gear column. The headings tell us what data is in each column. The title tells us what the table is about. Height of the bars shows how many of each bike sold (2 bikes) © Copyright NewPath Learning. All Rights Reserved. 93-4501 www.newpathlearning.com Collecting & Displaying Data

\|xiBAHBDy01641qzZ Tables The is the average of a set of numbers. To find the mean, add all the numbers in the set and divide the sum by the number of items in the set. The median is the when the data are in numerical order. The mode is the number that occurs in a set of data. Bike Color No. of Gears Price Ranger Outdoor Tourist Starburst Mountain Silver 5 10 $240 $295 $325 12 $375 $225 15 6 Blue Red Black White Types of Bikes Sold at the Bike Shop Mean Median Mode ÷ = The mean is 4 The median is 6 The mode is 5 2, 3, 3, 6, 8, 10, 12 3, 5, 5, 5, 6, 6, 8, 9 middle number Frequency Table A frequency table shows the totals of the tally marks. A bar graph is one way of showing data that can be counted. Each segment in a circle graph represents a fraction of a set of data. A line graph presents a set of data collected over time using line segments. Months Number of bikes sold Number of Bikes A stem-and-leaf plot shows data arranged by place value. 3 + 5 + 2 + 6 + 4 Key Vocabulary Terms • bar graph • circle graph • column • data • frequency table • graph • heading • line graph • mean • median • mode • poll • stem-and-leaf plot • survey • table • title Line Graph Circle Graph Bar Graph Stem–and–Leaf Plot Ranger Bike Tally Total Outdoor Tourist Starburst Mountain RangerOutdoorT ourist Starburst Mountain 0 1 2 3 4 5 6 7 8 9 10 Total 10 20 30 40 50 60 January F ebruaryM ar ch M ay A pril June July A ugust 15, 20, 28, 31, 35, 46, 49, 52 (arranged from least to greatest) Stem (tens digit) Leaf (ones digit) To find the number of gears of the Starburst bike, look across the Starburst row until it meets the Gear column. The headings tell us what data is in each column. The tells us what the table is about. © Copyright NewPath Learning. All Rights Reserved. 93-4501 www.newpathlearning.com Collecting & Displaying Data

Therefore, 3 ÷ 0.2 = 15 Therefore, 0.6 x 0.3 = 0.18 or Therefore, 0.59 x 4.8 = 2.832 m = 32.22 n = 6.75 18 100 Multiplying Whole Numbers by Decimals Using Grids to Multiply Multiplying Decimals by Decimals Dividing Decimals by Whole Numbers Dividing a Decimal by a Decimal • Multiply as you would with whole numbers. How many 2 tenths are there in 3 wholes? There are 15 sets of 2 tenths. • Add the number of decimal places in each factor. • Place the decimal point in the product. • The 18 overlapping squares (green) that are shaded twice show the product of 0.6 x 0.3. • Multiply as you would with whole numbers. • Add the number of decimal places in each factor. • Place the decimal point in the product. • Shade 0.6 of the grid. • Shade 0.3 of the grid with a different color or pattern in the other direction. • Change the divisor and the dividend to a whole number by multiplying each by the same power of 10. • Divide as you would divide whole numbers. Add zeros as needed. • Place the decimal point in the quotient directly above the decimal point in the dividend. Bring down the ones and divide. Step 2 The answer checks if the product is the same as the dividend Multiply: 6 x 5.37 = m Multiply: 0.6 x 0.3 = n Divide: 3 ÷ 0.2 = p Divide: 5.4 ÷ 0.8 = n • multiply: 1 x 6 • subtract: 8 – 6 • compare: 2 < 4 5.37 x 6 32.22 2 decimal places 0 decimal places move decimal point 2 places + 2 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 0.5 9 4.8 4 7 2 2 3 6 0 2 8 3 2 2 decimal places 1 decimal places move decimal point 3 places + 3 2 1 7 3 x . = 5.4 0.8 54 8 x10 x10 x10 x10 54.00 6.75 6 0 5 6 – – 40 40 0 – 48 08. 5.4 0.8 54. 8. © Copyright NewPath Learning. All Rights Reserved. 93-4502 www.newpathlearning.com Multiplying & Dividing Decimals

\|xiBAHBDy01654qzZ Therefore, 3 ÷ 0.2 = 15 Therefore, 0.6 x 0.3 = 0.18 or Therefore 0.59 x 4.8 = 2.832 m = 32.22 n = 6.75 18 100 Multiplying Whole Numbers by Decimals Using Grids to Multiply Dividing Decimals by Whole Numbers • Multiply as you would with whole numbers. How many 2 tenths are there in 3 wholes? There are 15 sets of 2 tenths. • Add the number of decimal places in each factor. • Place the decimal point in the product. • The 18 overlapping squares (green) that are shaded twice show the product of 0.6 x 0.3. • Multiply as you would with whole numbers. • Add the number of decimal places in each factor. • Place the decimal point in the product. • Shade 0.6 of the grid. • Shade 0.3 of the grid with a different color or pattern in the other direction. • Change the divisor and the dividend to a whole number by multiplying each by the same power of 10. • Divide as you would divide whole numbers. Add zeros as needed. • Place the decimal point in the quotient directly above the decimal point in the dividend. Multiply: 6 x 5.37 = m Multiply: 0.6 x 0.3 = n Divide: 3 ÷ 0.2 = p Divide: 5.4 ÷ 0.8 = n 5.37 x 6 2 decimal places 0 decimal places move decimal point 2 places + 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 0.5 9 4.8 + 7 3 x = 5.4 0.8 54.00 08. 5.4 0.8 54. 8. Key Vocabulary Terms • decimal • decimal place • decimal point • divide • dividend • divisor • multiply • power of 10 • product • quotient • tenth • whole number 2 decimal places 0 decimal places move decimal point 2 places Multiplying Decimals by Decimals Dividing a Decimal by a Decimal © Copyright NewPath Learning. All Rights Reserved. 93-4502 www.newpathlearning.com Multiplying & Dividing Decimals

Fahrenheit ( ºF ) Celsius ( ºC ) Measurement: Time & Temperature © Copyright NewPath Learning. All Rights Reserved. 93-4503 www.newpathlearning.com Number Line 8:00 a.m. 9:00 a.m. 10:00 a.m. 11:00 a.m. 12:00 p.m. 1:00 p.m. 1 hr 1 hr 45min Temperature Units of Time clock calendar digital clock Early American Timeline 60 seconds (s) 1 year 1 regular year 1 leap year 1 century 60 minutes 24 hours 52 weeks 365 days 366 days 100 years 12 months (mo) 7 days OCTOBER 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 2 3 30 31 29 28 27 26 25 12 6 9 3 1 11 2 10 4 5 7 8 pm 1607 First colony formed at Jamestown, VA 1706 Benjamin Franklin is born 1732 George Washington is born 1773 Boston Tea Party 1776 Declaration of Independence 1 minute (min) 1 hour (hr) 1 day (d) 1 week (wk) • Elapsed time is the difference between the Start and the End times. In the customary system of measurement, temperature is read in degrees Fahrenheit ( ºF ). Change in temperature ( ºF ) Change in temperature ( ºC ) In the metric system of measurement, temperature is read in degrees Celsius ( ºC ). • Add to find the End Time. • Count up to find Elapsed Time on a number line. • Subtract to find the Start Time. 1 year (yr) Elapsed Time End Time Start Time 8 hr 36 min 10 hr 24 min 9 hr 84 min 1 hr 48 min 10:24 a.m. 8:36 a.m. Elapsed Time (?) 3hr 46 min 8:28 a.m. End Time (?) 2:43 p.m. Start Time (?) – 3 hr 46 min 8 hr 28 min 11 hr 74 min 12 hr 14 min + = 1 hr 12 min 2 hr 43 min 1 hr 31 min – Rename 1 hr as 60 min. Rename 74 min as 1 hr 14 min – = End Time + = = – = 12 : 14 p.m. Start Time = 1 : 31 p.m. 1 hr 12 min start time 11:45a.m. 9:00a.m. Elapsed Time (?) Elapsed Time = 1 hr + 1 hr + 45 min = 2 hr 45 min 47 ºF to 69ºF = 22ºF 32 ºC to 56 ºC = 24 ºC 35 40 45 50 55 60 65 70 75 ºF 35 40 45 50 55 60 65 70 75 ºF ºC 25 30 35 40 45 50 55 60 65 25 30 35 40 45 50 55 60 65 ºC

© Copyright NewPath Learning. All Rights Reserved. 93-4503 www.newpathlearning.com \|xiBAHBDy01651pzY Fahrenheit ( ºF ) Celsius ( ºC ) Measurement: Time & Temperature Number Line 8:00 a.m. 9:00 a.m. 10:00 a.m. 11:00 a.m. 12:00 p.m. 1:00 p.m. Temperature Units of Time clock digital clock Early American Timeline 60 seconds (s) 60 minutes 24 hours 52 weeks 365 days 366 days 100 years 12 months (mo) 7 days 12 6 9 3 1 11 2 10 4 5 7 8 pm 1607 First colony formed at Jamestown, VA 1706 Benjamin Franklin is born 1732 George Washington is born 1773 Boston Tea Party 1776 Declaration of Independence 1 minute (min) • Elapsed time is the difference between the and the . In the customary system of measurement, temperature is read in degrees Fahrenheit ( ºF ). Change in temperature ( ºF ) Change in temperature ( ºC ) In the metric system of measurement, temperature is read in degrees Celsius ( ºC ). • Add to find the End Time. • Count up to find Elapsed Time on a number line. • Subtract to find the Start Time. Elapsed Time End Time Start Time 8 hr 36 min 10 hr 24 min 10:24 a.m. 8:36 a.m. Elapsed Time (?) 3hr 46 min 8:28 a.m. End Time (?) 2:43 p.m. Start Time (?) – 3 hr 46 min 8 hr 28 min + 1 hr 12 min 2 hr 43 min – – = End Time + = = – = Start Time = 1 hr 12 min start time 11:45a.m. 9:00a.m. Elapsed Time (?) Elapsed Time = 1 hr + 1 hr + 45 min = 2 hr 45 min 47 ºF to 69ºF = 22 ºF 32ºC to 56ºC = 24 ºC 35 40 45 50 55 60 65 70 75 ºF 35 40 45 50 55 60 65 70 75 ºF ºC 25 30 35 40 45 50 55 60 65 25 30 35 40 45 50 55 60 65 ºC Key Vocabulary Terms • Celsius • elapsed time • end time • Fahrenheit • number line • start time

Modeling Multiplication Multiplying Fractions Modeling Division Dividing Fractions 2 3 3 4 = = 1 2 6 12 ÷6 ÷6 ÷6 ÷6 6 12 x 2 3 2 3 3 4 3 4 x x x = = Multiply 2 3 3 4 x Multiply 3 16 9 16 ÷ Divide 2 3 6 ÷ Divide • Shade of the rectangle. • Divide rectangle into thirds. • Shade of the rectangle with a different color or pattern in the other direction. Step 1 3 4 Therefore, X = or 3 4 The answer of is in simplest form. 1 2 2 3 2 3 2 3 2 3 3 4 2 3 • The overlapping sections (green) that are shaded twice show the product of x . • There are 3 groups of in . Multiply the numerators. How many sets of are there in ? Step 2 Multiply the denominators. Step 3 Use the greatest common factor (GCF) to simplify the product, if necessary. The GCF of 6 & 12 is 6. 2 3 6 1 2 3 ÷ ÷ 6 1 3 2 x = Step 1 Write the whole number as a fraction. Step Dividend Divisor 2 Flip the divisor upside down to find the reciprocal. The reciprocal of is . Rewrite as multiplication using the reciprocal. Simplify before multiplying. Step 4 Step 3 6 12 3 16 3 16 3 16 3 16 9 16 9 16 3 16 9 16 6 12 1 2 Therefore, ÷ = 9 16 3 3 9 16 6 3 1 9 1 3 1 x = = 3 3 1 2 © Copyright NewPath Learning. All Rights Reserved. 93-4504 www.newpathlearning.com Multiplying & Dividing Fractions

Modeling Multiplication Multiplying Fractions Modeling Division Dividing Fractions 2 3 3 4 = = 6 12 x 2 3 3 4 x x x = = Multiply 2 3 3 4 x Multiply 3 16 9 16 ÷ Divide 2 3 6 ÷ Divide • Shade of the rectangle. • Divide rectangle into thirds. • Shade of the rectangle with a different color or pattern in the other direction. Step 1 3 4 Therefore, X = or 3 4 The answer of is in simplest form. 1 2 2 3 2 3 2 3 2 3 3 4 2 3 • The overlapping sections (green) that are shaded twice show the product of x . • There are 3 groups of in . Multiply the numerators. How many sets of are there in ? Step 2 Multiply the denominators. Step 3 Use the greatest common factor (GCF) to simplify the product, if necessary. The GCF of 6 & 12 is 6. 2 3 ÷ ÷ x = Step 1 Write the whole number as a fraction. Step Dividend Divisor 2 Flip the divisor upside down to find the reciprocal. The reciprocal of is . Rewrite as multiplication using the reciprocal. Simplify before multiplying. Step 4 Step 3 3 16 9 16 9 16 3 16 9 16 Therefore, ÷ = 9 16 3 3 16 6 x = = Key Vocabulary Terms • denominator • divide • divisor • fraction • greatest common factor (GCF) • multiply • numerator • product • reciprocal • whole number © Copyright NewPath Learning. All Rights Reserved. 93-4504 www.newpathlearning.com Multiplying & Dividing Fractions \|xiBAHBDy01655nzW

Identity (zero) Property Commutative Property of Addition 10 100 1 10 = = = = Ratio Fraction form Word form Using a colon boys to girls girls to the total number of students boys to the total number of students 5:7 5 to 7 7 to 12 5 to 12 7:12 5:12 10% 25 100 1 4 5 7 7 12 5 12 = = = = 25% 50 100 1 2 = = = = 50% 75 100 3 4 = = = = 75% 100 100 10 10 = = = = 100% 80 100 20 20 4 5 = = = xx = 1 5 1 5 1 5 1 5 Step 5 7 1 Equal Ratios: Count the number of boys: Count the number of girls: Write a ratio to compare. Ratios can be written in three different ways. Step 2 4 1 4 1 = = 12 3 12 3 8 2 8 2 4 1 4 1 4 4 4 4 11 ÷ = = 12 3 12 3 12 12 4 4 3 3 ÷ = = 8 2 8 2 8 8 4 4 2 2 ÷ = = Proportion Ratio Percent What percent of this grid is shaded? Lemonade Making Directions Percents show up everywhere in our daily lives – sales tax on purchases, tips at restaurants, discounts at stores, among others. Percent means “per hundred”. It is a ratio that compares a number to 100. For example, 36 percent is a ratio of 36 to 100 or 36 out of 100. A proportion is an equation showing that two ratios are equal. Ratios that are equal to each other are called equivalent fractions. A ratio is a comparison of two numbers. These numbers are called the terms of the ratio. Write a ratio to compare the number of girls and boys in your classroom. = boy = girl = water = lemon juice • Mix 4 parts water with 1 part lemon juice. • change to an equivalent fraction with a denominator of 100. 80% 4 5 © Copyright NewPath Learning. All Rights Reserved. 93-4505 www.newpathlearning.com Ratio, Proportion & Percents

1 10 = = = = Ratio Fraction form Word form Using a colon boys to girls girls to the total number of students boys to the total number of students 1 4 = = = = 1 2 = = = = 3 4 = = = = 100 100 10 10 = = = = 4 5 = = = xx = 1 5 1 5 1 5 1 5 Step 1 Equal Ratios: Count the number of boys: Count the number of girls: Write a ratio to compare. Ratios can be written in three different ways. Step 2 4 1 = = ÷ = = 5 to 7 : : : 5 to 7 5 to 7 ÷ = = ÷ = = Key Vocabulary Terms • denominator • equal ratio • equivalent fraction • fraction • percent • proportion • ratio Proportion Ratio Percent What percent of this grid is shaded? Lemonade Making Directions Percents show up everywhere in our daily lives – sales tax on purchases, tips at restaurants, discounts at stores, among others. Percent means “per hundred”. It is a ratio that compares a number to 100. For example, 36 percent is a ratio of 36 to 100 or 36 out of 100. A is an equation showing that two ratios are equal. Ratios that are equal to each other are called . A ratio is a comparison of two numbers. These numbers are called the terms of the ratio. Write a ratio to compare the number of girls and boys in your classroom. = boy = girl = water = lemon juice • Mix 4 parts water with 1 part lemon juice. • change to an equivalent fraction with a denominator of 100. % 4 5 % % % % % © Copyright NewPath Learning. All Rights Reserved. 93-4505 www.newpathlearning.com Ratio, Proportion & Percents \|xiBAHBDy01662lz[

Addition Subtraction Multiplication Division + + Add Step 1 2 3 2 1 6 3 Multiply 1 4 2 1 4 2 9 4 2 3 – – Subtract 3 4 4 5 8 2 Find the least common denominator (LCD) of and . 2 3 1 6 Step 1 Find the LCD and write equivalent fractions. LCD of and is 8. Step 2 Subtract the fractions first, then the whole numbers. Simplify the difference, if necessary. 3 4 5 8 Step 2 Write equivalent fractions with a denominator of 6. Step 1 Write the mixed number as an improper fraction. Step 1 Write the mixed number as improper fractions. Step 2 Rewrite as multiplication using the reciprocal of the divisor. Step 3 Multiply the numerators and denominators and simplify. Step 4 Write as a mixed number. Step 2 Multiply the numerators and denominators of the two factors. Step 3 Simplify the product. Step 4 Write the product as a mixed number, if it is an improper fraction. Step 3 Add the fractions. Then add the whole numbers. Simplify the sum, if necessary. 2 3 1 6 2 3 2 = 4 6 2 x2 x2 3 4 4 = 6 8 4 – 5 8 2 1 8 2 x2 x2 1 6 3 + 5 6 5 x = m Divide 3 7 1 2 3 1 ÷ = n = = factor factor product quotient divisor dividend multiples of 3: 3,6,9,12,15... multiples of 6: 6,12,18,24... © Copyright NewPath Learning. All Rights Reserved. 93-4506 www.newpathlearning.com Operations with Mixed Numbers 1 4 2 = x 2 3 x 2 3 9 4 = 18 12 18 12 = 3 2 ÷6 ÷6 35 30 = 7 6 ÷5 ÷5 3 2 = 1 2 1 5 3 = 2 3 1 10 7 = 3 7 1 improper fraction mixed number 7 6 = 1 6 1 improper fraction mixed number 5 3 7 10 35 30 x =

Addition Subtraction Multiplication Division + + Add Step 1 2 3 2 1 6 3 Multiply 1 4 2 1 4 2 9 4 2 3 – – Subtract 3 4 4 5 8 2 Find the least common denominator (LCD) of and . 2 3 1 6 Step 1 Find the LCD and write equivalent fractions. LCD of and is . Step 2 Subtract the fractions first, then the whole numbers. Simplify the difference, if necessary. 3 4 5 8 Step 2 Write equivalent fractions with a denominator of 6. Step 1 Write the mixed number as an improper fraction. Step 1 Write the mixed number as improper fractions. Step 2 Rewrite as multiplication using the reciprocal of the divisor. Step 3 Multiply the numerators and denominators and simplify. Step 4 Write as a mixed number. Step 2 Multiply the numerators and denominators of the two factors. Step 3 Simplify the product. Step 4 Write the product as a mixed number, if it is an improper fraction. Step 3 Add the fractions. Then add the whole numbers. Simplify the sum, if necessary. 2 3 1 6 2 3 2 = 3 4 4 = – 5 8 2 1 6 3 + x = m Divide 3 7 1 2 3 1 ÷ = n = = factor factor product quotient divisor dividend multiples of 3: , , , , ... multiples of 6: , , , ... © Copyright NewPath Learning. All Rights Reserved. 93-4506 www.newpathlearning.com Operations with Mixed Numbers 1 4 2 = x 2 3 x = = = = 2 3 1 = 3 7 1 improper fraction mixed number 7 6 = improper fraction mixed number 5 3 7 10 x = Key Vocabulary Terms • addition • dividend • division • divisor • equivalent fraction • factor • fraction • improper fraction • least common denominator (LCD) • mixed number • multiplication • numerator • product • quotient • reciprocal • subtraction 35 30 = \|xiBAHBDy01657rzu

Algebraic Expressions Translating word phrases into algebraic expressions Evaluating algebraic expressions • An algebraic expression is a mathematical phrase consisting of variables, numbers, and operations. Solving Equations • An equation is a mathematical sentence which shows that two expressions or values are equal. • Think of an equation as a balance scale. • To evaluate an algebraic expression, replace the variable with a number • Replace m with 4 in the expression The letter m is a variable which represents an unknown number. 3 x 2m is an algebraic expression evaluate m + 5 for m = 4 m + 5 4 + 5 = 9 Operation Word Phase Algebraic Expression Addition m + 9 Subtraction m – 9 Multiplication 2m + 9 2 x m 2 • m 2m Division • A number plus 9 • The sum of m and 9 • 9 more than a number • A number increased by 9 • The difference between a number and 9 • A number minus 9 • 9 less than a number • A number decreased by 9 • 9 more than twice a number • 2 x a number • A number multiplied by 2 • The product of 2 and a number • A number divided by 9 • 9 divided by a number • The quotient of a number and 9 m 9 9 m m 9 28 = m + 16 equal sign • What number plus 16 equals 28? Solve 16 + m = 28 Solution m = 12 12 + 16 = 28 28 = 28 • Solve the equation to find the value of the variable that makes the equation true. The value of the variable is called the solution. Examples of Algebraic Expressions Addition Subtraction Multiplication Division 6 + d, or d + 6 c - 6 6 x b, or 6b a ÷ 6, or a 6 expression expression 28 16 m © Copyright NewPath Learning. All Rights Reserved. 93-4507 www.newpathlearning.com Introduction to Algebra

Algebraic Expressions Translating word phrases into algebraic expressions Evaluating algebraic expressions • An algebraic expression is a mathematical phrase consisting of variables, numbers, and operations. Solving Equations • An equation is a mathematical sentence which shows that two expressions or values are equal. • Think of an equation as a balance scale. • To evaluate an algebraic expression, replace the variable with a number • Replace m with in the expression The letter m is a which represents an unknown number. 3 x 2m is an evaluate m + 5 for m = 4 m + 5 4 + 5 = 10 Operation Word Phase Algebraic Expression Addition Subtraction Multiplication Division • A number plus 9 • The sum of m and 9 • 9 more than a number • A number increased by 9 • The difference between a number and 9 • A number minus 9 • 9 less than a number • A number decreased by 9 • 9 more than twice a number • 2 x a number • A number multiplied by 2 • The product of 2 and a number • A number divided by 9 • 9 divided by a number • The quotient of a number and 9 • What number plus 16 equals 28? Solve 16 + m = 28 Solution m = 12 + 16 = 28 = 28 • Solve the equation to find the value of the variable that makes the equation true. The value of the variable is called the solution. Examples of Algebraic Expressions Addition Subtraction Multiplication Division 28 = m + 16 equal sign expression expression 28 16 m Key Vocabulary Terms • algebra • algebraic expression • difference • equation • increase • more • plus • product • quotient • solution • sum • variable © Copyright NewPath Learning. All Rights Reserved. 93-4507 www.newpathlearning.com Introduction to Algebra \|xiBAHBDy01648pzY

On which color is the spinner more likely to land? • The probability of an event shows the chance that some event will occur. • An event is all the possible outcomes. • An impossible event has a probability of zero. • A certain event has a probability of 1. Finding Probabilities • You can determine the probability of an event by comparing the number of favorable outcomes with the total number of possible outcomes. There’s an even chance that the spinner will land on a green or yellow section. It is more likely that the spinner will land on a green section; and less likely that it will land on a yellow section. It is certain that the spinner will land on a green section; and impossible that it will land on a yellow section. When we toss a number cube, there are 6 possible different outcomes. It can show either 1, 2, 3, 4, 5 or 6. What is the probability that you will pick a red ball? probability of an event = number of favorable outcomes number of possible outcomes Count the number of red balls. Step 1 Count the total number of balls. Step 2 Write a fraction. Step 3 probability of picking a red ball = 1 3 1 2 probability of picking a red ball = = = 1 3 4 12 number of red balls total number of balls probability of picking a red ball = = 1 3 4 12 probability of picking a green ball = = 1 3 4 12 probability of picking a red & a green ball + = = 2 3 1 3 1 3 If you pick 2 balls from the bag, what is the probability that they will be red and green? • • • • Predicting Outcomes © Copyright NewPath Learning. All Rights Reserved. 93-4508 www.newpathlearning.com Probability Concepts

\|xiBAHBDy01660rzu On which color is the spinner more likely to land? • The probability of an event shows the chance that some event will occur. • An event is all the possible . • An impossible event has a probability of . • A certain event has a probability of . Finding Probabilities • You can determine the probability of an event by comparing the number of favorable outcomes with the total number of possible outcomes. There’s an that the spinner will land on a green or yellow section. It is that the spinner will land on a green section; and that it will land on a yellow section. It is that the spinner will land on a green section; and that it will land on a yellow section. When we toss a number cube, there are 6 possible different outcomes. It can show either 1 , 2 , 3 , 4 , 5 or 6 . What is the probability that you will pick a red ball? probability of an event = number of favorable outcomes number of possible outcomes Count the number of red balls. Step 1 Count the total number of balls. Step 2 Write a fraction. Step 3 probability of picking a red ball = = probability of picking a green ball = = probability of picking a red & a green ball + = = If you pick 2 balls from the bag, what is the probability that they will be red and green? • • • • Predicting Outcomes probability of picking a red ball = probability of picking a red ball = = = number of red balls total number of balls © Copyright NewPath Learning. All Rights Reserved. 93-4508 www.newpathlearning.com Probability Concepts Key Vocabulary Terms • certain • chance • even chance • event • favorable outcome • impossible • less likely • more likely • possible outcome • probability

Congruence & Similarity Symmetry 1 line of symmetry 4 lines of symmetry line of symmetry mirror placed through the middle of letter A 3 lines of symmetry Transformations – Flips, Slides & Turns The three main transformations are: • The reflected part of letter A on the mirror looks exactly the same as the original part. • Similar figures are identical in shape, but not in size. • A figure has line of symmetry if it can be folded or reflected into two congruent parts that fit on top of each other. The fold line or line of reflection is called the line of symmetry. • Shapes can be congruent if one of them has been transformed by sliding, flipping or turning. • The figure is moved along a straight line. • The figure is flipped over a line creating a mirror image. • The figure is moved around a point. • Congruent figures are identical in both shape and size. © Copyright NewPath Learning. All Rights Reserved. 93-4509 www.newpathlearning.com Slide or Translation Flip or Reflection Turn or Rotation A A A B B B C C1 B1 A1 D1 D C C mirror image Congruence, Transformations & Symmetry

Congruence & Similarity Symmetry 1 line of symmetry 4 lines of symmetry 3 lines of symmetry Transformations – Flips, Slides & Turns The three main transformations are: • Similar figures are identical in , but not in . • A figure has line of symmetry if it can be folded or reflected into parts that fit on top of each other. The fold line or line of reflection is called the . • Shapes can be congruent if one of them has been transformed by , or . . • Congruent figures are in both and . © Copyright NewPath Learning. All Rights Reserved. 93-4509 www.newpathlearning.com Slide or Translation Flip or Reflection Turn or Rotation A A B B C D C Congruence, Transformations & Symmetry Key Vocabulary Terms • congruent • flip • fold line • line of reflection • line of symmetry • reflection • rotation • shape • similar • size • slide • symmetry • transformation • translation • turn \|xiBAHBDy01642nzW

Circles & Related Figures AB is a radius AC is a diameter EF is a cord ∠DBC is a center angle A E C 0 10 20 30 40 50 60 70 80 90 100 110 120 130 14 0 15 0 16 0 17 0 18 0 18 0 17 0 16 0 15 0 14 0 13 0 120 110 100 90 80 70 60 50 40 30 20 10 0 Lines Angles Measuring Angles Drawing Angles right angle straight angle acute angle obtuse angle right angle A D G H E F I An angle is made up of two rays that share the same endpoint called the vertex. A straight angle forms a straight line. A right angle forms a square corner. Place the center point of the protractor over the vertex (corner) of the angle. Draw the ray DF. Place the center point of the protractor on the end point of the ray. Line up the ray DF so that it passes through the 0º mark of the protractor. Make a mark at 115º and label it E. Draw ray DE from the end point of ray DF to the mark you made at 115º. Place the protractor so that ray AC is over the base line of the protractor and passes through the 0º mark. Read the measure where the other ray AB crosses the protractor. An acute angle is less than a right angle. An obtuse angle is greater than a right angle. A ray is part of a line with one endpoint and goes on forever in the other direction. A line segment is part of a line between two endpoints. A line is a straight collection of points that extend in two opposite directions without end. A point is a location in space. AB CD BAC • point A • point B AB CD AB CD A A B D C B C interior exterior side A B D A B C D E F A B D C Line Segment Line Ray Angle Point Measure ∠BAC Draw ∠EDF of 115º B D F center The measure of ∠BAC is 65º Step 1 Step 2 Step 3 Step 1 Step 2 Step 3 Step 4 Step 5 0 10 20 30 40 50 60 70 80 90 100 110 120 130 14 0 15 0 16 0 17 0 18 0 18 0 17 0 16 0 15 0 14 0 13 0 120 110 100 90 80 70 60 50 40 30 20 10 0 A center point B C © Copyright NewPath Learning. All Rights Reserved. 93-4510 www.newpathlearning.com Lines, Angles & Circles

\|xiBAHBDy01650sz\ Circles & Related Figures AB is a AC is a EF is a ∠DBC is a A E C 0 10 20 30 40 50 60 70 80 90 100 110 120 130 14 0 15 0 16 0 17 0 18 0 18 0 17 0 16 0 15 0 14 0 13 0 120 110 100 90 80 70 60 50 40 30 20 10 0 Lines Angles Measuring Angles Drawing Angles A D G H E F I Define: Example: Define: Example: Define: Example: Define: Example: Define: Example: Place the center point of the protractor over the vertex (corner) of the angle. Place the protractor so that ray AC is over the base line of the protractor and passes through the 0º mark. Read the measure where the other ray AB crosses the protractor. Line Segment Line Ray Angle Point Measure ∠BAC Draw ∠EDF of 115º B D F center The measure of ∠BAC is 65º Step 1 Step 2 Step 3 Step 1 Step 2 Step 3 Step 4 Step 5 Key Vocabulary Terms • acute angle • angle • circle • cord • diameter • line • line segment • obtuse angle • point • protractor • radius • ray • right angle • straight angle • straight line • vertex 0 10 20 30 40 50 60 70 80 90 100 110 120 130 14 0 15 0 16 0 17 0 18 0 18 0 17 0 16 0 15 0 14 0 13 0 120 110 100 90 80 70 60 50 40 30 20 10 0 A center point B C © Copyright NewPath Learning. All Rights Reserved. 93-4510 www.newpathlearning.com Lines, Angles & Circles

Math Grade 5

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