Sample. Do Not Duplicate. Fourth Grade Math Book Teacher Edition. Step Up to the TEKS by GF Educators, Inc. Student: Teacher: Classroom:

Transcription

1 Step Up to the TEKS by GF Educators, Inc. Student: Teacher: Classroom: Fourth Grade Math Book Teacher Edition Copyright 204

2 Step Up to the TEKS Fourth Grade Math Book by GF Educators, Inc. Table of Contents Numerical Representations and Relationships Interpret Base-Ten (4.2A)... Represent Value of Digits (4.2B)...5 Compare and Order-Represent (4.2C)... Round Whole Numbers (4.2D)...6 Represent Decimals (4.2E)...9 Compare and Order Decimals (4.2F) Relate Decimals to Fractions (4.2G)...29 Determine Decimal on Number Line(4.2H)...34 Represent Sum of Fractions (4.3A)...38 Decompose a Fraction (4.3B) Determine Equivalent Fractions (4.3C)...46 Represent Comparison of Fractions (4.3D) Represent Distance from Zero (4.3G) Computations and Algebraic Relationships Represent/Solve Add/Sub Fractions (4.3E)...60 Evaluate Reasonableness Fractions (4.3F)...66 Add/Subtract whole and Decimals (4.4A)...69 Determine Products (4.4B) Represent Products (4.4C)...79 Multiply Using Strategies/Algorithms (4.4D)...83 Represent Quotients (4.4E)...87 Divide Using Strategies/Algorithms (4.4F)...9 Round 0, 00, or,000 (4.4G)...95 Solve with Fluency (4.4H) Represent Multi-Step Problems (4.5A) Represent Input-Output (4.5B)...2 Geometry and Measurement Solve Problems Perimeter/Area (4.5D)...8 Identify Attributes (4.6A)...24 Identify Symmetry (4.6B)...28 Identify Triangles (4.6C)...32 Classify by Lines and Angles (4.6D)...36 Determine Measurement of Angles (4.7C)...42 Draw Angles Given Measure (4.7D)...48 Determine Angle Adjacent Angles (4.7E)...52 Identify Measurement Units (4.8A)...56 Convert Measurements (4.8B)...60 Solve Measurement Problems (4.8C)...64 Data Analysis and Personal Financial Literacy Represent Data (4.9A)...70 Solve Problems Using Data (4.9B)...75 Distinguish Between Fixed/Variable Expenses (4.0A)...79 Calculate Profit (4.0B) Describe Financial Instructions (4.0E)...85

3 BI Background Information Describe Base-Ten Place Value Category Student Expectations - Supporting Standard TEKS Number and operations. The student applies mathematical process standards to 4.2A represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to interpret the value of each place-value position as 0 times the position to the right and as one-tenth of the value of the place to its left. Vertical Alignment Vocabulary The student will demonstrate an understanding of how to represent and manipulate numbers and expressions. Composing and Decomposing Numbers: Place Value Grade st 2nd 3rd 5th 6th Base-Ten, 0 Times, Place Value, Tenth, Hundredths Understanding the TEKS Student is expected to... None None Since the number system we use is based on 0, then each place value to the left is multiplied by 0, and each place value to the right is multiplied by 0 or divided by 0. Essential Question(s) Each place value to the right is multiplied by. Each place value to the left is multiplied by. 3.2B describe the mathematical relationships found in the base-ten place value system through the hundred thousands place 5.2A represent the value of the digit in decimals through the thousandths using expanded notation and numerals None 4th Grade Mathematics 204

4 BI Background Information Describe Base-Ten Place Value Base-Ten Make a desk chart for each student to have on their desk as a reference to learn the relationship between the place values. Write the value of the number in the box that represents the words. (Multiplying by 0 is the same as dividing by 0. million = 0 x hundred thousands hundred thousand = 0 x million hundred thousand=0 x ten thousands ten thousand = 0 x hundred thousand ten thousands = 0 x thousands thousand = 0 x ten thousand thousand = 0 x hundreds hundred = 0 x thousand hundred = 0 x tens tens = 0 x hundred tens = 0 x ones ones = 0 x tens ones = 0 x tenths tenths = 0 x ones tenths = 0 x hundredths hundredths = 0 x tenths th Grade Mathematics

5 A Engaging Activity Describe Base-Ten Place Value TEKS 4.2A Supporting Every time you cross over to another place value to the left, it is times 0. Every time you cross over to another place value to the right, it is times 0 divided by 0. How many zeros are in 00? So 0 is multiplied 2 times. 0 x 0 2 How many zeros are in,000? Base-Ten and Zeros Thousands Hundreds Tens Tenths Hundredths X X X X , So 0 is multiplied 3 times. 0 x 0 x 0 3 Each place value to the right is multiplied by 0. What does 0 of 0 look like in decimals? or 4 What does 0 of 0 look like in decimals? 4th Grade Mathematics 3 204

6 A Engaging Activity Describe Base-Ten Place Value TEKS 4.2A Supporting Number , , , ,000, , , ,000 Base-Ten 0 Times the Number 0 of the Number th Grade Mathematics

7 TM Teaching Model Interpret Base-Ten Place Value I can... interpret the value of a number as 0 times or as /0 of a number. Complete the table. Number Putting the Pieces Together Thinking Mathematically 0 Times the Number Make sure the students understand how multiplying by 0 moves the place value to the left. 0 x 0 = X 0 =,000,000 x 0 = 0,000 Make sure the students understand how multiplying by the right. 00 x 0 = 0 0 x 0 = X 0 = x 0 of the Number , ,000, Each place value to the right of the decimal point is multiplied by 0. Each place value to the left of the decimal point is multiplied by 0. 0 moves the place value to 0 = 0.0 4th Grade Mathematics 5 204

8 GP Guided Practice Interpret Base-Ten Place Value TEKS 4.2A Supporting If 37,000 is 37 x,000, then 68,000 is x, Complete this statement: 00 is 0 times as much as. 3 Complete these statements with 0 times as much or 0 as much : 300 is as is as ,000 is as is as 8, Lana has been saving only dimes in two different piggy banks during the month of September. She visited the bank and exchanged her dimes for dollar bills. Complete the following chart. Number of Dimes Number of Dollars & Cents Explain what you did to change the dimes to dollars? How many total dollars will she be able to exchange for her dimes? You must show your work th Grade Mathematics

9 AK Answer Key Interpret Base-Ten TEKS 4.2A Supporting Activity Activity , , ,000-, ,600,000-36, ,700,000,000-27,000, , ,290,000-72, ,840,000-38, ,720,000-47, Teaching Model , ,000,000, ,000, Guided Practice , 0, 0, 0 4. $5.50, $7.60 Divided by 0 $3 and dime Independent Practice Page 3 SE. B 2. D 3. C 4. B Page 4 SE. A 2. D 3. C 4. A 5. A 6. B Teaching Model: They must understand the concept of multiplying by 0 when moving one place value to the left. and multiplying by 0 when moving one place value to the right. Add-on a zero to the left and take a zero away to the right. Guided Practice: There are three different formats on this page pertaining to this concept. Make sure the students understand each. Page 3 SE: Interpret is presented in the first problem and must be read carefully. The others pertain to the student s interpretation of 0, 0, and 00. Page 4 SE: Reinforce when to multiply by 0 and when to multiply by B 4th Grade Mathematics 7 204

10 BI Background Information Represent Value of Digits Place Value Category Student Expectations - Readiness Standard TEKS Number and operations. The student applies mathematical process standards to 4.2B represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to represent the value of the digit in whole numbers through,000,000,000 and decimals to the hundredths using expanded notation and numerals. Vertical Alignment Vocabulary The student will demonstrate an understanding of how to represent and manipulate numbers and expressions. Composing and Decomposing Numbers: Place Value Grade st 2nd 3rd 5th 6th Standard Form, Expanded Form, Word Form, Digit, Decimals, Numerals Understanding the TEKS Student is expected to....2c use objects, pictures, and expanded and standard forms to represent numbers up to B use standard, word, and expanded forms to represent numbers up to, A compose and decompose numbers up to 00,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate 5.2A represent the value of the digit in decimals through the thousandths using expanded notation and numerals None The students need to understand the concept of composing a number by placing ones, tens, and hundreds into one number. Standard Form (526) The concept of decomposing by breaking it down into its value. Expanded Form ( ) The fluency and analysis involved in the process skills manipulates decomposing through the 5-break down. (772 = ) Great for understanding rounding later. Essential Question(s) What is a digit? What is a number? What is the difference in a digit and a number? th Grade Mathematics

11 A Engaging Activity Represent Value of Digits Place Value TEKS 4.2B Readiness Standard Form Expanded Form Word Form 357,00 3,340,0 482,067,000, , , , , four million,six hundred thousand, two seven hundred thousand, fifty-three 30, ,000 +, th Grade Mathematics 9 204

12 TM Teaching Model Represent Value of Digits Place Value I can represent a value of a digit as a number or expanded notation. Which of the following is represented in expanded notation? A B C D Which of the following is true about the number 6.48? A The digit 4 has the value of B The digit 6 has the value of 600. C The digit 8 has the value of D The digit 4 has the value of 40. Putting the Pieces Together Numbers can be composed and decomposed. Numbers can be manipulated to solve problems. Use place value and the ability to manipulate numbers to solve problems. Thinking Mathematically What is a digit? A symbol used to make numbers. 0,, 2, 3, 4, 5, 6, 7, 8, 9 What is a number? An amount or measure: 245, 4,.05 What is the difference between a digit and a number? Digits are used to make up numbers. 345 is a number. The 3, 4, and 5 are all digits th Grade Mathematics

13 GP Guided Practice Represent Value of Digits Place Value TEKS 4.2B Readiness Create a number with: a 5 in the ten-thousands place a 2 in the tens place a 9 in the hundredths place Write digits in the boxes to represent the number. 2 Ella entered this number into her calculator. 7:00 2,345 mc m+ m- mr What number should she add to this number to increase the digit in the thousands place by 6? 3 By how much would the value of 4,536 be decreased if the 4 were replaced by a? A 3,,. B 300 C 3,000 D 30,000 4 I am a number. When you switch my ten-thousands digit with my hundreds digit, I become 95,874. What number am I? A 958,74 B 985,74 C 98,574 D 95,874 5 Which statement about the number is not true? A The digit 2 has the value of 20. B The digit 8 has the value of C The digit has the value of 0. D The digit 4 has the value of Which statement about the number is true? A The digit 4 has the value of 40. B The digit 8 has the value of 80. C The digit 7 has the value of D The digit 5 has the value of th Grade Mathematics 204

14 AK Answer Key Represent Value of Digits TEKS 4.2B Readiness Activity:,503, ,00 4,600,002 3,340,0 230, , ,067 26,070 Teaching Model. D 2. C Guided Practice. Answers May Vary 2. 6, C 4. B 5. C 6. C Independent Practice Page 7 SE. B 2. D 3. B 4. A Page 8 SE. B , D 4. D 5. C Page 9 SE. B 2. D 3. C Page 0 SE. B 2. A 3. B Activity: Numbers seen in different ways for flexibility. Teaching Model: Digits make up a number. Digits are symbols, and numbers have value. Use them that way when you talk to the students. Guided Practice: Several different formats are presented for understanding. Independent Practice: Several different formats are presented developing fluency and flexibility with numbers th Grade Mathematics

15 BI Background Information Compare and Order and Represent Place Value Category Student Expectations - Supporting Standard TEKS Number and operations. The student applies mathematical process standards to 4.2C represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to compare and order whole numbers to,000,000,000 and represent comparisons using the symbols >, <, or =. Vertical Alignment Vocabulary The student will demonstrate an understanding of how to represent and manipulate numbers and expressions. Comparing and Ordering Numbers Grade st 2nd 3rd 5th 6th Symbols: <, >, = Greater than, Less than, Digit, Order Understanding the TEKS Student is expected to... The students will be comparing whole numbers only to,000,000,000. If the first digits are the same, then go to the next place value and compare. Example: 34, , ,523.2E use place value to compare whole numbers up to 20 using comparative language..2f order whole numbers up to 20 using place value and open number lines..2g represent the comparison of two numbers to 00 using the symbols >, <, or =. 2.2D use place value to compare and order whole numbers up to,200 using comparative language, numbers, and symbols (>, <, or =). 3.2D compare and order whole numbers up to 00,000 and represent comparisons using the symbols >, <, or = 5.2B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or = 6.2D order a set of rational numbers arising from mathematical and real-world contexts Compare and Order goes through 00,000 in third grade. Essential Question(s) The symbol > always points to the The symbol < always points away from the number. number. 4th Grade Mathematics 3 204

16 A Engaging Activity Compare and Order and Represent TEKS 4.2C Supporting Place Value Greater Than, Less Than am pl e Use the digits to make 5 different numbers. Now use these numbers to make these statements true. ic at e 2 D u pl N o 5 D S ot 4 4 4th Grade Mathematics

17 TM Teaching Model Compare and Order-Represent Place Value I can... I can compare and order whole number through,000,000,000. A group of numbers is shown below. 254,374, ,375, ,385, ,375,238 Which statement about two of these numbers is true? A 254,385,228 = 254,375,228, because 228 = 228 B 254,374,728 > 254,375,228, because 728 > 228 C 254,375,228 < 254,375,238, because 28 < 38 D 254,374,728 > 254,375,238 because 728 > 238 Putting the Pieces Together The students need to understand place value and to look carefully at the two largest place values of the numbers being compared. If the first numbers are the same, then look at the second and keep going until the numbers are different and can be compared. Thinking Mathematically The symbol > always points to the smallest number. The symbol < always points away from the largest number. 4th Grade Mathematics 5 204

18 GP Guided Practice Compare and Order-Represent Place Value TEKS 4.2C Supporting Which pair of numbers is true? A 5,09 > 5,90 B 7,805 < 7,850 C 7,805 > 7,98 D 5,09 = 5,90 2 Four people collect baseball cards as shown on the table. Charles Jose James Juan Name Baseball Cards Since Jose had more cards than anyone else, he decided to give 55 of his cards to James. Which statement is true after Jose gave away 55 of his cards? A James' cards < Juan's cards B Charles' cards > James' cards C James' cards > Juan's cards D James' cards > Jose's cards 3 Charlie manages an amusement park. On July 2nd there were 794,329 tickets sold. On July 3rd there were 6,978,30 tickets sold. On July 4th there were 35,439,30 people that enjoyed the park. On July 5th, a Sunday, 6,898,739 people came. Compare the number of tickets sold each day using <, >, and =. You must show your work th Grade Mathematics

19 AK Answer Key Compare and Order-Represent TEKS 4.2C Supporting Activity Answer may vary Teaching Model. C Guided Practice. B 2. C ,329 < 6,978,30 6,978,30 < 35,439,30 35,439,30 > 6,898,739 Independent Practice Page 3 SE. <, >, >, <, < 2. D 3. D 4. C 5. D 6. D 7. D Page 4 SE. C 2. B 3. D 4. D Page 5 SE. A 2. D 3. >, <, >, < 4. B 5. C 6. >, <, >, < Teaching Model: The digits in the place values are the same until the ten thousands place. The students must keep comparing until they reach numbers that are different. Guided Practice: Watch out for problem two. The changes must be made before they can be compared. Independent Practice: Look carefully at the digits and the place values each represents. 4th Grade Mathematics 7 204

20 BI Background Information Round Whole Numbers Place Value Category Student Expectations - Supporting Standard TEKS 4.2D Vertical Alignment Vocabulary The student will demonstrate an understanding of how to represent and manipulate numbers and expressions. Number and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to round whole numbers to a given place value through the hundred thousands place. Applying Strategies for Estimation Round, Nearest Grade st 2nd 3rd 5th 6th Understanding the TEKS Student is expected to... None None 3.4B round to the nearest 0 or 00 or use compatible numbers to estimate solutions to addition and subtraction problems 5.2C round decimals to tenths or hundredths None The students are expected to be able to round place value to the hundred thousands place. Essential Question(s) What strategy do you use when rounding? th Grade Mathematics

21 A Engaging Activity Round Whole Numbers Place Value TEKS 4.2D Supporting Round each number to the place value specified. Round 27,688 to the nearest ten thousand. 2 Round 2,797,559 to the nearest hundred thousand. 3 Round 7,589,307 to the nearest thousand. 4 Round 254,580 to the nearest hundred. 5 Round 2,583,48 to the nearest hundred thousand. 6 Round 473,582 to the nearest ten. 7 Round 973,97 to the nearest ten thousand. 8 Round 77,59 to the nearest thousand. 9 Round,534,768 to the nearest hundred thousand. 0 Round 3,745,890 to the nearest ten thousand. Round 286,24 to the nearest ten. Rounding 2 Round 3,456,23,765 to the nearest hundred thousand. 4th Grade Mathematics 9 204

22 TM Teaching Model Round Whole Numbers Place Value I can round numbers to a specific place value. The cost of tuition at Cornell University is $43,000 per year when rounded to the nearest thousand. What is the greatest possible amount the tuition could be before it was rounded? What is the least possible amount the tuition could be before it was rounded? Greatest Least Putting the Pieces Together Make sure the students can verbalize the strategy they are using when rounding. Determine the approach and strategy to rounding. Thinking Mathematically What strategy do you use when rounding? Answers may vary When do we usually need to round numbers? When we want a quick, but not exact amount th Grade Mathematics

23 GP Guided Practice Round Whole Numbers Place Value TEKS 4.2D Supporting Mrs. Smith s class is learning about healthy eating habits. The students learned that the average child should consume about 2,000 calories each week. Kerry consumed 2,748 calories last week. Tyler consumed,702 calories last week. Round each to the nearest thousand. 2,748,702 2 A pilot wanted to know about how many kilometers he flew on his last 3 flights. From NYC to London he flew 5,572 kilometers. Then, from London to Beijing he flew 8,47 kilometers. Finally, he flew 0,996 kilometers from Beijing back to NYC. Round each number to the nearest hundred kilometers. 3 It takes 39,090 gallons of water to manufacture a new car. Sammy thinks that it should be rounded up to 40,000 gallons. Susie thinks it should be rounded to 39,000 gallons. Who rounded to the nearest thousand, Sammy or Susie? Explain your answer. 4 Marsha s brother wanted help with the first question on his homework. The question asked the students to round 28,902 to the nearest thousand and then to explain the answer. Marsha s brother thought that the answer was 28,000. Was his answer correct? A Yes, because 28,902 rounded to the nearest thousand is 29,000. B No, because 28,902 rounded to the nearest thousand is 29,000. C Yes, because 28,902 rounded to the nearest thousand is 28,000. D No, because 28,902 rounded to the nearest thousand is 30, Louise s family went on vacation to Disney World. Their vacation cost $5,990. Sophia s family went on vacation to Niagara Falls. Their vacation cost $4,720. Both families budgeted about $5,000 for their vacation. Round to the nearest thousand, whose family stayed closer to the budget? A Louise s family because $5,990 rounded to the nearest thousand is $5,000. B Louise s family because $5,990 rounded to the nearest thousand is $6,000. C Both Louise and Sophia because $4,720 and $5,990 would both be rounded $5,000. D Sophia s family because $4,720 rounded to the nearest thousand is $5,000 and $5,990 would be rounded to $6,000. 4th Grade Mathematics 2 204

24 AK Answer Key Round Whole Numbers TEKS 4.2D Supporting Activity. 270, ,800, ,589, , ,600, , , ,000 9.,500, ,750, , ,500,000 Teaching Model. 43, ,500 Guided Practice. 3,000--2, ,600--8,00--, Susie--39,000 Look at hundred place 4. B 5. D Independent Practice Page 8 SE. A 2. B 3. D 4. 25, , , , , ,000 Activity: Look carefully at the place value being asked to round. Teaching Model: This problem gives the student the opportunity to explain the range for rounding this number to the nearest thousands. Guided Practice: Read each answer choice carefully and interpret it fully. Independent Practice: With rounding, just look at the number before the one being rounded, then make your decision th Grade Mathematics

25 BI Background Information Represent Decimals Decimals Category Student Expectations - Supporting Standard TEKS 4.2E Vertical Alignment Vocabulary The student will demonstrate an understanding of how to represent and manipulate numbers and expressions. Number and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to represent decimals, including tenths and hundredths, using concrete and visual models and money. Composing and Decomposing Numbers: Place Value Grade st 2nd 3rd 5th 6th Concrete and Visual Models Understanding the TEKS Student is expected to... None None None 5.2A represent the value of the digit in decimals through the thousandths using expanded notation and numerals None Students should actually use hands-on manipulatives to model decimals. Students are not expected to represent decimals smaller than hundredths. Essential Question(s) What is the value of each small square in the one large square? How can a model represent a decimal? 4th Grade Mathematics

26 A Engaging Activity Represent Decimals TEKS 4.2E Supporting Decimals Fill in the grid to show the decimal. 2 tenths and 7 tenths am pl e 0.8 and 37 hundredths 75 hundredths 0.62 at e N o D S ot D u pl ic Write the decimal represented by the grid. 24 4th Grade Mathematics

27 TM Teaching Model Represent Decimals Decimals I can... represent a decimal from a model. Which decimal tells how much is shaded? A 75 B 7.5 C 0.75 D Putting the Pieces Together The zero is very important. It can change 0.7 (tenths) to 0.07 (hundredths). Require the students to place the zero in the ones place if there are no whole numbers. Thinking Mathematically What is the value of each small square in the one large square? Each small square represents 00 of the large square. How can a model represent a decimal? Decimals using place value of /0 or /00 can be represented using a 0 grid or a 00 grid model. 4th Grade Mathematics

28 GP Guided Practice Represent Decimals Decimals TEKS 4.2E Supporting The model is shaded to show what number? 2 The model is shaded to show what number? 3 Which answer tells how much is shaded? A.06 B.4 C.6 D 0.4 You must show your work. Caution: Be sure students are counting all of the shaded squares out of 00 total squares. Caution: Be sure students are counting all of the shaded squares out of 0 total squares th Grade Mathematics

29 AK Answer Key Represent Decimals TEKS 4.2D Supporting Activity Visual Evaluation Teaching Model. C Guided Practice B Independent Practice Page 2 SE. D 2. Visual Evaluation 3. Visual Evaluation Page 22 SE. A 2. C 3. B 4. C 5. B Page 23 SE. D Teaching Model: The large square represents the whole number. It is then divided into hundredths, so any part would be less than one: 0.0, 0.02, etc. The rows are tenths. The student could count the rows for the tenths place and then the individual boxes for the hundredths place. Guided Practice: A row represents tenths. A square represents hundredths. Independent Practice: Page 23: Read carefully. Which grid is shaded to represent a decimal greater than 0.89? 4th Grade Mathematics

30 BI Background Information Compare and Order Decimals Decimals Category Student Expectations - Supporting Standard TEKS Number and operations. The student applies mathematical process standards to 4.2F represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to compare and order decimals using concrete and visual models to the hundredths. Vertical Alignment Vocabulary The student will demonstrate an understanding of how to represent and manipulate numbers and expressions. Comparing and Ordering Numbers Grade st 2nd 3rd 5th 6th Tenths, Hundredths, Decimal, Models Understanding the TEKS Student is expected to... None None None 5.2B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or = 6.2D order a set of rational numbers arising from mathematical and real-world contexts Zeros make a great difference in numbers. Even if it does not have a value, it represents a place. They are really important in decimals. 0.8 and 0.08 are not even close to being equal. It would be like saying that 80 is equal to 800 on the other side of the decimal point. Essential Question(s) What is the difference in the two diagrams above? Each model represents a value th Grade Mathematics

31 A Engaging Activity Compare and Order Decimals Decimals TEKS 4.2F Supporting Convert each model into a decimal, then order the decimals from least to greatest. Convert Order 2 Convert Order 4th Grade Mathematics

32 TM Teaching Model Compare and Order Decimals Decimals I can compare and order decimals using models. B Which model represents a greater value: B or C? Explain your thinking. Putting the Pieces Together Students need to be able to visually compare models to determine order. Handson manipulatives should be used in class. Thinking Mathematically What is the difference in the two diagrams above? The first model shows hundredths and the second model shows tenths. Each model represents a value less than one. C th Grade Mathematics

33 LIBERTY LIBERTY IN GOD D D D LIBERTY LIBERTY D P P P P IN GOD D D LIBERTY LIBERTY P P LIBERTY D D LIBERTY LIBERTY IN GOD D D LIBERTY IN GOD D LIBERTY IN GOD D D P P D P D D IN GOD D P P IN GOD D GP Guided Practice Compare and Order Decimals Decimals TEKS 4.2F Supporting Naomi has an amount of money that wold make the comparison below true. > Which amount of money would make the comparison true? A B C D I N L I B I N E PLURIBUS UNUM UNITED STATES OF AMERICA QUARTER DOLLAR G O D L W E IN GOD WE TRUST T R U S T 2007 I B E R T Y I N UNITED STATES OF AMERICA QUARTER DOLLAR L E R T Y G O D W E IN GOD WE TRUST E PLURIBUS UNUM T R U S T 2007 I B E R T Y L G O D IN GOD WE UNITED STATES OF AMERICA TRUST QUARTER DOLLAR WE TRUST 2005 L IN GOD WE TRUST E PLURIBUS UNUM I B E R T Y E PLURIBUS UNUM L IN GOD WE TRUST UNITED STATES OF AMERICA QUARTER DOLLAR I N G O D W E T R U S T 2007 W E T R U S T E PLURIBUS UNUM UNITED STATES OF AMERICA 2007 QUARTER DOLLAR IN GOD WE TRUST I N L I B E R T Y G O D E PLURIBUS UNUM 95 W E T R U S T UNITED STATES OF AMERICA I B E R T Y QUARTER DOLLAR IN GOD WE TRUST I N L I B E R T Y UNITED STATES OF AMERICA I B E R T Y L I B E R T Y WE TRUST 2005 QUARTER DOLLAR I N IN GOD WE TRUST E PLURIBUS G O D UNUM I N W E G O D T R U S T L I B E R T Y W E I N 95 T R U S T IN GOD WE TRUST G O D G O D 2007 W E W E L I B L IN GOD WE TRUST I B E R T Y L I B E R T Y 95 E PLURIBUS UNUM UNITED STATES OF AMERICA L QUARTER DOLLAR IN GOD WE T R U S T TRUST 2007 I B E R T Y E PLURIBUS UNUM UNITED STATES OF AMERICA QUARTER DOLLAR T R U S T E R T Y 2007 L I B WE TRUST 2005 I N E R T Y I N G O D WE TRUST 2005 G O D L I B W E E R T Y E PLURIBUS UNUM W E T R U S T WE TRUST 2005 T R U S T 2007 UNITED STATES OF AMERICA QUARTER DOLLAR 2007 I N LIBERTY G O D W E T R U S T 2007 E PLURIBUS UNUM UNITED STATES OF AMERICA QUARTER DOLLAR L L IN GOD WE IN GOD WE TRUST TRUST I B E R T Y L I B E R T Y WE TRUST 2005 I B E R T Y IN GOD WE TRUST E PLURIBUS UNUM UNITED STATES OF AMERICA QUARTER DOLLAR E PLURIBUS UNUM UNITED STATES OF AMERICA QUARTER DOLLAR L I B E R T Y 95 L I B E R T Y WE TRUST 2005 You must show your work. D 2007 L I B E R T Y L I B E R T Y IN GOD WE TRUST IN GOD WE TRUST L I B E R T Y 95 IN GOD WE TRUST th Grade Mathematics 3 204

34 GP Guided Practice Compare and Order Decimals Decimals TEKS 4.2F Supporting A B C D List these models in order from least to greatest. A A A, B, C, D B D, C, B, A C D, B, C, A D A, C, B, A B Statement : A < C Statement 2: D > B Statement 3: C < B 2 Which statements are true? A Statement 2 only B Statement & 3 only C All of the statements D None of the statements C D You must show your work th Grade Mathematics

35 AK Answer Key Compare and Order Decimals TEKS 4.2F Readiness Activity. Convert: 0.2, 0.6, 0.04 Order: 0.6, 0.2, Convert: 0.6, 0.7, 0.75 Order: 0.75, 0.7, 0.6 Teaching Model. B B has 0.04 more than C. Guided Practice. B Guided Practice. B 2. B Independent Practice Page 27 SE. C 2. B 3. D 4. C 5. D 6. B Page 28 SE. Visual Evaluation 2. A 3. D Teaching Model: The rows represent tenths. The squares represent hundredths. Guided Practice: Money represents decimals. Coins represent amounts under a dollar. They are coins that represent 0.0, 0.25, 0.05, 0.0. There are ten hundredths doing across and ten hundredths going down so it does not matter if the row is across or down. Independent Practice: Understand that each row that represents a tenth, 0., is made up of 0 hundredths, = 0.0 Read carefully on Page 28 and do what is asked. Analyze the results on the next question. 4th Grade Mathematics

36 BI Background Information Relate Decimals to Fractions Decimals Category Student Expectations - Readiness Standard TEKS Number and operations. The student applies mathematical process standards to 4.2G represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to relate decimals to fractions name tenths and hundredths. Vertical Alignment Vocabulary The student will demonstrate an understanding of how to represent and manipulate numbers and expressions. Representing and Relating Numbers Using Number Lines Determining Equivalence and Comparing Part-to-Whole Relationships Grade st 2nd 3rd 5th 6th Tenths, Hundredths Understanding the TEKS Student is expected to... None 2.2F name the whole number that corresponds to a specific point on a number line. 3.3A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines 3.3B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line None 6.2B identify a number, its opposite, and its absolute value 6.2C locate, compare, and order integers and rational numbers using a number line 6.5C use equivalent fractions, decimals, and percents to show equal parts of the same whole Students should have an understanding of place value for decimals and how it relates to a fractional piece of 0 or 00. Essential Question(s) How do fractions and decimals relate? Why is place value important? th Grade Mathematics

37 A Engaging Activity Relate Decimals to Fractions Decimals TEKS 4.2G Readiness Describe the shaded portion of each grid as a fraction with a denominator of 00, as a simplified fraction, and as a decimal number. Fraction with a denominator of 00: Simple fraction: Decimal number: Fraction with a denominator of 00: Simple fraction: Decimal number: Fraction with a denominator of 00: Simple fraction: Decimal number: Fraction with a denominator of 00: Simple fraction: Decimal number: 4th Grade Mathematics

38 TM Teaching Model Relate Decimals to Fractions Decimals I can relate fractions and decimals to each other. Susan is making a beaded necklace. She gathered 20 beads for the necklace. She has 5 yellow, 5 red, 3 blue and 7 green beads. What fraction represents the number of red beads? What decimal represents the number of red beads? What fraction represents the number of blue beads? What decimal represents the number of blue beads? What fraction represents the number of green beads? What decimal represents the number of green beads? What fraction represents the number of yellow beads? What decimal represents the number of yellow beads? Putting the Pieces Together Students should be able to use the beads in the problem above to represent a fraction or a decimal out of the whole necklace. Students should relate these 20 beads to how many out of 00 beads. The understanding of place value should then be used to determine the decimal. Thinking Mathematically How do fractions and decimals relate? A fraction is another form of writing a decimal and a decimal is another form of a decimal. Both represent a part of the whole. Why is place value important? Place value determines the part of the whole needed th Grade Mathematics

39 GP Guided Practice Relate Decimals to Fractions Decimals TEKS 4.2G Readiness The models below are shaded to represent four different fractions Which decimal is not represented by one of these models? A B 0.68 C 0.5 D The models below are shaded to represent the part of pizzas eaten by the Hernandez family. Which fraction and decimal represent the part of these pizzas eaten by the Hernandez family? A 7 0 and 0.7 B 7 0 and.7 C 7 20 and.7 D 7 0 and.07 You must show your work. Caution: Make sure students are counting the shaded squares out of the total 0 or 00. 4th Grade Mathematics

40 AK Answer Key Relate Decimals to Fractions TEKS 4.2G Readiness Activity. 50/00, /2, /00, /0, /00, 4/0, /00, 7/0 + 6/00, 0.76 Teaching Model. 5/ / / / Guided Practice. A 2. B Independent Practice Page 3 SE. C 2. D 3. C 4. C 5. A 6. A Page 32 SE. B 2. C 3..2 > A 5. Visual Evaluation 6. 45/ cents Page 33 SE. A 2. B Teaching Model: The total beads is 20 so this represents the denominator. Guided Practice: Read carefully problem : not. Read carefully problem 2: Which fraction of the pizza was eaten? The shaded pieces are the eaten pieces. Independent Practice: Read carefully and analyze each problem before answering th Grade Mathematics

41 BI Background Information Determine Decimal on Number Line Decimals Category Student Expectations - Supporting Standard TEKS Number and operations. The student applies mathematical process standards to 4.2H represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line. Vertical Alignment Vocabulary The student will demonstrate an understanding of how to represent and manipulate numbers and expressions. Representing and Relating Numbers Using Number Lines Grade st 2nd 3rd 5th 6th Corresponding, Specified Understanding the TEKS Student is expected to... None None Students are expected to determine the corresponding decimal point to the tenths and hundredths place on a number line. Essential Question(s) How do you represent a tenth on a number line? How do you represent a hundredth on a number line? 3.3C explain that the unit fraction /b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number None None 4th Grade Mathematics

42 A Engaging Activity Determine Decimal on Number Line Decimals TEKS 4.2H Supporting Write the correct letter on the blank line next to each decimal. a c e g i k 0 2 b d c Place the letter for the each number on the number line. A 5.2 B 6.75 C 6.99 D 5.7 E 6.3 F 5.45 f h j l th Grade Mathematics

43 TM Teaching Model... Determine Decimal on Number Line I can determine the placement of a decimal on a number line. Decimals Point U best represents what number? Putting the Pieces Together Students need to be able to graph on a number representing tenths and hundredths. In looking at the number lines above, students can count by tenths to find the location of U. Thinking Mathematically How do you represent a tenth on a number line? To represent a tenth, one unit needs to be divided into 0 pieces. How do you represent a hundredth on a number line? To represent a hundredth, one unit needs to be divided into 00 pieces or the label needs to show each unit. U 4th Grade Mathematics 4 204

44 GP Guided Practice Determine Decimal on Number Line Decimals TEKS 4.2H Supporting A B C D 0 2 Which letter best represents 0.2? 2 Which letter best represents 0.4? A B C D Which letter best represents.? 4 Which letter best represents 0.82? 5 Which point on the number line best represents 5.3? P Q R S A P C R B Q D S You must show your work. Hint: Additional lines may be added to the number line for more precise fractional pieces th Grade Mathematics

45 AK Answer Key Determine Decimal on Number Line TEKS 4.2H Supporting Activity. c 2. e 3. h 4. g 5. i 6. b 7. k 8. a 9. l 0. d. j 2. f A, F, D, E, B, C Teaching Model Guided Practice. A 2. B 3. D 4. C 5. C Independent Practice Page 36 SE. C 2. B U 6. A 7. B Page 37 SE. Visual Evaluation 2. A 3. C 4. A 5. D 6. C Activity: Watch out for numbers like 0.25 or These would be between markers. Teaching Model: Each marker is a tenth. Guided Practice: Look for closeness to 0, /2, as in question, 2, 3 and 4. Independent Practice: Look for closeness to 0, /2, or look at tenths. 4th Grade Mathematics

46 BI Background Information Represent Sum of Fractions Fractions Category Student Expectations - Supporting Standard TEKS Number and operations. The student applies mathematical process standards to 4.3A represent and generate fractions to solve problems. The student is expected to represent a fraction a/b as a sum of fractions /b, where a and b are whole numbers and b > 0, including when a > b. Vertical Alignment Vocabulary The student will demonstrate an understanding of how to represent and manipulate numbers and expressions. Representing Fraction Concepts Sum Grade st 2nd 3rd 5th 6th Understanding the TEKS Student is expected to... None None 3.3D compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts /b None 6.2E extend representations for division to include fraction notation such as a/b represents the same number as a b where b 0 When paired with revised SE 4()(D), students may represent a/b as a sum of fractions /b using concrete and pictorial models, which includes improper fractions when a>b. Essential Question(s) th Grade Mathematics

47 A Engaging Activity Represent Sum of Fractions Fractions TEKS 4.3A Supporting Draw a model that represents the given fraction as the sum of its unit fractions. Then write the related addition problem. Example: = th Grade Mathematics

48 TM Teaching Model Represent Sum of Fractions Fractions I can represent a fraction a/b using the sum of unit fractions. Look at the strip diagram below. What is the fraction represented by the shaded area? What is the fraction that is represented by each piece of the shaded area? Write an addition problem that represents this shaded area. Putting the Pieces Together Students need to understand how a fraction can be represented using the sum of its unit fractions. Using models or pictures can reinforce this understanding. Thinking Mathematically How can I represent a fraction using the sum of unit fractions? Models or pictures can be used to demonstrate the decomposition of fractions into the sum of its unit fractions. Why is a unit fraction important? The unit fraction represents the base unit of a fraction. What models will I use to represent the sum of a fraction? Fraction strips work well to represent the sum of a fraction th Grade Mathematics

49 GP Guided Practice Represent Sum of Fractions Fractions TEKS 4.3A Supporting Look at the number line below. You must show your work. 0 Write the fraction represented by the model. 2 Write the fraction representation for each piece. 3 Write the related addition problem. Look at the number line below. 0 4 Write the fraction represented by the model. 5 Write the fraction representation for each piece. 6 Write the related addition problem. 4th Grade Mathematics

50 AK Answer Key Activity Visual Evaluation Teaching Model. 5/6, /6, /6 + /6 + /6 + /6 + /6 Guided Practice. 2/4, or 4/8 2. /4 or /8 3. /4 + /4 or /8 + /8 + /8 + /8 4. 5/6 5. /6 6. 2/6 + 3/6 Independent Practice Page 40 SE. B 2. A 3. C Page 4 SE. A Represent Sum of Fractions TEKS 4.3A Supporting Teaching Model: Emphasize unit fractions as in /6 Guided Practice: Determine the unit fraction first. (How many sections are between 0 and?) On the first problem, recognize that 2/8 is equal to /4. Recognize that 2/4 or 4/8 equals /2. Independent Practice Determine the unit fraction and interpret each fraction that is being added to find the sum th Grade Mathematics

51 BI Background Information Decompose a Fraction Fractions Category Student Expectations - Supporting Standard TEKS Number and operations. The student applies mathematical process standards to 4.3B represent and generate fractions to solve problems. The student is expected to decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations. Vertical Alignment Vocabulary The student will demonstrate an understanding of how to represent and manipulate numbers and expressions. Representing Fraction Concepts Decompose Understanding the TEKS This SE focuses on students being expected to express 5/2=3/2+2/2; 5/2=/2+4/2; 5/2=2/2+2/2+/2; and 2 ½=++/2. Students are expected to use concrete models such as fraction strips or fractions bars and pictorial models such as strip diagrams and to record the appropriate number sentences. Essential Question(s) Grade st 2nd 3rd 5th 6th Student is expected to... None None 3.3D compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts /b None None 4th Grade Mathematics

52 A Engaging Activity Decompose a Fraction Fractions TEKS 4.3B Supporting Decompose Example: 2 Decompose Decompose Decompose Decompose Decompose in three different ways = = 5 7 in three different ways. in three different ways. in three different ways. in three different ways. in three different ways = th Grade Mathematics

53 TM Teaching Model Decompose a Fraction Fractions I can... decompose a fraction into the sum of fractions. Draw a picture to show why these equations are true. Explain your reasoning. 7 8 = = Putting the Pieces Together Students should draw a model for each number sentence to describe their thinking for a decomposition of a fraction into different parts. Thinking Mathematically Why would you want to decompose a fraction? By decomposing of fractions, you can recognize equivalent parts of fractions. How do we know what the sum of a fraction is equal to? You can look at the parts to recognize equivalence. 4th Grade Mathematics 5 204

54 GP Guided Practice Decompose a Fraction Fractions TEKS 4.3B Supporting Use the number line below to show = Which one of these addition sentences represents the fraction 8 5? A B C D Draw a model to represent the given sum of a fraction problem. 4 5 = Draw a model to represent the given sum of a fraction problem. 8 = Draw a model to represent the given sum of a fraction problem. 5 2 = th Grade Mathematics

55 AK Answer Key Decompose a Fraction TEKS 4.3B Supporting Activity. Example 2. 2/2 + 5/2 or 6/2 + /2 etc Answers may vary Teaching Model. Answer may vary Guided Practice. Visual Evaluation 2. B 3. Visual Evaluation 4. Visual Evaluation 5. Visual Evaluation Independent Practice Page 44 SE. 2/4 + 3/4, /4 + 4/4, 3/4 + 2/4, 4/4 + /4 2. C 3. 5/7 + 5/7, 8/7 + 2/7, 6/7 + 4/7, etc. 4. C Page 45 SE. B 2. A Teaching Model: Question 2: The examples from the specifications are both proper and improper fractions as well as mixed numbers. Have the students draw out each fraction into a strip diagram so they may visual see the whole and fractions. Guided Practice: Question : Decompose 5/4 into 2 fractions Question 2: Remember, only the numerators are added. Question 4: What does represent? 5/5 Independent Practice: Recognize that the fractions are coming from different wholes. 4th Grade Mathematics