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© Carson-Dellosa • Jump Into Math • CD-104226 3
Table of Contents
Skills Index ..................................................................4Introduction ................................................................6
NumerationPart I: Place Value to the Millions Period
Diagnostic Test .........................................................7Teacher Notes and Teaching Activities ......................8Place Value ............................................................. 10Number Word Form ............................................... 13Expanded Form ...................................................... 14
Part II: Ordering and Comparing NumbersDiagnostic Test ....................................................... 16Teacher Notes and Teaching Activities .................... 17Ordering Numbers ..................................................20Comparing Numbers ...............................................23
Addition ReviewPart I: Addition with and without Regrouping
Diagnostic Test ....................................................... 26Teacher Notes and Teaching Activities ....................27Addition without Regrouping ..................................30 Adding Three 1-Digit Numbers ...............................33Adding 2- and 1-Digit Numbers, Regrouping Once ..36Adding 2- and 3-Digit Numbers, Regrouping Once ..39
Part II: RegroupingDiagnostic Test .......................................................42Teacher Notes and Teaching Activities ....................43Regrouping Twice ................................................... 47Regrouping across Zero...........................................50Regrouping Three Times .........................................52Ragged Addition .....................................................55
Subtraction ReviewPart I: 2-Digit Subtraction
Diagnostic Test .......................................................58Teacher Notes and Teaching Activities ....................59Subtraction Fact Review ..........................................64Subtracting 2-Digit Numbers without Regrouping .... 67Subtracting 1-Digit Numbers from 2-Digit Numbers,
Regrouping Once ............................................70Subtracting 2-Digit Numbers, Regrouping Once ...........73Subtracting 2-Digit Numbers with Zeros .................. 76
Part II: 3- and 4-Digit SubtractionDiagnostic Test .......................................................79Teacher Notes and Teaching Activities ....................80Subtracting 3-Digit Numbers, Regrouping Once ...... 84Subtracting 3-Digit Numbers, Regrouping Twice ...... 87Subtracting 3-Digit Numbers with Two Zeros ......... 90Regroup, No Regroup, Regroup ...............................93
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Multiplication and DivisionPart I: Multiplication
Diagnostic Test .......................................................96Teacher Notes and Teaching Activities ....................97Multiplying Three 1-Digit Numbers ....................... 103Multiplying Larger Numbers by 1-Digit Numbers ... 106Multiplying by Multiples of 10 ............................... 110Multiplying 2-Digit Numbers by 2-Digit Numbers ...114Multiplying Larger Numbers by 2-Digit Numbers ... 118
Part II: DivisionDiagnostic Test ..................................................... 122Teacher Notes and Teaching Activities .................. 123Dividing by 1-Digit Divisors .................................. 128Dividing by Multiples of 10 ................................... 132Dividing by 2-Digit Divisors .................................. 136
Fraction ConceptsDiagnostic Test ..................................................... 140Teacher Notes and Teaching Activities .................. 141Equivalent Fractions .............................................. 145Simplifying Fractions ............................................. 148Comparing and Ordering Fractions ....................... 151
Addition and Subtraction of FractionsPart I: Addition of Fractions
Diagnostic Test ..................................................... 152Teacher Notes and Teaching Activities .................. 153Adding with Like Denominators ............................ 156Adding with Unlike Denominators ........................ 160
Part II: Subtractions of FractionsDiagnostic Test ..................................................... 164Teacher Notes and Teaching Activities .................. 165Subtracting with Like Denominators ...................... 168Subtracting with Unlike Denominators .................. 172
Exploring Fractions and DecimalsPart I: Relating Fractions and Decimals
Diagnostic Test ..................................................... 176Teacher Notes and Teaching Activities .................. 177Writing Fractions and Decimals ............................. 179Equivalent Decimals.............................................. 183
Part II: Decimal OperationsDiagnostic Test ..................................................... 185Teacher Notes and Teaching Activities .................. 186Adding Decimals .................................................. 187
• Subtracting Decimals ............................................ 190
End of Book Test ...................................................... 193Answer Key.............................................................. 197Certificate ................................................................208
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CD-104226 • Jump Into Math • © Carson-Dellosa6
Jump Into Math is designed to provide practical suggestions for overcoming common stumbling blocks students encounter with computational skills. Often, teachers have difficulty planning a meaningful and successful corrective instructional program for learners who are having trouble with computational skills. Jump Into Math is a ready-to-use program of study for these struggling learners that offers a systematic analysis of troublesome concepts, step-by-step instruction for teachers, and meaningful practice for students.
Overview
The development of computational skills is a major component of any mathematics program. Computation is included in the Numbers and Operations strand as outlined by The National Council of Teachers of Mathematics in their Principles and Standards for School Mathematics (2000). The NCTM Standards advocate computational fluency for students and further suggest that students who are able to compute efficiently and accurately can significantly increase their scores on standardized tests and build a sturdy foundation for success with higher math, such as algebra. Poor computation skills are a significant handicap to many mathematics students. Therefore, a comprehensive diagnosis of students’ errors and misconceptions in arithmetic, followed by corrective instruction and focused practice, is essential.
Computational errors are not always the result of carelessness or improper procedures. Teachers sometimes have the misconception that “practice makes perfect,” but perfection comes with improvement over time. If students practice the same mistakes over and over again, improvement will be slow or will not happen at all. For a student to improve and reach “perfection,” the “practice” must be accompanied by carefully planned developmental instruction that is designed to help students overcome their specific problems.
Careful observations of students at work and an analysis of their written work are key components of meaningful instruction. There are four general categories of errors in computation: wrong operation, fact errors, defective algorithms, and random responses (guessing). Most student errors can be eliminated if they have a thorough understanding of the procedures used to perform a computation. This requires the student to experience hands-on practice with the underlying skills and concepts. Teachers must plan a developmental sequence of skills that provides the struggling learner with success-oriented experiences that eliminate frustration and failure.
How to Use Jump Into Math
Each grade-level book in the Jump Into Math series is divided into specific number and computational skills. Each section includes a diagnostic test with teacher notes, teaching activities, and student activities targeted to specific items on the test. In addition, a comprehensive test is included at the end of the book. The components of the Jump Into Math program are described below.
Diagnostic Tests—The diagnostic tests target the fundamental concepts of each skill. The tests are illustrative and can be modified by the teacher to meet individual program requirements. The intent is to provide an example of how diagnostic tests can be used to analyze students’ errors. Some teachers will want to use the tests in order. Others may want to begin with Part II then, based on students’ scores, either drop back to Part I or move on to other parts. The diagnostic tests may also be used to quickly determine placement of new students who enroll during the school year.
Teacher Notes and Teaching Activities—Following each diagnostic test is an analysis of each part of the test that references the specific skills addressed in each test item. The teacher notes have been designed to provide information about potential problem areas for students. Sample teaching strategies, activities, sample problems, and suggestions for follow-up instruction are included.
Student Activities—Student activities for practice are included for each problem type on the diagnostic tests. These activities provide practice of the skills, remediation, reteaching, extension to related skills, and maintenance of skills (review). Each practice page is correlated to a specific test item.
Comprehensive Test—At the end of the book, there is a multiple-choice test that includes items covering all of the computational skills appropriate to the grade level.
Introducing Jump Into Math • A DIAGNOSTIC GUIDE •
© Carson-Dellosa • Jump Into Math • CD-104226 7
Directions: Shade the boxes that correspond to correct test items.
TOTAL CORRECT: ______________
TEACHER ASSESSMENT AREA
NAME: __________________________________________________________________________ DATE: ________________________________________
TEACHER ASSESSMENT AREA
NAME: __________________________________________________________________________ DATE: ________________________________________
Diagnostic Test: Numeration Directions: Write the answer to each question in the space provided.
Skill Item Number
Place Value 1 2 4 9 10Number Word Form 3 5Expanded Form 6 7 8
Part I: Place Value to the Millions Period
1. Whatdigitisinthemillionsplace?
2,573,146
_____________________________________
2. Whatistheplacevalueoftheunderlineddigit?
7,123,456
_____________________________________
3. Writethenumberthreemillionninehundredtwenty-onethousandeighthundredfourteen.
_____________________________________
4. Whatisthevalueoftheunderlineddigit?
14,769,421
___________________________________
5. Writethenumberonehundredforty-twomillionthreehundredfifty-sixthousandeighty-seven.
_____________________________________
6. Write2,568,457inexpandedform.
_____________________________________
_____________________________________
7. Write2,000,000+30,000+1,000+500+20+7instandardform.
_____________________________________
8. Write60,000+100+3,000,000+10+700,000+8+2,000instandardform.
_____________________________________
9. Usethedigitsbelowtowritethelargestnumberpossible.
1428576
_____________________________________
10. Usethedigitsbelowtowritethelargestnumberpossible.
7162534
_____________________________________
Teacher Notes and Activities
CD-104226 • Jump Into Math • © Carson-Dellosa8
NUMERATION PART I: PLACE VALUE TO THE MILLIONS PERIOD
TEACHER NOTES: Place Value(Diagnostic Test Part I: Test Items 1–2, 4, 9 –10)
Today, numbers in the millions are commonplace. Students are constantly exposed to very large numbers in print and on television. Introduce the millions period as shown below.
, ,
The place value chart above shows the number 143,678,290. A comma separates the millions, thousands, and ones periods. In expanded form, the number is 100,000,000 + 40,000,000 + 3,000,000 + 600,000 + 70,000 + 8,000 + 200 + 90 + 0. In words, the number is read one hundred forty-three million six hundred seventy-eight thousand two hundred ninety.
TEACHING ACTIVITIES: “Newspaper Numbers” (Place Value)
Have students search through science and history books to find examples of numbers in the millions. Students should write down the numbers and what the numbers represent. For example, “I found the number 296,410,404. This was the population of the United States in 2005.” “I found the number 200,000,000. Scientists say dinosaurs lived on Earth 200,000,000 years ago.”
Divide the chalkboard into Millions Period, Thousands Period, and Ones Period as shown below. Choose students to be the millions recorder, thousands recorder, and ones recorder. As each student reads and describes her number, have the recorders write the number in the chart. Continue until you have five to ten numbers on the chart.
, ,
Practice reading each number in the chart. Then, lead students in comparing the numbers. Ask questions like, “Which number is the largest? Smallest?”
THOUSANDSHundreds Tens Ones
6 7 8
ONESHundreds Tens Ones
2 9 0
MILLIONSHundreds Tens Ones
1 4 3
THOUSANDSHundreds Tens Ones
640
710
800
ONESHundreds Tens Ones
240
900
040
MILLIONSHundreds Tens Ones
122
490
360
© Carson-Dellosa • Jump Into Math • CD-104226 9
NUMERATION PART I: PLACE VALUE TO THE MILLIONS PERIOD
“Patterns” (Place Value)
Number patterns can be used to help students see the relationships between large numbers. Help students see these relationships by displaying a chart like the one shown below.
10 hundreds = 1,00010 thousands = 10,000
10 ten thousands = 100,00010 hundred thousands = 1,000,000
After students have spent some time creating and studying different number pattern charts, ask questions like these:
“How many tens are in 1,000?” (100) “How many hundreds are in 10,000?” (100) “How many thousands are in 1,000,000?” (1,000)
TEACHER NOTES: “Number Word Form and Expanded Form”(Diagnostic Test Part I: Test Items 3, 5 – 8)
Students should be able to write large numbers not only in standard form, but also in number word form and expanded form.
TEACHING ACTIVITY: “A Number of Ways”(Number Word Form and Expanded Form)
Discuss the following ways to write large numbers with students. For example, there are several different ways to write the number 260,000,000.
Standard Form: 260,000,000Number Word Form: Two hundred sixty millionShort Number Word Form: 260 million Expanded Form: 200,000,000 + 60,000,000
Have students write the following numbers in standard form, number word form, short number word form, and expanded form.
For more practice, have students write examples of large numbers from science and history books on sheets of paper. Have them write their numbers in number word form, short number word form, and expanded form.
1. 17,525,813 2. 9,999,999 3. 329,546,809 4. 2,609,078
NAME: ___________________________________________________________________________ DATE: ________________________________________
CD-104226 • Jump Into Math • © Carson-Dellosa10
Directions: Write the number in each hundreds place.
1. 256,135____________________________
3. 321,506,829________________________
5. 234,567____________________________
2. 45,729,456_________________________
4. 535,490,691________________________
6. 2,214,936 __________________________
Directions: Write the number in each thousands place.
7. 478,013____________________________
9. 564,220 ___________________________
11. 357,405____________________________
8. 69,556,052_________________________
10. 753,899,678________________________
12. 8,347,615 __________________________
Numeration: Place Value What’s My Place?Test Items 1–2, 4, 9–10
Directions: Write the number in each ten millions place.
13. 133,456,256________________________
15. 358,569,321________________________
14. 462,582,453________________________
16. 693,258,092 _______________________
NAME: ___________________________________________________________________________ DATE: ________________________________________________________________________________
© Carson-Dellosa • Jump Into Math • CD-104226 11
Directions: Write the place of the underlined digit. Then, give its value.
1. 1,634,879
_____________________________________
_____________________________________
3. 25,454,623
_____________________________________
_____________________________________
5. 17,597,181
_____________________________________
_____________________________________
7. 45,978,412
_____________________________________
_____________________________________
2. 4,817,258
_____________________________________
_____________________________________
4. 36,550,790
_____________________________________
_____________________________________
6. 850,265,105
_____________________________________
_____________________________________
8. 239,690,258
_____________________________________
_____________________________________
Numeration:
Place Value
What’s My Value?Test Items 1–2, 4, 9–10
NAME: ___________________________________________________________________________ DATE: ________________________________________
CD-104226 • Jump Into Math • © Carson-Dellosa12
Directions: Use place value to write the largest number possible with the given digits. On the second line, use the same digits to write the smallest number possible.
Dancing Digits
1. 2,0,7,3,8 ___________________
___________________
3. 3,6,9,7,4 ___________________
___________________
5. 5,1,3,6,7,2 ___________________
___________________
7. 5,8,3,0,6,1,1 ___________________
___________________
2. 1,4,7,3,2,5 ___________________
___________________
4. 6,4,1,3,0,0,1 ___________________
___________________
6. 4,1,0,2,3,9 ___________________
___________________
8. 9,0,5,8,6,7,4 ___________________
___________________
Directions: Follow the directions to write each number.
9. Usethesedigitstowritethelargestnumberpossiblewiththe8inthetenmillionsplace:4,9,0,2,1,8,9,1,7.
____________________________________________________________________________________
10. Usethesedigitstowritethesmallestnumberpossiblewiththe4intheonemillionsplace:6,3,0,4,7,6,1,2.
____________________________________________________________________________________
Numeration: Place Value
Test Items 1–2, 4, 9–10
Answer Key
PAGE 7 (DIAGNOSTIC TEST)
1. 2; 2. hundred thousand; 3. 3,921,814; 4. 4 million or 4,000,000; 5. 142,356,087; 6. 2,000,000 + 500,000 + 60,000 + 8,000 + 400 + 50 + 7; 7. 2,031,527; 8. 3,762,118;
9. 8,765,421; 10. 7,654,321
PAGE 10
1. 1, 2. 4, 3. 8, 4. 6, 5. 5, 6. 9, 7. 8, 8. 6, 9. 4, 10. 9, 11. 7, 12. 7, 13. 3, 14. 6, 15. 5, 16. 9
PAGE 11
1. hundreds, 800; 2. ones, 8; 3. thousands, 4,000; 4. tens, 90; 5. millions, 7,000,000; 6. hundred millions, 800,000,000; 7. hundred thousands, 900,000; 8. ten millions, 30,000,000
PAGE 12
1. 87,320; 20,378; 2. 754,321; 123,457; 3. 97,643; 34,679; 4. 6,431,100; 1,001,346; 5. 765,321; 123,567; 6. 943,210; 102,349; 7. 8,653,110; 1,013,568; 8. 9,876,540; 4,056,789; 9. 989,742,110; 10. 14,023,667
PAGE 13
1. eight hundred twenty-three, 2. three thousand twenty-one, 3. eighty-seven thousand four hundred ninety, 4. five hundred thousand five, 5. four million seventy-eight thousand nine hundred thirteen, 6. sixty-two million three hundred thousand one hundred fifty-two, 7. nine hundred ten million eight hundred forty-four thousand seven hundred thirty-seven, 8. seven hundred million two hundred three thousand
PAGE 14
1. 10,000 + 5,000 + 400 + 70 + 8; 2. 20,000 + 8,000 + 800 + 90 + 5; 3. 8,000 + 400 + 50 + 6; 4. 71,999; 5. 50,000 + 9,000 + 800 + 20 + 4; 6. 80,000 + 1,000 + 500 + 70 + 2; 7. 7,496; 8. 56,580; 9. 30,000,000 + 3,00,000 + 800,000 + 20,000 + 9,000 + 500 + 70 + 6; 10. 2,000,000 + 400,000 + 40,000 + 4,000 + 900 + 10
PAGE 15
1. C, 2. B, 3. C, 4. A, 5. C, 6. B, 7. A, 8. D
PAGE 16 (DIAGNOSTIC TEST)
1. 3,297,469; 2. 2,300,000; 3. 6,442,243; 4. 2,800,000; 3,200,000; 4,500,000; 5. 2,560,000; 2,785,500; 2,800,000; 6. <; 7. <; 8. <; 9. >; 10. <
PAGE 20
1. 358, 458, 558, 658, 758, 858; 2. 2,461; 3,461; 4,461; 5,461; 6,461; 7,461; 8,461; 9,461; 3. 38,562; 48,562; 58,562; 68,562; 78,562; 88,562; 4. 98,703; 108,703; 208,703; 308,703; 408,703; 508,703; 5. 4,650,926; 5,650,926; 6,650,926; 7,650,926; 8,650,926; 9,650,926; 6. 41,053,669; 51,053,669; 61,053,669; 71,053,669
PAGE 21
1. 892; 2. 3,391; 3. 4,640; 4. 18,350; 5. 8,665; 6. 69,333; 7. 20,892; 8. 157,426; 9. 37,554; 10. 89,000
© Carson-Dellosa • Jump Into Math • CD-104226 197
