Unit 1 Mustang List

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Copyright 2011 Corwin Not for sale reproduction or distribution. Name Date Class,Diagnostic Test,Fraction Concepts, Multiple Choice Circle the correct answer If your answer is not given circle Not here. 1 How much of the circle is shaded 2 How much of the rectangle is not shaded. E Not here E Not here,3 What part of the group,of circles is shaded. A B C D 7 E Not here, In items 4 and 5 which number names the point shown on the number line. 1 1 1 2 3 7 7 3,A B C D A B C 1 D 1,5 6 7 7 4 8 8 4. E Not here E Not here, 6 On which number line is the point correctly named.
0 4 5 0 2 3,0 11 4 0 4 5,E Not here, Copyright 2011 Corwin Not for sale reproduction or distribution. 7 Which list shows all factors of 18 8 Which is not a multiple of 35. A 2 3 6 9 B 1 2 3 6 9 18 A 5 B 35 C 70 D 105,C 1 2 6 9 18 D 18 36 54 E Not here. E Not here, 9 Which is the greatest common factor GCF of 10 Which is the least common multiple LCM of. 24 and 36 20 and 24,A 6 B 12 C 18 D 72 A 4 B 20 C 120 D 480. E Not here E Not here, 11 Which is a prime number 12 Which is the prime factorization of 60.
A 1 B 2 C 25 D 51 A 5 12 B 2 2 15,E Not here C 2 3 5 D 2 2 3 5. E Not here,13 Which diagram shows shaded,E Not here. 14 Which is equivalent to,A 8 B C D 64 E Not here, 15 Which is equivalent to 16 Which shows in simplest form. 16 9 4 8 2 6 1 2,A B C D A B C D,20 10 10 15 18 9 3 3. E Not here E Not here, 17 Which shows an improper fraction for 3 18 Which shows the mixed number for in.
simplest form,120 29 24 15 5 1 1,A B C D A 2 B 1 C 4 D 2. 8 8 8 8 4 2 4,E Not here E Not here, Copyright 2011 Corwin Not for sale reproduction or distribution. 19 Which tells about how much is,A less than B about C about D more than. E Not here,20 Which is correct,2 3 1 9 12 5 3 5,A B 2 1 C D. 3 4 2 10 18 6 5 8,E Not here, 21 Which of these numbers is the greatest or are they all equal.
A 2 B 2 C D They are all equal,22 Which is correct. 2 2 2 11 7 5 1 1 1 6 9 1,5 4 3 12 12 12 2 3 4 10 20 5. E Not here,23 Which means the same as,A 3 4 B 4 3 C 3 4 D 3 4 E Not here. 24 Which shows as a decimal,A 0 4 B 0 8 C 1 2 D 1 25 E Not here. Copyright 2011 by Corwin All rights reserved Reprinted from Strategies for Teaching Fractions Using Error Analysis for Intervention and. Assessment by David B Spangler Thousand Oaks CA Corwin www corwin com Reproduction authorized only for the local school site or. 38 nonprofit organization that has purchased this book. Copyright 2011 Corwin Not for sale reproduction or distribution. ITEM ANALYSIS FOR DIAGNOSTIC TEST,Fraction Concepts.
Using the Item Analysis Table, The correct answer for each item on the Diagnostic Test is indicated by a. in the Item Analysis Table on page 41, Each incorrect answer choice is keyed to a specific error pattern and cor. responding Intervention Activity found on pages 42 through 85 Because. each item on the Diagnostic Test is an item that is analyzed in one of the. error patterns teachers may be able to use the Intervention Activities with. identical problems that students may have missed on the test. Students should be encouraged to circle Not here if their obtained. answer is not one of the given answer choices Although Not here is. never a correct answer on the Diagnostic Test the use of this answer. choice should aid in the diagnostic process The intention is that students. who do not see their obtained answer among the choices will select Not. here rather than guess at one of the other choices This should strengthen. the likelihood that students who select an incorrect answer choice actu. ally made the error associated with the error pattern. The Item Analysis Table should only be used as a guide Although many. errors are procedural in nature others may be due to an incorrect recall. of facts or to carelessness A diagnostic test is just one of many tools that. should be considered when assessing student work and making prescrip. tive decisions Before a teacher may be certain that a student has a mis. conception about a procedure or concept further analysis may be needed. see below This is especially true for students who frequently select. Not here as an answer choice, A set of practice exercises keyed to each of the four parts of the. Diagnostic Test is provided on pages 86 87 Answers are on page 209. Because the four parts of the set of practice exercises are parallel to the. four parts on the Diagnostic Test the set of practice exercises could be. used as a posttest,Using Teacher Directed Questioning and Journaling. Discussions and observations should be used to help distinguish miscon. ceptions about concepts and procedures from student carelessness or lack of. fact recall This should be done in a positive manner with the clear purpose. being to get inside student thinking The Intervention Activities are replete. with teacher directed questioning frequently asking students to explain their. reasoning Students should also be asked to write about their thinking as they. work through a problem and when alternative methods are used explain. why they may prefer one method rather than another. FRACTION CONCEPTS 39, Copyright 2011 Corwin Not for sale reproduction or distribution.
Additional Resources for Fraction Concepts, Instructional games worksheets and activities designed to promote stu. dents understanding of fraction concepts are on pages 159 169 in blackline. master form Answers are on pages 209 210 Although these materials may be. used at any point in the instructional process specific points of use with teacher. suggestions are provided within the Intervention Activities as listed below. Resource Blackline Master s Teacher Suggestions,Number Lines marked 0 to 1 160 47 48. Number Lines 161 52 53,marked beyond 1,Activity Multiples in Motion 162 61 62. Unit Wholes length model 163 66 67,Instructional Game Equivalent 164 165 67 68. Fractions Cover All,Activity Fraction Card Match 166 75.
Benchmark Fractions 167 75,Activity Paper Folding to 168 169 84 85. Find Fraction Decimal,Equivalents, Technology Resources Online A list of suggested online interactive software. programs applets that provide virtual manipulatives games activities and. tutorials that you may want to integrate into your lessons is provided on. pages 225 227 The resources at each Web site that support this unit are listed. under the heading Resources for Unit 1 Fraction Concepts. 40 STRATEGIES FOR TEACHING FRACTIONS, Copyright 2011 Corwin Not for sale reproduction or distribution. ITEM ANALYSIS TABLE, The correct answer for each item on the Diagnostic Test is indicated by a in this table. Answer Choices,Item A B C D Topic Exercises, 1 Error 1b Error 1a Error 1c Introduction to fractions and Part 1 p 86.
mixed numbers, 2 Error 1b Error 1a Error 1d Introduction to fractions and Part 1 p 86. mixed numbers, 3 Error 1a Error 1c Error 1d Introduction to fractions and Part 1 p 86. mixed numbers, 4 Error 2 Error 2 Error 2 Introduction to fractions and Part 1 p 86. mixed numbers, 5 Error 3b Error 3a Error 3a Introduction to fractions and Part 1 p 86. mixed numbers, 6 Error 3a Error 3c Error 3b Introduction to fractions and Part 1 p 86.
Part 1 mixed numbers, 7 Error 4b Error 4b Error 4c Factors multiples and primes Part 2 pp 86 87. 8 Error 5 Error 4a Error 4a Factors multiples and primes Part 2 pp 86 87. 9 Error 7c Error 7a Error 7b Factors multiples and primes Part 2 pp 86 87. 10 Error 8b Error 8a Error 8c Factors multiples and primes Part 2 pp 86 87. 11 Error 6b Error 6a Error 6a Factors multiples and primes Part 2 pp 86 87. Part 2 12 Error 6c Error 6c Error 6c Factors multiples and primes Part 2 pp 86 87. 13 Errors 9a 11c Errors 9a 1e Errors 9a 1e Equivalence and simplest form Part 3 p 87. 14 Error 10 Error 10 Error 10 Equivalence and simplest form Part 3 p 87. 15 Error 11a Error 11b Error 11c Equivalence and simplest form Part 3 p 87. 16 Error 12a Error 12c Error 12b Equivalence and simplest form Part 3 p 87. 17 Error 13a Error 13b Error 13b Equivalence and simplest form Part 3 p 87. Part 3 18 Error 14a Error 14b Error 14c Equivalence and simplest form Part 3 p 87. 19 Error 15 Error 15 Error 15 Estimation comparing ordering Part 4 p 87. and division interpretation, 20 Error 16a Error 16a Error 16a Estimation comparing ordering Part 4 p 87. or 16b or 18 or 16b and division interpretation, 21 Error 17b Error 16b Error 18 Estimation comparing ordering Part 4 p 87. and division interpretation, 22 Error 17a Error 17a Error 15 Estimation comparing ordering Part 4 p 87. or 17b and division interpretation, 23 Error 19 Error 19 Error 19 Estimation comparing ordering Part 4 p 87.
and division interpretation, 24 Error 20 Error 20 Error 20 Estimation comparing ordering Part 4 p 87. Part 4 and division interpretation,FRACTION CONCEPTS 41. Copyright 2011 Corwin Not for sale reproduction or distribution. ERROR PATTERNS INTERVENTION ACTIVITIES,Fraction Concepts. Error Pattern 1, Error Pattern 1a When writing a fraction to tell how much is shaded some. students compare the number of shaded parts of a figure or objects in a group. to the number of parts or objects that are not shaded. The student responds The student responds,of the figure that.
of the group of,is shaded circles is shaded, Error Pattern 1b When writing a fraction to tell how much of a figure is shaded. some students compare the parts that are not shaded to the total When asked. to find how much of a figure is not shaded some students compare the shaded. parts to the whole,The student responds The student responds. that of the figure is that of the figure is,shaded not shaded. Error Pattern 1c Some students interchange the numerator with the denominator. The student responds The student responds,of the group of that. of the figure is,circles is shaded not shaded, Error Pattern 1d Some students simply count the number of objects or parts of.
The student responds,that the part of the,group that is shaded. 42 STRATEGIES FOR TEACHING FRACTIONS, Copyright 2011 Corwin Not for sale reproduction or distribution. Error Pattern 1e Some students do not realize that to write a fraction to show how. much of a figure is shaded the figure must be divided into parts of the same size. The student responds that each of these,figures shows shaded. Intervention, Pearn and Stephens 2007 citing the research of others state that rational. number ideas are sophisticated and different from natural number ideas and that. children have to develop the appropriate images actions and language to precede. the formal work with fractions p 601 The cited research also suggests that a key. reason why students have difficulties with fractions is because fractions are the first. set of numbers they learn about that are not based on a count or a counting algo. rithm Rather fractions show a relationship between a part and a whole According. to Pearn and Stephens 2007 this required shift in thinking causes difficulty for. many students p 601 Thus it is especially important that early fraction concepts. be developed gradually and with meaning That is the goal of this unit. Accessing Language fracture fraction Mention that if you break a bone it is. called a fracture Usually such a break divides a whole bone into smaller parts. of different sizes Mention that the word fraction comes from the Latin fractus. meaning broken as in a piece broken off of something Historically fractions. have often been referred to as broken numbers, Display the diagram shown below at right A free NCTM applet to create.
fraction models is available at http illuminations nctm org ActivityDetail. aspx ID 44 Ask How many parts is the circle divided into Do the parts. look equal in size 5 yes Ask a volunteer to shade 1 of the 5 equal parts. Explain that a fraction can be used to tell what part of the whole you are consid. ering when the parts are equal in size Relate that to fair shares Explain that. we say one fifth of the circle is shaded and we write the fraction as When. you divide a whole into equal parts each part is a fraction of the whole Ask. How is a fracture different from a fraction Sample A fracture generally. involves parts of different sizes a fraction involves parts of the same size. Each part is a fraction of the whole because,a fracture each part is the same size. FRACTION CONCEPTS 43, Copyright 2011 Corwin Not for sale reproduction or distribution. Ask Suppose the 5 parts of the circle were not equal in size Would it still. make sense to say that of the circle is shaded Explain No Sample You. would not be talking about fair shares In fact you would not really know what. part of the circle was being discussed, Accessing Language numerator denominator Point out that the 5 in is called. the denominator Underline the letters nom in denominator and mention that. in French nom means name Explain that the denominator of a fraction. tells the name of the fraction in this case fifths Ask What does the. related word nominate mean Sample Nominate means to name someone. to run for office, Mention that the 1 in is called the numerator and that numerator comes. from the Latin enumerate meaning to count out So students can think of the. num in numerator as meaning number Explain that th. Unit 1 Fraction Concepts Diagnostic Test 36 The 24 question Diagnostic Test for Fraction Concepts in multiple choice format consists of four parts 1 introduction to fractions and mixed numbers 2 factors multiples and primes 3 equivalence and simplest form and 4 estimation comparing ordering and division interpretation of fractions The test allows you to pinpoint specific

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