Test Details Subject - Math Topic - Multiplying & Dividing Decimals; Angle & Lines; Ratios & Unitary Method. Exam Code – 542570 Date - 25 August 2016 Class 7 – Section B Teacher – Rekha Vinodh School - Kamala Niketan Montessori School
CLASS DISCUSSION PRIORITY C, 6, 24%
L, 12, 48% R, 7, 28%
Key Ideas Assessed - The following areas were assessed in the test. The performance of your class in each area and the class performance in each question are displayed below Concept Area Multiplying Decimals
Question No. % of student answering correctly
Concept Area Dividing Decimals
Question No. % of student answering correctly
Concept Area
.
1
2
3
4
5
Avg
48
42
65
40
62
51
6
7
8
9
10
Avg
54
94
40
31
20
48
Question No. % of student answering correctly
11
12
13
14
15
16
Avg
57
68
68
94
74
97
76
Concept Area Question No. Parallel Lines & % of student Transversal answering correctly
17
18
19
20
Avg
60
20
22
22
31
Concept Area Question No. Ratios & % of student Unitary Method answering correctly
21
22
23
24
25
Avg
34
51
57
74
68
57
Angle Pairs
Inferences and Action Points – • Class Average: 5.5 / 10 • Class Range: 2.0 - 9.0 (Scores are rounded off to the nearest 0.5) • Best Performed Area: • Angle Pairs • Areas Recommended for Remediation: • Parallel Lines & Transversal • Dividing Decimals
Critical Recommended Low
Recommended Remediation Critical •Problem Solving - Angles Formed by Transversal of Parallel Lines •Common Wrong Answer – Option 4 (57 %)
Critical •Division of a Decimal Number by a Decimal Number •Common Wrong Answer – Option 1 (37%)
Critical •Understanding the Term Corresponding Angles •Common Wrong Answer – Option 4 (57 %)
Remediation Support Concept: Problem Solving - Angles Formed by Transversal of Parallel Lines
MISCONCEPTION EXPLANATION: To answer this question correctly, Students should understand the angles made by transversal and properties of angles. Students who have selected option 3 correctly understood that the angle marked x is the sum of the third unknown angle of the triangle and the alternate interior angle of 40° i.e 40+(180 -(40+75)) = 105°. Students who have selected option 1 may have taken the angle marked x and 40° as the pair of alternate interior angles and so x = 40°. Students who have selected option 2 may have taken x as the third angle of the triangle = 180 -(40+75)=65°. Students who have chosen option 4 may have taken x as 40+75.
REMEDIAL MEASURE: Help students become familiar with the terms used when describing angles formed by transversals. Make them aware of which angles will be equal in measure when the lines being transversed are parallel. Help them understand the need for the lines to be parallel in such cases. Students may be given ample practice in exploring this concept hands on by allowing them to use paper or cardboard cut-outs to compare angles. The following online interactive tool may also be used in the classroom: http://www.mathopenref.com/transversal.html .
Encourage students, when facing problems such as this one, not to simply try to match one of the values given in the diagram without proper analysis, nor to rely on visual estimation. Rather, develop in them the skill of carefully analysing the given diagram and determining what information has been given, what needs to be found out, and how to go about this. They may be encouraged to ask themselves questions such as the following: Which pairs of lines are parallel? Which line(s) are the transversals of the parallel lines? Which pairs of interior/exterior and alternate interior/exterior angles will be equal? Which angles will be supplementary? Which pairs of corresponding angles will be equal? Ask them to study the given figure and try to determine the measure of any of the unknown angles. Are they able to see which angles would be equal to 60°? Help the students work through the problem step by step. Make them aware that in order to find the measure of ∠ x , they need to find the unknown angle of the triangle which is 65° and the angle between the line l and the triangle, which is the alternate interior angle of 40°. Then they can find x as 65° + 40° = 105° (Students may find it helpful to use the following interactive tool to learn about opposite angles: http://www.mathopenref.com/anglesvertical.html ). Finally, you could challenge students to find the measure of all of the angles in the figure.
Concept: Division of a Decimal Number by a Decimal Number
MISCONCEPTION EXPLANATION: Students should understand the concept of place value and they should know the division of decimals to answer this question correctly. Students who have chosen option 4 correctly calculated the result. Students who have selected option 1 may have felt that the quotient should have as many decimal places as the dividend and divisor put together - an extension of the rule they use for multiplication. Students who have selected option 2 may have felt that as the dividend has 2 decimal points and the divisor has 1 decimal point, the quotient should also have 2-1=1 decimal point. Students who have chosen option 3 are not clear on where to place the decimal point.
REMEDIAL MEASURE: Investigate if students understood the concept of place value of decimals. Check whether they are extending the rule they use in multiplication to place the decimal point. Help students arrive at these rules by themselves by appropriately using the notions of place value and the meaning of decimals. Insist that they solve a number of problems writing out all the steps in full. 3.5÷0.07 = 35 10 ÷ 7 100 = 35 10 × 100 7 = 3500 70 = 50 Make sure that they are thorough with multiplication and division of fractions and know the justification for the procedures used. Doing a lot of problems in this fashion will help them arrive at the rules themselves and hence internalise them better. Inculcate in them the habit of checking if their answer is reasonable. For example is it possible that 3.5 ÷ 0.007 = 0.005? Ask them to check back if 0.005 × 0.007 = 3.5. If they do this they will realise their mistake.
Concept: Understanding the Term Corresponding Angles
MISCONCEPTION EXPLANATION: This question tests students' understanding of angles formed by a transversal. Students who chose option 1 have correctly identified corresponding angles. Students who chose option 4 may have felt that corresponding angles are formed only when a pair of parallel lines are cut by a transversal. Students who chose option 2 and 3 may not know the term " corresponding angles" and may have randomly guessed the answer. REMEDIAL MEASURE: Make students aware that the term "corresponding angles" has got to do with the positioning of the angles when two lines are cut by a transversal, and not with whether the lines are parallel. Construct sufficient examples to help them see that corresponding angles are equal in measure when the lines are parallel and not otherwise.
Class Performance Across DA DA 1
L, 11, 46%
DA 2
C, 3, 12%
DA 3 C, 6, 24%
R, 10, 42%
L, 8, 32%
C, 8, 32%
L, 12, 48% R, 7, 28%
R, 9, 36%
Planned vs. Actual Curriculum Flow
DA 1 DA 2 DA 3 DA 4 DA 5 DA 6 DA 7 DA 8
Planned Type Chapters Regular 1,2 Regular 3,4 Revision 1,2,3,4 Project Regular 5,6 Regular 7,8 Project Revision 5,6,7,8
Actual Difference Reason Type Chapters Regular 1,2,3 Added Ch 3 Ch 3 was completed Regular 4,5 Added Ch 5 Since 3 was covered in DA 1