RAPID MATHEMATICS ASSESSMENT
FOR KEY STAGE 3 LEARNERS
TEACHER’S BOOKLET
Dear Teacher,
In any assessment, it is important to read the general instructions, study the assessment
tasks carefully, and prepare the necessary assessment materials before administration.
This Rapid Mathematics Assessment for Key Stage 3 toolkit consists of the following:
● Teacher’s Booklet
This booklet guides you in administering the assessment. It includes the
tasks, preparations for the tasks, the time allotted for the assessment, the
answers, and the instructions you will give to the learners. The assessment
items in this booklet are written in English.
The assessment has a time allotment of 90 minutes. If the learners finish
ahead of time, instruct them to review their answers.
● Learner’s Booklet
This booklet contains the assessments that learners need to complete in
writing. The learner must have a copy of this booklet during the test
administration.
● Learner’s Answer Sheet
This sheet is where the learners write their answers for each item.
General Instructions
Before the test administration
1.
Ensure you have the complete toolkit and have thoroughly studied the tasks.
2.
Prepare all the materials needed.
3.
The estimated administration time for the test is 90 minutes.
4.
Make sure to remind the learners to bring pencils and clean sheets of paper.
5.
Make the classroom conducive and well-ventilated for the test.
6.
Be familiar with the assessment items.
Grade 7 learners shall only be evaluated and profiled based on the items
intended for Grade 7 learners, while Grades 8,9 and 10 shall be evaluated using
the items for Grades 7 and 8, Grades 7 to 9, and Grades 7-10, respectively.
During the test administration
1. Inform the learners of the following:
a. Your score in this test will not affect your grade in mathematics,
however, do your best to answer each item.
b. All items will require you to write the answer. Use the answer
sheet provided.
c. The assessment is timed. You have to do it within the allotted
time.
d. If you finish ahead of time, you may review your answers.
e. No test questionnaires will be collected before the allocated time.
Maximize the allotted time to review your answers.
2. Let the learner answer the assessment within the allotted time.
3. After the learners have answered, check their answers and record the
scores in the automated scoresheet within 5 days. The answer key is
provided in the Teacher’s Booklet.
4. Strictly follow the time allotted for this assessment.
After the test administration
1. Thank the learners for their participation.
2. Refer to the automated scoresheets for the profile of the learners.
3. Prepare the test materials for the next class.
Rapid Mathematics Assessment for Grades 7 - 10
CODES AND SCORING GUIDE
Item #1
Full credit
Correct computation:
16 - 15 = 1
2
Partial credit
4 x 4 - 5 x 3 = 1;
16 - 15 only
1
No credit
Wrote the expression and equated to a number other than 1;
incorrect application of MDAS
0
No answer
NA
Full credit
6x6-7x5
1
No credit
Other expressions
0
No answer
NA
b and c
2
b only or
1
Item #2
Item #3
Full credit
c only
No credit
Any responses containing a, d, or e
0
Other responses
No answer
NA
1
Item #4
Full credit
Since the numerical expressions in Box 1 simplify to 1, the correct
algebraic expression should also simplify to 1.
The learner correctly simplified the algebraic expression in either b or c
to 1.
e.g.
2
(𝑛)(𝑛) − [(𝑛 + 1)(𝑛 − 1)]
2
2
2
2
= 𝑛 − (𝑛 − 1) = 𝑛 − 𝑛 + 1
=1
or,
(𝑛 − 1)(𝑛 − 1) − 𝑛(𝑛 − 2)
2
2
= 𝑛 − 2𝑛 + 1 − (𝑛 − 2𝑛) =
=1
2
2
𝑛 − 2𝑛 + 1 − 𝑛 + 2𝑛
The chosen algebraic expression was used to generate at least one
number expression in Box 1.
2
e.g.
For (𝑛)(𝑛) − [(𝑛 + 1)(𝑛 − 1)], if n = 2, then this expression becomes
(2)(2) − [(2 + 1)(2 − 1)] = 2×2 − 3×1
or
For (𝑛 − 1)(𝑛 − 1) − 𝑛(𝑛 − 2), if n = 3, then this expression
becomes
(3 − 1)(3 − 1) − 3(3 − 2) = 2×2 − 3×1
Partial credit
The algebraic expression in b is correctly simplified to 1 by using a
value for n from the set {2, 3, 4, 5}.
e.g., for 𝑛 = 2:
1
(2)(2) − [(2 + 1)(2 − 1)]
= 4 − (3)(1) = 4 − 3
=1
or
The algebraic expression in c is correctly simplified to 1 by using a
value for n from the set {3, 4, 5, 6}.
e.g. for 𝑛 = 3: (3 − 1)(3 − 1) − 3(3 − 2)
= (2)(2) − (3)(1) = 4 − 3
=1
No credit
Incorrect simplification of any of the expressions in the choices
0
No answer
NA
2
Item #5
Full credit
Defined n correctly in relation to the selected option:
● If b is chosen, then n is the first number in the numerical
expression
● If c is chosen, then n is the third number in the numerical
expression
1
No credit
Other answers
0
No answer
NA
1024 = 210 so it is a power of 2.
1
Item #6
Full credit
64 x 16 = 1024 => 26 x 24 = 210
Other similar expressions, such as 32 x 32 = 1024 => 25 x 25 = 210
26 x 2 x 2 x 2 x 2 = 1024 or other solution where one factor is in
exponential form
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024
No credit
other responses
0
No answer
NA
Full credit
210
1
No credit
other responses
0
No answer
NA
Full credit
64 or 128
1
No credit
Other responses or scribbles
0
No answer
NA
Item #7
Item #8
3
Item #9
Full credit
Yes, with a correct example.
Any number starting with 0.998, followed by one or more digits, with at
least one non-zero digit. Examples: 0.99801, 09984, 0.998000005
1
No credit
Yes, with incorrect example: Any decimal number equal to or less than
0.998 or any number equal to or greater than 0.999 OR
Incorrectly formatted numbers with extra decimal point, such as 0.998.5
0
No
No answer
NA
Full credit
Set up the correct subtraction expression with the correct answer:
0.999 - 0.998 = 0.001
2
Partial credit
Correct set up only: 0.999 - 0.998
1
No credit
Incorrect set-up even if the result or difference is 0.001.
Example: 0.998 - 0.999 = 0.001
0
Item #10
Other incorrect set-up or other incorrect computation
No answer
NA
Item #11
Full credit
Examples of correct response and method:
Used equivalent fraction, e.g
to make
3
4
=
6
8
2
and then added 1 to the numerator
7
.
8
3
Converted 4 to 0.75 and then used a number greater than 0.75 but
4
less than 1 such as 0.8 and converted it to the fraction, 5 .
3
1
Solved for the difference between 4 and 1, which is 4 , then selected a
1
3
1
1
number less than the 4 and added it to 4 . e.g., 8 is less than 4 , and
3
7
added it to 4 . The result is 8 .
Partial credit
Correct fraction, but no solution or explanation.
1
No credit
Incorrect fraction
0
No answer
NA
4
Item #12
Full credit
5 students
1
No credit
Other number of students or scribbles
0
No answer
NA
There are five points with y-coordinates below 84.
1
Item #13
Full credit
There are five points below the horizontal line at 84.
No credit
Other explanations
e.g. The x-coordinate, or the 'partner,' of the point with a y-coordinate
of 84 is 5.
0
No answer
NA
Full credit
b and c
2
Partial credit
b only or
c only
1
No credit
other responses or scribbles
0
No answer
NA
Item #14
5
Item #15
Full credit
Partial credit
No credit
Mentioned that Purok 1 is more varied or diversed and the explanation
here uses technical statistical terms and/or the statistics represented.
●
Because the range of Purok 1 (40-8 = 32) is greater than that of
Purok 2 (24-15 = 9).
●
Because the difference between the maximum monthly income
and minimum monthly income of Purok 1 is greater than that of
Purok 2.
●
Because the differences of the monthly income of Purok 1 from
the center value or average of the monthly income of Purok 1 are
greater than the differences of the monthly income of Purok 2 from
the center value of the monthly income of Purok 2.
Mentioned that Purok 1 is more varied and the explanations here are
less technical or are based on the visuals. e.g, the word bar is used
instead of monthly income.
●
Because the distance between the first and last bars in Purok 1 is
greater than in Purok 2.
●
Because Purok 1 has more different values of monthly income than
the values of monthly income of Purok 2.
●
Because the bars of Purok 1 are more spread out than those of
Purok 2.
●
Because Purok 1 has more bars than Purok 2.
Mentioned Purok 2 is more varied with correct explanation
2
1
0
Mentioned Purok 1 is more varied with incorrect explanation such as:
●
Technical statistical terms were mentioned, such as adding all
the monthly income and measures of central tendency (mean,
median, mode), BUT NONE were related to measures of
variability.
●
Technical statistical terms were mentioned, such as measures
of variability, adding all the monthly income, and measures of
central tendency (mean, median, mode), BUT they were
INACCURATE in relation to the given data.
●
Technical statistical terms were mentioned, such as measures
of variability, adding all the monthly income, and measures of
central tendency (mean, median, mode), BUT ONLY ONE
PUROK was cited.
No answer
NA
6
Item #16
Full credit
The response may be Yes or No. What is being assessed here is if the
learner can use statistics to make a decision.
2
The explanation must mention VARIABILITY and information that can
be read or interpreted from the graph. Some examples of references to
the statistical graph are the following:
Partial credit
●
Purok 1’s monthly family incomes are farther from the average
compared to those in Purok 2. As a result, the monthly average
doesn’t reflect the incomes of most families in Purok 1. This means
many families may get more or less than they actually need.
●
I see that the minimum family income earners are in Purok 1, but
the highest family income earners are also in Purok 1. The financial
aid must be given to families below a certain income cutoff instead,
whether that family is in Purok 1 or Purok 2.
The response may be Yes or No. What is being assessed here is if the
learner can use statistics to make a decision.
1
The basis of the decision must mention information that can be read or
interpreted from the graph but did NOT mention variability and mention
ONLY CENTRAL TENDENCY.
E.g. Since both Purok 1 and Purok 2 have the same average monthly
income, it would seem reasonable for them to receive equal financial
aid.
No credit
Yes or No but no explanation.
0
No answer
NA
Full credit
49
1
No credit
Other numbers
0
No answer
NA
Item #17
7
Item #18
Full credit
19
1
No credit
Other numbers
0
No answer
NA
Item #19
Full credit
18
110
No credit
Other numbers
0
No answer
NA
Question uses other concepts not shown directly in the table
3
or
9
55
or 0.16 or
0.163636…
1
Item #20
Full credit
E.g. Illustrate the data in Table 2 in Venn diagram.
Questions that presented a logical and relevant scenario requiring a
transformation of the values provided in the table.
E.g. If a new student joins the school and participates in both activities,
how would this affect the number of students who did not participate in
either activity?
Partial credit
Questions involving probability
2
E.g. What is the probability of selecting a student who participated in
music activity and did not participate in sports activity?
Questions involving frequencies only
E.g. How many students did not participate in sports activity? or
1
How many students participated in music activity and did not participate
in sports activity?
No credit
Questions cannot be answered with the given table. For example,
questions like: Why did the students not participate in the music
activity?
0
Created their own similar table
Question is the same as #17- #19
No answer
NA
8
Item #21
Full credit
c or -300 only
1
No credit
other letters or values
0
No answer
NA
Full credit
0
1
No credit
other numbers; any scribbles
0
No answer
NA
Full credit
(4, 4)
1
No credit
Incorrect notation for coordinates of a point:
0
Item #22
Item #23
e.g. 4,4 or 4 4 or [4, 4] or {4, 4} or (4;4)
Other responses or scribbles
No answer
NA
Any of these combinations:
2
Item #24
Full credit
b, d, and f
b and d
b and f
d and f
Partial credit
b only or
d only or
f only
1
No credit
Any responses containing a, c, or e
0
Other responses or scribbles
No answer
NA
9
Item #25
Full credit
e or (𝑥, −𝑥+2) only
1
No credit
Other answer
0
No answer
NA
Correct area of triangle ABC which is 12 sq units.
2
Item #26
Full credit
Any of the following methods:
Method 1: used the formula A = ½ bh
Method 2: used rectangle method; 1st rectangle has diagonal AB (area
of 1st rectangle is 4x4 and so half of it is 8); the 2nd rectangle has
diagonal BC and its area is 2x4 and so half of it is 4. The total area of
the two triangles is 8+4 = 12.
Method 3: Using the argument in Method 2 but with a rectangle where
segment AC is a side and point B is on the side opposite segment AC.
Partial credit
Correct area (12 sq units) but NO or INCORRECT method is shown
1
No credit
Other responses or scribbles
0
No answer
NA
School or B
1
Item #27
Full credit
or
House to School or A to B
No credit
Other responses
0
No answer
NA
10
Item #28
Full credit
Possible explanation or method
1. drew a circle with AB or AC as radius
2
2. used distance formula to find the length of 𝐴𝐵 and 𝐴𝐶
3. applied Pythagorean theorem to calculate 𝐴𝐵 and 𝐴𝐶
Partial credit
Used nonstandard measuring tool such as edge of paper or pencil to
compare length
1
No credit
Incorrect method or any other scribbles
0
No answer
NA
Full credit
-5, -27, and 99
3
Partial credit
Any two of {-5, -27, 99}
2
Any one of {-5, -27, 99}
1
Any set of answers that includes other numbers (-82, 46, or 122)
other responses or scribbles
0
No answer
NA
Item #29
No credit
Item #30
Full credit
d and e ;
3: 100 = 𝑛: cost and cost =
2
100𝑛
3
Partial credit
d only or
c only
1
No credit
Any responses containing a, b, or c
0
Other responses or scribbles
No answer
NA
11
Item #31
Full credit
Two pairs such that 𝑏 = 𝑎 + 14
(e.g., a=0, b=14; a=1, b=15…)
2
Partial credit
Only one pair such that 𝑏 = 𝑎 + 14
(e.g., a=0, b=14; a=1, b=15…)
1
No credit
Any values for a and b where 𝑏 ≠ 𝑎 + 14
(e.g., a=0, b=0, a=14, b=0, …)
0
No answer
NA
Full credit
c only
1
No credit
Other responses or scribbles
0
No answer
NA
Full credit
c only
1
No credit
Other responses or scribbles
0
No answer
NA
Full credit
P1250
1
No credit
Any other number or scribbles
0
No answer
NA
Full credit
c only
1
No credit
Other responses
0
No answer
NA
Item #32
Item #33
Item #34
Item #35
12
Item #36
Full credit
The cost/rate per day of renting the tricycle
1
No credit
Other responses or scribbles
0
No answer
NA
Full credit
c only
1
No credit
Other responses
0
No answer
NA
a and e or
2
Item #37
Item #38
Full credit
q = 10 and r = 140 and q = 100 and r = 50
Partial credit
a only or
e only
1
No credit
Any responses containing b, c, or d
0
Other responses or scribbles
No answer
NA
c and e or
2
Item #39
Full credit
The value of p is 70 and the value of q is 50 and The value of r plus p
is 130
Partial credit
c only or
e only
1
No credit
Any responses containing a, b, or d
0
Other responses or scribbles
No answer
NA
13
Item #40
Full credit
c and d or
2
The exterior angle and one of the interior angles adjacent to it form a
linear pair and The measure of the exterior angle of a triangle is equal
to the sum of the two remote interior angles
Partial credit
c only or
d only
1
No credit
Any responses containing a, b, e, or f
0
Other responses
No answer
NA
Full credit
a only
1
No credit
Any responses containing b, c, or d
0
Item #41
Other responses or scribbles
No answer
NA
Full credit
Yes. Since the base of the toy storage is parallel to the floor (which is
the base of the dog house), their corresponding base angles are equal
(or congruent). Then, by AA Similarity Theorem, the two triangles (toy
storage and dog house) are similar. Corresponding sides of two similar
triangles are proportional.
2
No credit
Yes (other explanation or without explanation)
0
Item #42
No (with or without explanation)
No answer
NA
Full credit
a only
1
No credit
Any responses containing b, c, or d
0
Item #43
Other responses or scribbles
No answer
NA
14
Item #44
Full credit
Answer: The area of the sidewalk is 34.54 sq. m.
3
Solution:
Area of the small circle (the pool) = 52(3.14)
Area of the big circle (pool & sidewalk) = 62(3.14)
Area of the sidewalk
= 62(3.14) - 52(3.14)
= (62 - 52)(3.14) = (36-25)(3.14) = 11(3.14) = 34.54
Partial credit
Correct answer (34.54 sq.m.) but no solution
2
Partial solution such as area of at least one of the circles but no final
answer.
1
Correct solution but wrong final answer.
No credit
Answer other than 34.54 sq.m.
0
No answer
NA
25π(2.1)
2
Item #45
Full credit
d.
cubic meters only
1
No credit
Other responses or scribbles
0
No answer
NA
15
Item #46
Full credit
Using pi = 3.14
The circumference of the circle:
C = pi x diameter
C = 3.14(60) = 188.4
Since there are 5 rolls:
188.4 x 5 = 942 cm or 9.42 m
2
Or
The circumference of the circle:
C = pi x diameter
C = π(60) = 60π
Since there are 5 rolls:
60π x 5 =300π m
Partial credit
Gave only the correct distance travelled (942 cm or 300π cm) but the
complete solution is not shown.
1
No credit
Other responses or scribbles
0
No answer
NA
1800O
(The degree measure of a circle is 360 degrees. 360O x 5 rolls = 1800O)
2
Item #47
Full credit
or
1800 only without the degree symbol
Partial credit
Responses showing any of the following:
a. 360O x 5 rolls
b. wrong computation but able to set up 360O x 5 rolls
1
No credit
Other responses or scribbles
0
No answer
NA
16