Inductive/Deductive
Inductive or Deductive?
A teacher notices that in three different classes, students who practice math problems daily tend to score higher on tests. The teacher concludes that daily practice improves test performance.
Inductive - The teacher is making a general conclusion based on specific observations.
Sum of the interior angles of a triangle is ______
180 degrees
What's the formula for the sine rule/law of sines?
a/SinA = b/SineB = c/SineC
OR
SinA/a = SinB/b = SinC/c
Determine the acute angle A so that sine A = 0.44 (round your answer to the nearest degree)
26 degrees
School policy states: “All students who attend bi-weekly tutorials will receive extra support in higher-order thinking problems.”
Alex attends the bi-weekly tutorials. Therefore, Alex will receive extra support.
Deductive – The conclusion follows logically from a general rule applied to a specific case.
Sum of interior angles formula
Sn=(n-2)180
What is the formula for the cosine rule/Law of Cosines?
a^2=b^2+c^2-2bcCosA OR
b^2=a^2+c^2-2acCosB OR
c^2-a^2+b^2-2abCosC
Determine the two angles between 0 degrees and 180 degrees that have the sine ratio of 0.125 (round to 2 decimal places)
angle 1 = 7.18 degrees
angle 2 = 180-7.18 = 172.82 degrees
You observe the following pattern in a sequence:
2, 4, 8, 16, …
What conjecture can you make about the next term in the sequence?
The pattern shows each term is multiplied by 2. The next term is 32.
Find the size of an interior angle of a regular hexagon
120 degrees
In triangle ABCABCABC,
∠A=40∘, ∠B=75∘, and a=12 cm
Find the length of side b (to 1 decimal place)
18.0 cm
In triangle ABC, you are given:
∠A=40∘, side a=8 cm, and side b=10 cm (adjacent to ∠A).
Is this an SSA (Side-Side-Angle) situation?
Yes
Inductive or deductive? Make a conjecture
A rule states: If a number is divisible by 4, then it is also divisible by 2.
Given that 24 is divisible by 4, what can you conclude?
24 is divisible by 2.
This is deductive reasoning because the conclusion follows from a general rule applied to a specific case.
Find the supplement angle of 50 degrees
130 degrees
In triangle XYZ
x=8 cm, y=6 cm, ∠Z=120∘
Find the length of side z (round to the nearest whole number)
12cm
In triangle ABC
∠A=40∘, side a=12 cm, side b=15 cm.
Find possible sizes for ∠B (round to the nearest degree)
53 degrees and 127 degrees
Make a conclusion
You observe that in several math tutorial sessions, students who attend regularly tend to perform better on higher-order thinking problems. Based on this pattern, what general conclusion can you draw about the impact of attending these tutorials?
Regular attendance at the tutorials is likely associated with improved performance on challenging math problems. This suggests that participation in these sessions may enhance problem-solving skills.
Find the size of an exterior angle of a regular pentagon
72 degrees
Triangle PQR has sides p=10 cm, q=7 cm, r=9 cm. Find ∠R. (round to the nearest angle)
61 degrees
Which set of measurements can produce two possible triangles?
A. ∠A=62∘, a=3.2 cm, b=4.0
B. ∠A=90∘, a=5.0 cm, b=7.0 cm
C. ∠A=45∘, a=6.0 cm, b=6.0
D. None of the above
A