TESSELLATION DETECTIVES
Ana wants to cover a rectangular notebook completely with identical squares without leaving gaps or overlaps. Can squares form a tessellation? Explain why.
Yes. Squares tessellate because they fit together without gaps or overlaps.
A triangle is moved 5 units to the right without changing its size or orientation. What transformation occurred?
Translation
Maria has ₱12.50 and receives ₱7.25. How much money does she have altogether?
₱19.75
You have ₱50.00 and spend ₱18.75. How much remains?
₱31.25
One notebook costs ₱15.50. How much will 2 notebooks cost?
₱31.00
Ben uses circles to cover a floor. He notices that spaces remain between the circles. What property of tessellation is missing?
There should be no gaps.
A shape is flipped over a vertical line. Its size remains the same, but its orientation changes. What transformation is this?
Reflection
A runner completes 2.75 km in the morning and 3.40 km in the afternoon. How far did the runner travel altogether?
6.15 km
A ribbon is 8.5 meters long. You use 3.75 meters. How much ribbon is left?
4.75 meters
One meter of cloth costs ₱45.25. How much would 3 meters cost?
₱135.75
A regular triangle, square, and regular hexagon can tessellate individually. If you had to choose one for a floor pattern that is easiest to arrange repeatedly, which could you use and why?
Any of the three; each can tessellate by itself because the shapes fit without gaps or overlaps.
A student turns a shape 90° around a fixed point. The shape stays the same size. What transformation occurred?
Rotation
Which is greater: 12.45 + 3.8 or 10.75 + 5.6? Show your reasoning.
12.45 + 3.80 = 16.25; 10.75 + 5.60 = 16.35. Therefore, 10.75 + 5.6 is greater.
Which is larger: the difference between 15.60 and 7.25 or the difference between 18.50 and 10.75?
15.60 − 7.25 = 8.35; 18.50 − 10.75 = 7.75. Therefore, the first difference is larger.
A bottle contains 1.5 liters of water. How many liters are in 4 bottles?
6 liters
A designer wants a repeating pattern made only from one type of regular polygon. Which would work: a regular pentagon or a regular hexagon? Explain your choice.
Regular hexagon, because six 60° angles meet to form 360° around a point.
A logo is moved 3 spaces left and 2 spaces up. It is not flipped or turned. What transformation was used?
Translation
A store sells a notebook for ₱35.75 and a pen for ₱12.50. If you buy two notebooks and one pen, how much will you spend?
₱84.00
A water tank contains 25.5 liters. After using 8.75 liters, how much water remains?
16.75 liters
A student says that 2.5 × 0.4 = 10. Is the answer reasonable? Explain.
No. The correct answer is 1.0.
Imagine a floor pattern has 4 squares meeting at every corner. Each square has a 90° angle. How can you prove that the pattern can continue without leaving gaps?
4 × 90° = 360°, so the angles completely surround each point with no gap.
A student says that rotating a square 90° changes its size. Is the student correct? Explain using the properties of rotation.
No. Rotation changes the position/orientation but preserves the size and shape.
Carlo estimates that 14.75 + 8.30 is about 23. Is his estimate reasonable? Why?
Yes. 14.75 + 8.30 = 23.05, which is close to 23.
A student calculated 20.00 − 7.85 = 13.85. Is the answer correct? If not, identify the correct answer.
No. The correct answer is 12.15.
A store gives each of 8 customers 1.25 kg of rice. How many kilograms of rice are needed altogether? If the store has 12 kg, how much will remain?
10 kg used; 2 kg remain.