Singapore Math 5A · Independent learning
6 questions · 24 points
Using the digits 4, 0, 2, 9, 0, 6, 0, 3, 1 once each, form the greatest nine-digit number and the least nine-digit number. Find their difference. Show a mathematical method and explain or check your result. Include any appropriate units.
A research team collects 48,306 samples per year. It plans for 1,000 years at the same rate. Calculate the total and estimate its order of magnitude. Show a mathematical method and explain or check your result. Include any appropriate units.
A 7,250 m path is marked in equal 1,000 m lengths. Give the exact number of 1,000 m lengths, including a fractional length, and interpret the remainder in meters. Show a mathematical method and explain or check your result. Include any appropriate units.
A venue arranges 270 chairs in each of 400 identical sections. Find the total without writing out repeated addition. Show a decomposition. Show a mathematical method and explain or check your result. Include any appropriate units.
A stadium has 96,000 seats in equal blocks of 800. Determine the blocks and explain why dividing both numbers by 100 is valid. Show a mathematical method and explain or check your result. Include any appropriate units.
An event serves 2,400 guests a day for 30 days. It repacks the resulting number of meals into crates of 400. How many crates are needed? Express both operations using round factors. Show a mathematical method and explain or check your result. Include any appropriate units.
7 questions · 28 points
A theatre charges $9 per ticket and a flat $12 booking fee for each order. Write and evaluate expressions for three orders of 4 tickets and one order of 12 tickets. Which costs less? Show a mathematical method and explain or check your result. Include any appropriate units.
A student says 56 ÷ 7 + 2 × 9 = 90 because they worked strictly left to right. Find the correct value and identify the error. Show a mathematical method and explain or check your result. Include any appropriate units.
Without changing the numbers or operators, add parentheses to 18 − 12 ÷ 3 × 2 so that its value is 4. Show your grouping and verify. Show a mathematical method and explain or check your result. Include any appropriate units.
Translate 'subtract twice the sum of four and seven from sixty' into symbols, then rewrite it using distribution and evaluate. Show a mathematical method and explain or check your result. Include any appropriate units.
A camp buys 6 tents costing $85 each and receives a $40 total discount. Write an expression for the final bill and evaluate it. Show a mathematical method and explain or check your result. Include any appropriate units.
A bookstore has 9 crates of 24 books. It sets aside 36 books, then arranges the rest equally on 6 shelves. Express the entire process and calculate books per shelf. Show a mathematical method and explain or check your result. Include any appropriate units.
Two pupils translate 'four times the sum of 9 and 6, minus 8'. Pupil A writes 4(9+6)−8; Pupil B writes 4×9+6−8. Evaluate both and explain which matches the words. Show a mathematical method and explain or check your result. Include any appropriate units.
8 questions · 32 points
Use an area-model decomposition to compute 47×32. Label the tens and ones contributions. Show a mathematical method and explain or check your result. Include any appropriate units.
The school orders 53 boxes of 27 rulers. How many rulers? Show a multiplication algorithm and check its magnitude. Show a mathematical method and explain or check your result. Include any appropriate units.
A shipment of 8,820 tiles is packed in identical boxes of 70 tiles. How many boxes? Explain why removing a factor of ten from both amounts works. Show a mathematical method and explain or check your result. Include any appropriate units.
Determine 95÷16 as a quotient and remainder. Verify and explain why 6 is not a valid quotient. Show a mathematical method and explain or check your result. Include any appropriate units.
A library has 864 journals placed evenly into 32 boxes. How many in each box? Explain a long-division step. Show a mathematical method and explain or check your result. Include any appropriate units.
An orchard packs 997 oranges into cartons of 36. How many full cartons and how many oranges left over? Verify. Show a mathematical method and explain or check your result. Include any appropriate units.
A town prints 5,184 flyers and bundles them into packets of 48. Determine the number of packets and verify with multiplication. Show a mathematical method and explain or check your result. Include any appropriate units.
A supplier has 5,219 screws. It places 43 screws in each packet. How many full packets can it make and how many screws remain? Verify with multiplication. Show a mathematical method and explain or check your result. Include any appropriate units.
8 questions · 32 points
Plot 5/8 on a 0-to-1 number line marked in eighths, then explain the division that gives the fraction. Show a mathematical method and explain or check your result. Include any appropriate units.
A recipe uses 5/6 cup oats and 1/4 cup seeds. What is the combined amount? Show equivalence and simplify. Show a mathematical method and explain or check your result. Include any appropriate units.
A cord is 11/12 m long; 2/9 m is cut off. How much remains? Use equivalent fractions. Show a mathematical method and explain or check your result. Include any appropriate units.
A walk covers 1 3/8 miles before lunch and 2 1/4 miles after. How far altogether? Show separate whole and fraction parts. Show a mathematical method and explain or check your result. Include any appropriate units.
Two ribbons are 3 7/8 m and 2 5/6 m. Find the combined length; explain why the fraction parts produce an extra whole. Show a mathematical method and explain or check your result. Include any appropriate units.
A tank holds 8 5/6 L and releases 3 1/2 L. How much remains? Show fraction renaming without borrowing. Show a mathematical method and explain or check your result. Include any appropriate units.
A path is 7 1/6 km; 3 5/12 km is repaved. How many kilometers remain unfinished? Explain your exchange. Show a mathematical method and explain or check your result. Include any appropriate units.
A trek has two stages, 4 5/6 km and 3 7/12 km. The walkers return by a 2 3/4 km shortcut. How far do they walk in total? Show a mathematical method and explain or check your result. Include any appropriate units.
10 questions · 40 points
Optional sitting split after question 30.
Each strip is 2/7 m. Nine equal strips make a chain. Find its exact total as a mixed number. Show a mathematical method and explain or check your result. Include any appropriate units.
A club spends 5/12 of its 84-dollar grant on paint. How many dollars is that? Show grouping. Show a mathematical method and explain or check your result. Include any appropriate units.
Of 72 concert seats, 7/9 are filled. How many are occupied? Draw or describe equal groups and state the whole. Show a mathematical method and explain or check your result. Include any appropriate units.
A map square is partitioned into 5 columns and 6 rows. First mark 2/5 of its width and then 1/6 of its height. What fraction is in the overlap? Explain with cells. Show a mathematical method and explain or check your result. Include any appropriate units.
Find 4/9 × 3/8 using an overlapping partition, then reduce. Explain why the answer is smaller than both factors. Show a mathematical method and explain or check your result. Include any appropriate units.
A pupil claims 9/14 × 7/15 = 63/210 and stops. Give a simplified product and explain a cancellation before multiplication. Show a mathematical method and explain or check your result. Include any appropriate units.
A rectangular mat is 2 1/2 m long and 1 3/5 m wide. Find its area in square meters using improper fractions. Show a mathematical method and explain or check your result. Include any appropriate units.
A library starts with 120 donated books. It distributes 1/4, then gives 2/9 of the remainder to a second school. How many books stay in the library? Show a mathematical method and explain or check your result. Include any appropriate units.
A student says that the reciprocal of 2 1/2 is 1/2 1/2. Correct the claim and prove the product equals one. Show a mathematical method and explain or check your result. Include any appropriate units.
A garden plot measures 3 1/3 m by 1 1/2 m. Two-fifths of the plot is planted with vegetables. What is the vegetable area? Show a mathematical method and explain or check your result. Include any appropriate units.
6 questions · 24 points
One-fifth of a meter of ribbon is divided among 4 crafts. What length does each craft receive? Draw or describe equal pieces. Show a mathematical method and explain or check your result. Include any appropriate units.
A 7/8 kg packet of spice fills 7 identical jars equally. How many kilograms per jar? Explain the grouping. Show a mathematical method and explain or check your result. Include any appropriate units.
A bakery has 7 L of glaze. Each batch needs 1/4 L. How many batches are possible? Show inverse multiplication. Show a mathematical method and explain or check your result. Include any appropriate units.
A 9-meter cloth roll is cut into 2/3-meter scarves. How many whole scarves can be made, and how much cloth remains? Show a mathematical method and explain or check your result. Include any appropriate units.
A scout divides 2/3 kg of nuts among 4 hikers, while another scout packs 4 kg into 2/3-kg bags. Solve both and identify the different meanings of division. Show a mathematical method and explain or check your result. Include any appropriate units.
A 3/4-L jar is divided equally into 6 sample cups. How many such cups could a separate 3-L jug fill at that same cup size? Show a mathematical method and explain or check your result. Include any appropriate units.
7 questions · 28 points
A ribbon is 1 3/5 km long. Express its length in meters and in centimeters. Show each conversion. Show a mathematical method and explain or check your result. Include any appropriate units.
A garden bed is 5/6 m long and 9/10 m wide. Compute area and justify the square unit. Show a mathematical method and explain or check your result. Include any appropriate units.
The base of a garden triangle is 13 m and its perpendicular height is 8 m. Calculate the area and identify the necessary geometric condition on the height. Show a mathematical method and explain or check your result. Include any appropriate units.
A triangle's perpendicular height is 9 cm, drawn to the extension of an 18-cm base. Find the area and explain why the extension does not change the formula. Show a mathematical method and explain or check your result. Include any appropriate units.
A courtyard consists of a 10 m × 8 m rectangle plus a right triangle with base 6 m and perpendicular height 8 m attached along an edge, without overlap. Find its area. Show a mathematical method and explain or check your result. Include any appropriate units.
A triangular metal sheet with 15 cm base and 12 cm perpendicular height has a rectangular hole 4 cm by 5 cm cut out. Find the remaining metal area. Show a mathematical method and explain or check your result. Include any appropriate units.
A rectangular floor patch is 1 1/4 m long and 3/5 m wide. What is its area in cm²? Show the correct square-unit factor. Show a mathematical method and explain or check your result. Include any appropriate units.
8 questions · 32 points
A transparent box contains 6 rows of 4 cubes on each level and 3 stacked levels. Count its volume in unit cubes and explain the hidden layers. Show a mathematical method and explain or check your result. Include any appropriate units.
A storage box is 8 cm by 7 cm by 6 cm internally. What volume can it hold? Show all three factors and units. Show a mathematical method and explain or check your result. Include any appropriate units.
A tank has internal volume 1,080 cm³, width 9 cm, and height 8 cm. Find the internal length and check by multiplication. Show a mathematical method and explain or check your result. Include any appropriate units.
A stepped block consists of a 12×4×2 cm base and an added 5×4×3 cm upper cuboid; their interiors do not overlap. Calculate the total volume. Show a mathematical method and explain or check your result. Include any appropriate units.
A measuring jug contains 3.6 L. Express the capacity in mL and the equivalent cubic centimeters. Show a mathematical method and explain or check your result. Include any appropriate units.
A rectangular basin has internal dimensions 30 cm by 24 cm by 15 cm. It is filled to 2/3 of capacity. How many liters of water does it contain? Show a mathematical method and explain or check your result. Include any appropriate units.
A stepped solid has a lower block 10×5×4 cm and an upper block 6×3×2 cm with no overlapping interiors. Find its total volume in cm³, then state the volume of water it displaces in mL when fully submerged. Show a mathematical method and explain or check your result. Include any appropriate units.
An empty rectangular tank has internal base 40×25 cm. Pour 6 liters of water into it. What depth of water results, assuming the base is level? Show a mathematical method and explain or check your result. Include any appropriate units.