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MCAS Math Grade 3 study materials
MCAS Math Grade 3 study resources

MCAS Math Grade 3 practice questions

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Question 1Mathematics (Grade 3) - official content domains not enumerated in source

A third-grade class reads that a school library has 4 shelves with 35 books on each shelf. How many books are on the 4 shelves in all?

  1. 140 Correct answer.
  2. 130
  3. 120
  4. 160

Explanation

Multiply the number of shelves by the number of books on each shelf: 4 × 35. Since 4 × 30 = 120 and 4 × 5 = 20, the total is 120 + 20 = 140 books.

Question 2Mathematics (Grade 3) - official content domains not enumerated in source

Which number sentence correctly shows 48 shared equally into 6 groups?

  1. 48 ÷ 8 = 6
  2. 48 ÷ 6 = 8 Correct answer.
  3. 6 × 48 = 288
  4. 48 − 6 = 42

Explanation

Sharing 48 objects equally into 6 groups means finding the size of each group, which is 48 ÷ 6. Because 6 × 8 = 48, each group has 8 objects, so 48 ÷ 6 = 8.

Question 3Mathematics (Grade 3) - official content domains not enumerated in source

A rectangle has a length of 9 inches and a width of 4 inches. What is the area of the rectangle in square inches?

  1. 36 Correct answer.
  2. 26
  3. 18
  4. 13

Explanation

The area of a rectangle equals length times width, so multiply 9 × 4 = 36 square inches. Area is measured in square units because it counts the unit squares that cover the figure.

Question 4Mathematics (Grade 3) - official content domains not enumerated in source

Which fraction is equal to the whole number 1?

  1. 1/4
  2. 1/2
  3. 4/1
  4. 4/4 Correct answer.

Explanation

A fraction equals 1 when its numerator and denominator are the same nonzero number, because all the equal parts are present. In 4/4, four of four equal parts are shaded, which is one whole.

Question 5Mathematics (Grade 3) - official content domains not enumerated in source

A number rounds to 500 when rounded to the nearest hundred. Which number could it be?

  1. 550
  2. 462
  3. 538 Correct answer.
  4. 449

Explanation

To round to the nearest hundred, look at the tens digit. Numbers from 450 through 549 round to 500, and 538 has a tens digit of 3, so it stays at 500.

Question 6Mathematics (Grade 3) - official content domains not enumerated in source

Which list shows the fractions ordered from least to greatest?

  1. 1/2, 1/4, 1/8, 3/4
  2. 1/4, 1/8, 1/2, 3/4
  3. 3/4, 1/2, 1/4, 1/8
  4. 1/8, 1/4, 1/2, 3/4 Correct answer.

Explanation

For unit fractions with numerator 1, a larger denominator means smaller parts, so 1/8 is smallest and 1/2 is larger than 1/4. The fraction 3/4 is closest to one whole, so it is greatest.

Question 7Mathematics (Grade 3) - official content domains not enumerated in source

A pattern starts 7, 12, 17, 22. What is the rule for the pattern?

  1. Add 5 each time Correct answer.
  2. Add 4 each time
  3. Add 6 each time
  4. Multiply by 2 each time

Explanation

Subtract consecutive terms: 12 − 7 = 5 and 17 − 12 = 5. The same difference repeats, so the rule is to add 5 each time, giving 27 as the next term.

Question 8Mathematics (Grade 3) - official content domains not enumerated in source

A square has a side length of 6 centimeters. What is the perimeter of the square?

  1. 12 centimeters
  2. 24 centimeters Correct answer.
  3. 18 centimeters
  4. 36 centimeters

Explanation

A square has four equal sides, so the perimeter is 4 × 6 = 24 centimeters. Perimeter measures the distance around the outside of the figure.

Question 9Mathematics (Grade 3) - official content domains not enumerated in source

A student says that 6 × 7 = 42, so 7 × 6 must also equal 42. Which property of multiplication does this show?

  1. Commutative property Correct answer.
  2. Zero property
  3. Identity property
  4. Associative property

Explanation

The commutative property of multiplication states that changing the order of the factors does not change the product, so 6 × 7 = 7 × 6. The identity property involves multiplying by 1, and the zero property involves multiplying by 0.

Question 10Mathematics (Grade 3) - official content domains not enumerated in source

A baker makes 96 muffins and packs them into boxes of 8. How many boxes does the baker fill?

  1. 12 Correct answer.
  2. 11
  3. 10
  4. 14

Explanation

Divide the total number of muffins by the number in each box: 96 ÷ 8. Since 8 × 12 = 96, the baker fills 12 boxes.

Question 11Mathematics (Grade 3) - official content domains not enumerated in source

Which number is equal to 3,000 + 40 + 7?

  1. 3,047 Correct answer.
  2. 3,407
  3. 3,470
  4. 347

Explanation

Place value tells how much each digit is worth: 3 thousands, 0 hundreds, 4 tens, and 7 ones. Writing those digits in order gives 3,047.

Question 12Mathematics (Grade 3) - official content domains not enumerated in source

A rectangle has an area of 24 square units. Which pair of side lengths could be its length and width?

  1. 6 and 4 Correct answer.
  2. 5 and 5
  3. 7 and 3
  4. 8 and 4

Explanation

The area of a rectangle is length times width, so the pair must multiply to 24. The factors 6 and 4 give 24, so a rectangle with those side lengths has area 24 square units.

Question 13Mathematics (Grade 3) - official content domains not enumerated in source

A number line shows a point exactly halfway between 2 and 3. Which fraction names that point?

  1. 2 1/2 Correct answer.
  2. 2 1/3
  3. 2 2/3
  4. 3 1/2

Explanation

The point halfway between 2 and 3 splits the interval from 2 to 3 into two equal parts. Each part is one half, so the point is 2 wholes and 1/2, written 2 1/2.

Question 14Mathematics (Grade 3) - official content domains not enumerated in source

A student measures a pencil as 14 centimeters long. Which tool and unit are most appropriate for this measurement?

  1. A measuring cup in liters
  2. A ruler marked in centimeters Correct answer.
  3. A clock in minutes
  4. A balance scale in grams

Explanation

Length is measured with a ruler, and centimeters are a metric unit of length. A pencil is about 14 centimeters long, so a centimeter ruler fits both the attribute and the size.

Question 15Mathematics (Grade 3) - official content domains not enumerated in source

A bag has 3 red marbles and 5 blue marbles. What fraction of the marbles are red?

  1. 5/8
  2. 1/3
  3. 3/8 Correct answer.
  4. 3/5

Explanation

The denominator counts all the marbles: 3 + 5 = 8. The numerator counts the red marbles, which is 3, so 3/8 of the marbles are red.

Question 16Mathematics (Grade 3) - official content domains not enumerated in source

Which statement about a rhombus is always true?

  1. It has four sides of equal length. Correct answer.
  2. It has four right angles.
  3. It has exactly one pair of parallel sides.
  4. It has three sides.

Explanation

A rhombus is a quadrilateral whose four sides are all the same length. A square is a special rhombus that also has right angles, but right angles are not required in every rhombus.

Question 17Mathematics (Grade 3) - official content domains not enumerated in source

A student solves 45 ÷ 5 by thinking 5 × ? = 45. What is the missing factor, and why does it answer the division?

  1. 5, because 5 × 5 = 25
  2. 10, because 5 × 10 = 50
  3. 8, because 5 × 8 = 40
  4. 9, because 5 × 9 = 45 Correct answer.

Explanation

Division and multiplication are inverse operations, so 45 ÷ 5 asks what number times 5 equals 45. Since 5 × 9 = 45, the missing factor is 9 and 45 ÷ 5 = 9.

Question 18Mathematics (Grade 3) - official content domains not enumerated in source

A number rounds to 300 when rounded to the nearest hundred. Which number could it be?

  1. 278 Correct answer.
  2. 250
  3. 249
  4. 351

Explanation

Numbers from 250 through 349 round to 300. The number 278 has a tens digit of 7, so it rounds up to 300, and it lies inside that range.

Question 19Mathematics (Grade 3) - official content domains not enumerated in source

A shape is divided into 6 equal parts, and 4 of the parts are shaded. Which fraction is equivalent to the shaded part?

  1. 4/6
  2. 1/2
  3. 2/3 Correct answer.
  4. 3/4

Explanation

The shaded part is 4/6, and dividing the numerator and denominator by 2 gives 2/3. Equivalent fractions name the same amount, so 4/6 and 2/3 describe the same shaded region.

Question 20Mathematics (Grade 3) - official content domains not enumerated in source

A student uses the distributive property to find 6 × 14 as 6 × 10 plus 6 × 4. What is the value of 6 × 14?

  1. 60
  2. 64
  3. 84 Correct answer.
  4. 74

Explanation

The distributive property splits 14 into 10 + 4, so 6 × 14 = 6 × 10 + 6 × 4. That gives 60 + 24 = 84.

Question 21Mathematics (Grade 3) - official content domains not enumerated in source

A bar graph shows that 12 students chose soccer, 8 chose basketball, and 5 chose swimming. How many more students chose soccer than swimming?

  1. 20
  2. 4
  3. 3
  4. 7 Correct answer.

Explanation

To compare two categories, subtract the smaller count from the larger count: 12 − 5 = 7. The basketball count is not used because the question compares soccer and swimming only.

Question 22Mathematics (Grade 3) - official content domains not enumerated in source

A rectangle has a perimeter of 20 centimeters and a length of 6 centimeters. What is its width?

  1. 8 centimeters
  2. 7 centimeters
  3. 4 centimeters Correct answer.
  4. 14 centimeters

Explanation

Perimeter equals twice the length plus twice the width, so 20 = 2 × 6 + 2 × width. That gives 20 = 12 + 2 × width, so 2 × width = 8 and the width is 4 centimeters.

Question 23Mathematics (Grade 3) - official content domains not enumerated in source

A pattern begins 3, 6, 12, 24. If the rule continues, what is the next number, and which rule produces it?

  1. 36, because the rule is add 12
  2. 48, because the rule is multiply by 2 Correct answer.
  3. 30, because the rule is add 6
  4. 27, because the rule is add 3

Explanation

Each term is twice the term before it: 3 × 2 = 6, 6 × 2 = 12, and 12 × 2 = 24. Continuing the rule gives 24 × 2 = 48.

Question 24Mathematics (Grade 3) - official content domains not enumerated in source

A student claims that 1/3 is greater than 1/2 because 3 is greater than 2. Which reasoning corrects the claim?

  1. 1/2 is greater because halves are larger parts than thirds. Correct answer.
  2. The fractions are equal because both have numerator 1.
  3. 1/3 is greater because the denominator is larger.
  4. 1/3 is greater because 3 is an odd number.

Explanation

The denominator tells how many equal parts make one whole, so more parts means each part is smaller. Halves are larger parts than thirds, so 1/2 is greater than 1/3.

Question 25Mathematics (Grade 3) - official content domains not enumerated in source

A class reads 4 pages on day 1, 8 pages on day 2, 12 pages on day 3, and continues the same rule. How many pages does the class read on day 6?

  1. 20
  2. 28
  3. 16
  4. 24 Correct answer.

Explanation

The rule is to add 4 pages each day, so day 4 is 16, day 5 is 20, and day 6 is 24. Another way is to multiply the day number by 4: 6 × 4 = 24.

Question 26Mathematics (Grade 3) - official content domains not enumerated in source

A student writes the number 4,082 in expanded form. Which expression shows 4,082 written in expanded form?

  1. 4,000 + 80 + 2 Correct answer.
  2. 400 + 80 + 2
  3. 4,000 + 80 + 20
  4. 4,000 + 800 + 2

Explanation

Expanded form breaks a number into the value of each digit by place. In 4,082 the 4 is in the thousands place (4,000), the 0 is in the hundreds place, the 8 is in the tens place (80), and the 2 is in the ones place (2).

Question 27Mathematics (Grade 3) - official content domains not enumerated in source

A student skip-counts by 100 starting at 350: 350, 450, 550, 650. Which number comes next in this count?

  1. 751
  2. 660
  3. 700
  4. 750 Correct answer.

Explanation

Skip-counting by 100 adds one hundred each step, so the hundreds digit increases by 1 while the tens and ones stay the same. Adding 100 to 650 gives 750.

Question 28Mathematics (Grade 3) - official content domains not enumerated in source

A student rounds 672 to the nearest ten. Which number is the result?

  1. 680
  2. 600
  3. 700
  4. 670 Correct answer.

Explanation

To round to the nearest ten, look at the ones digit. The ones digit of 672 is 2, which is less than 5, so the tens digit stays the same and the ones digit becomes 0, giving 670.

Question 29Mathematics (Grade 3) - official content domains not enumerated in source

A student needs to find 8 × 7 but does not remember the fact. The student knows 8 × 5 = 40. Which additional product lets the student use the distributive property to find 8 × 7?

  1. 8 × 2 Correct answer.
  2. 8 × 7
  3. 8 × 12
  4. 8 × 3

Explanation

The distributive property lets you split 7 into 5 + 2, so 8 × 7 = 8 × 5 + 8 × 2. Since 8 × 5 is already known, the student needs 8 × 2 to finish.

Question 30Mathematics (Grade 3) - official content domains not enumerated in source

A student divides a rectangle into 4 equal parts and shades 3 of them. A second identical rectangle is divided into 8 equal parts. How many of those 8 parts must be shaded so the shaded area matches the first rectangle?

  1. 5
  2. 7
  3. 4
  4. 6 Correct answer.

Explanation

Shading 3 of 4 equal parts gives the fraction 3/4. Multiplying numerator and denominator by 2 gives 6/8, so 6 of the 8 equal parts must be shaded to cover the same area.

Question 31Mathematics (Grade 3) - official content domains not enumerated in source

A student compares 2/3 and 2/5. Both fractions have numerator 2. Which comparison is correct, and why?

  1. 2/3 > 2/5, because thirds are larger parts than fifths Correct answer.
  2. 2/3 > 2/5, because 3 is greater than 5
  3. 2/3 = 2/5, because both have numerator 2
  4. 2/3 < 2/5, because 3 is less than 5

Explanation

When the numerators are the same, the fraction with the smaller denominator is larger because the whole is split into fewer, bigger parts. Thirds are bigger than fifths, so 2/3 is greater than 2/5.

Question 32Mathematics (Grade 3) - official content domains not enumerated in source

A student plots 7/4 on a number line. Between which two whole numbers does 7/4 lie?

  1. Between 2 and 3
  2. Between 0 and 1
  3. Between 1 and 2 Correct answer.
  4. Between 3 and 4

Explanation

The fraction 7/4 equals 1 and 3/4, because 4/4 makes 1 whole and 3/4 remains. So the point lies after 1 but before 2 on the number line.

Question 33Mathematics (Grade 3) - official content domains not enumerated in source

A student measures the mass of a pencil and the mass of a textbook. Which unit is most reasonable for reporting the mass of the textbook?

  1. Kilograms Correct answer.
  2. Centimeters
  3. Grams
  4. Liters

Explanation

Mass is measured in grams or kilograms, and a textbook is heavy enough that kilograms give a sensible number. Liters measure liquid volume and centimeters measure length, so neither fits mass.

Question 34Mathematics (Grade 3) - official content domains not enumerated in source

A student starts reading at 9:15 a.m. and reads for 45 minutes. At what time does the student stop reading?

  1. 9:60 a.m.
  2. 10:00 a.m. Correct answer.
  3. 10:15 a.m.
  4. 9:50 a.m.

Explanation

Adding 45 minutes to 9:15 gives 9:60, and 60 minutes make one hour, so the time becomes 10:00 a.m. Carrying the extra hour is required because minutes only go up to 59.

Question 35Mathematics (Grade 3) - official content domains not enumerated in source

A student counts the square units inside a rectangle that is 5 units long and 3 units wide. What is the area of the rectangle?

  1. 16 square units
  2. 8 square units
  3. 30 square units
  4. 15 square units Correct answer.

Explanation

Area of a rectangle equals length times width, so 5 × 3 = 15 square units. Counting rows of squares, 3 rows of 5 squares each also gives 15.

Question 36Mathematics (Grade 3) - official content domains not enumerated in source

A student draws a quadrilateral with exactly one pair of parallel sides. Which name correctly describes this shape?

  1. Square
  2. Rectangle
  3. Rhombus
  4. Trapezoid Correct answer.

Explanation

A trapezoid is defined as a quadrilateral with exactly one pair of parallel sides. Squares, rhombuses, and rectangles all have two pairs of parallel sides.

Question 37Mathematics (Grade 3) - official content domains not enumerated in source

A student says a shape is a square. Which set of attributes must the shape have for this to be true?

  1. Four right angles only
  2. Four right angles and four equal sides Correct answer.
  3. Four equal sides only
  4. Two pairs of equal sides and no right angles

Explanation

A square must satisfy both conditions: all four angles are right angles and all four sides are equal. Having only one of these properties describes a rhombus or a rectangle but not necessarily a square.

Question 38Mathematics (Grade 3) - official content domains not enumerated in source

A student partitions a rectangle into 6 rows of equal squares with 4 squares in each row. How many equal squares are in the whole rectangle?

  1. 20
  2. 10
  3. 24 Correct answer.
  4. 28

Explanation

Equal rows form an array, and the total number of squares is the number of rows times the number in each row. So 6 × 4 = 24 equal squares.

Question 39Mathematics (Grade 3) - official content domains not enumerated in source

A student has 48 stickers and puts the same number on each of 6 pages. Which equation shows how many stickers go on each page?

  1. 48 − 6 = 42
  2. 48 × 6 = 288
  3. 48 + 6 = 54
  4. 48 ÷ 6 = 8 Correct answer.

Explanation

Sharing a total equally among a number of groups is division, so the number per page is 48 ÷ 6 = 8. Multiplication would grow the total rather than split it.

Question 40Mathematics (Grade 3) - official content domains not enumerated in source

A student knows 4 × 9 = 36. Which division fact is in the same fact family?

  1. 36 ÷ 6 = 6
  2. 9 ÷ 4 = 2
  3. 36 ÷ 4 = 8
  4. 36 ÷ 9 = 4 Correct answer.

Explanation

The fact family for 4, 9, and 36 includes 4 × 9 = 36, 9 × 4 = 36, 36 ÷ 9 = 4, and 36 ÷ 4 = 9. Only 36 ÷ 9 = 4 uses the same three numbers correctly.

Question 41Mathematics (Grade 3) - official content domains not enumerated in source

A student multiplies 7 × 60 by thinking of 60 as 6 tens. What is the product?

  1. 4,200
  2. 67
  3. 420 Correct answer.
  4. 42

Explanation

Multiplying 7 by 6 tens gives 42 tens, and 42 tens equals 420. Multiplying by a multiple of ten means multiplying the basic fact and then attaching a zero.

Question 42Mathematics (Grade 3) - official content domains not enumerated in source

A student solves 84 ÷ 7 by breaking 84 into 70 and 14. Which pair of quotients completes the work?

  1. 70 ÷ 7 = 7 and 14 ÷ 7 = 2, so 84 ÷ 7 = 9
  2. 70 ÷ 7 = 1 and 14 ÷ 7 = 2, so 84 ÷ 7 = 3
  3. 70 ÷ 7 = 10 and 14 ÷ 7 = 7, so 84 ÷ 7 = 17
  4. 70 ÷ 7 = 10 and 14 ÷ 7 = 2, so 84 ÷ 7 = 12 Correct answer.

Explanation

Splitting the dividend into parts that are easy to divide lets you add the partial quotients. 70 ÷ 7 = 10 and 14 ÷ 7 = 2, and 10 + 2 = 12.

Question 43Mathematics (Grade 3) - official content domains not enumerated in source

A student describes a pattern: the number of tiles is 5 on figure 1, 8 on figure 2, 11 on figure 3, and 14 on figure 4. Which rule gives the number of tiles for figure n?

  1. Add 5 each time
  2. Add 2 each time
  3. Multiply by 2 each time
  4. Add 3 each time Correct answer.

Explanation

Comparing consecutive figures, 8 − 5 = 3, 11 − 8 = 3, and 14 − 11 = 3, so the pattern grows by 3 tiles per figure. The rule is add 3.

Question 44Mathematics (Grade 3) - official content domains not enumerated in source

A student says that multiplying a whole number by 1 always changes the number. Which statement corrects this?

  1. Multiplying by 1 always gives 1, because 1 times anything is 1.
  2. Multiplying by 1 doubles the number.
  3. Multiplying by 1 makes the number zero.
  4. Multiplying by 1 keeps the number the same, because 1 group of a number is that number. Correct answer.

Explanation

The identity property of multiplication states that any number times 1 equals that same number. One group containing that many objects has exactly that many objects.

Question 45Mathematics (Grade 3) - official content domains not enumerated in source

A picture graph uses one star to stand for 4 students. A row for chess club shows 6 stars. How many students are in chess club?

  1. 12 students
  2. 24 students Correct answer.
  3. 6 students
  4. 10 students

Explanation

When each symbol stands for 4 students, multiply the number of symbols by 4. Six stars represent 6 × 4 = 24 students.

Question 46Mathematics (Grade 3) - official content domains not enumerated in source

A line plot shows the lengths of pencils in inches: three pencils at 3 inches, two pencils at 4 inches, and one pencil at 5 inches. How many pencils were measured in all?

  1. 6 pencils Correct answer.
  2. 3 pencils
  3. 5 pencils
  4. 9 pencils

Explanation

On a line plot, the number of marks at each value shows how many items have that measurement. Adding 3 + 2 + 1 gives 6 pencils measured.

Question 47Mathematics (Grade 3) - official content domains not enumerated in source

A student finds the perimeter of a rectangle with length 9 centimeters and width 4 centimeters. Which expression gives the perimeter?

  1. 9 + 4 + 9
  2. 9 × 4
  3. 2 × (9 + 4) Correct answer.
  4. 9 + 4

Explanation

Perimeter is the distance around the shape, and a rectangle has two lengths and two widths. So perimeter = 2 × (9 + 4) = 26 centimeters.

Question 48Mathematics (Grade 3) - official content domains not enumerated in source

A student has a rectangle with area 36 square units. Which pair of whole-number side lengths is impossible for this rectangle?

  1. 5 units and 7 units Correct answer.
  2. 3 units and 12 units
  3. 6 units and 6 units
  4. 4 units and 9 units

Explanation

Side lengths of a rectangle must multiply to the area, so each pair must have a product of 36. The product 5 × 7 = 35, which is not 36, so that pair cannot work.

Question 49Mathematics (Grade 3) - official content domains not enumerated in source

A student compares the areas of two rectangles: one is 6 by 2, the other is 3 by 4. Which statement about their areas is true?

  1. The 3 by 4 rectangle has a larger area.
  2. The two rectangles have equal areas. Correct answer.
  3. The 6 by 2 rectangle has a larger area.
  4. The areas cannot be compared without drawing them.

Explanation

Area equals length times width. The first rectangle has area 6 × 2 = 12 square units, and the second has area 3 × 4 = 12 square units, so the areas are equal even though the shapes differ.

Question 50Mathematics (Grade 3) - official content domains not enumerated in source

A student solves 6 × 8 by doubling 3 × 8. Which statement explains why this works?

  1. Doubling one factor doubles the product. Correct answer.
  2. Changing a factor does not change the product.
  3. Doubling one factor halves the product.
  4. Doubling a factor keeps the product the same.

Explanation

If one factor is doubled while the other stays the same, the product also doubles. Since 3 × 8 = 24, doubling the 3 gives 6 × 8 = 48.