← SSAT® Elementary

Quantitative: 30 Questions in 30 Minutes

Everything the math section can ask an eight or nine year old — counting, cutting, tiling, weighing, graphing and spinning, all of it drawn.

32 topics · 126 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Adding and Subtracting with Regrouping

  1. How it worksHow does a bundle of ten ones turn into one single ten and slide over a column?
  2. Worked exampleWalk me through adding 47 and 38 with blocks, showing where the brand new ten comes from.
  3. Worked exampleFind 62 minus 27 by breaking one of the tens apart into ten loose ones first.
  4. Common mistakeWhy doesn't 62 minus 27 come out as 45 when you take the small digit from the big one?
Your turneasy1 of 3
A jar holds 58 red beads and 35 blue beads. How many beads are in the jar altogether?

Multiplication as Rows and Columns

  1. How it worksHow does a block of dots 4 across and 6 down show you what 4 times 6 means?
  2. Worked exampleFind 7 times 8 by chopping the dot rectangle into 7 times 4 and 7 times 4.
  3. Going furtherWhat happens to the dot rectangle when one side grows from 5 dots to 6 dots?
  4. Common mistakeWhy isn't multiplying the same thing as adding, when 3 times 5 and 3 plus 5 look so alike?
Your turneasy1 of 3
A tray of cupcakes has 7 rows, and each row holds 7 cupcakes. How many cupcakes are on the tray?

Division: Sharing Out, Grouping Up, and Undoing

  1. How it worksHow do 12 counters dealt one at a time into 4 piles show you that 12 divided by 4 is 3?
  2. Worked exampleFind 35 divided by 5 by scooping counters into groups of 5 until the pile runs out.
  3. How it worksWhy does knowing 6 times 7 is 42 hand you 42 divided by 7 for free?
  4. Going furtherWhat happens to the piles when 13 cookies are shared among 4 friends and one is left over?
Your turneasy1 of 3
A box holds 70 pencils. They are shared fairly between 5 children. How many pencils does each child get?

Fact Families and Missing Numbers

  1. How it worksHow does an arrow that goes forwards and then backwards find a hidden number for you?
  2. Worked exampleFind the missing number in 7 plus something equals 15 by walking the arrow back the other way.
  3. Common mistakeWhy isn't 9 minus 4 the same as 4 minus 9, when 9 plus 4 and 4 plus 9 match perfectly?
  4. Going furtherWhat changes about the arrows when the thing you have to undo is a doubling instead of an adding?
Your turneasy1 of 3
7 plus a hidden number makes 24. What is the hidden number?

Place Value

  1. How it worksHow do the ones, tens and hundreds columns hand each digit its size?
  2. Worked exampleShow me what happens to 452 when the 4 and the 2 swap columns with each other.
  3. Worked exampleFind what the 7 is worth in 3704 and then what it is worth in 7304.
  4. Common mistakeWhy isn't the 0 in 507 a wasted digit when it seems to stand for nothing at all?
  5. Going furtherWhat happens to every single digit in 36 when the whole number gets multiplied by 10?
Your turneasy1 of 3
In the number 377, what is the 7 worth?

Comparing and Ordering Numbers

  1. How it worksHow do you sort out 4318 and 4381 by checking one column at a time starting from the left?
  2. Worked exampleShow me 219, 291, 129 and 912 dropped onto a number line from smallest to biggest.
  3. Common mistakeWhy doesn't 89 beat 132 even though the 8 at the front is bigger than the 1?
  4. Going furtherWhat makes the greater-than sign open its wide mouth towards one number and not the other?
Your turneasy1 of 3
Which of these three numbers is the biggest: 279, 361 or 185? Write it.

Rounding and Estimating

  1. How it worksHow does a number line show you which ten a number is sitting closest to?
  2. Worked exampleFind 348 rounded to the nearest ten, and then to the nearest hundred, showing both jumps.
  3. Common mistakeWhy doesn't 45 round down to 40 when it sits exactly halfway between two tens?
  4. How it worksHow can a fast guess of 600 prove that 4200 is a silly answer for 293 plus 311?
  5. Going furtherWhat happens to 297 when rounding to the nearest ten makes it leap into a whole new hundred?
Your turneasy1 of 3
Round 67 to the nearest ten.

Odd and Even Numbers

  1. How it worksHow does pairing counters off two by two tell you in a second whether a number is even?
  2. Worked exampleShow me what happens when you add the odd numbers 7 and 5 and pair all the counters up.
  3. Common mistakeWhy isn't a number even just because it looks big or happens to end in a 5?
  4. Going furtherWhat happens to odd and even when an odd number gets multiplied by an even one?
Your turneasy1 of 3
A class of 70 children pairs up two by two for a dance. How many pairs are there?

Positive and Negative Numbers

  1. How it worksHow does the number line keep marching to the left of zero into the negative numbers?
  2. Worked exampleFind how many degrees warmer 5 degrees is than 3 degrees below zero by counting the steps.
  3. Common mistakeWhy isn't negative 8 bigger than negative 3 when 8 is clearly bigger than 3?
Your turneasy1 of 3
At dawn the temperature is 7 degrees below zero. By noon it is 9 degrees above zero. How many degrees warmer is noon than dawn?

Prime Numbers

  1. How it worksHow does trying to build rectangles out of a pile of counters tell you if a number is prime?
  2. Worked exampleShow me every rectangle that 18 counters can make, and why that stops 18 being prime.
  3. Going furtherWhat makes 2 the only even prime in the entire number line?
  4. Common mistakeWhy isn't 1 called a prime number when hardly anything divides into it?
Your turneasy1 of 3
Ana has 74 counters. She lays them out in 2 equal rows. How many counters are in each row?

Factors and Multiples (4th Grade Only)

  1. How it worksHow do you list every factor of 24 by pairing up numbers that multiply together to make it?
  2. Worked exampleFind all the factors of 36 by climbing up from 1 and pairing each one with its partner.
  3. Worked exampleFind the first number that both 3 and 5 land on when they hop along a number line together.
  4. Common mistakeWhy doesn't a factor of a number ever turn out bigger than the number itself?
Your turneasy1 of 3
A frog hops along the number line in jumps of 7. Which number does it land on at hop number 6?

Properties of Addition and Multiplication

  1. How it worksHow does sliding the brackets around inside 2 times 3 times 5 leave the answer untouched?
  2. Worked exampleFind 6 times 14 by cutting it into 6 times 10 plus 6 times 4 and adding the two pieces.
  3. Common mistakeWhy doesn't the any-order trick work on 20 minus 8 minus 3?
  4. Going furtherWhat happens to a number the moment you multiply it by 1, and then by 0?
Your turneasy1 of 3
Work out 7 plus 78 plus 3 in whichever order is easiest.

What a Fraction Means

  1. How it worksHow does the bottom number of a fraction tell you how many cuts the whole thing got?
  2. Worked exampleShow me three quarters of a chocolate bar by cutting it up and shading the right pieces.
  3. Going furtherWhat does 5 over 4 look like when one pizza is not enough to hold it?
  4. Common mistakeWhy isn't one third bigger than one half just because 3 is a bigger number than 2?
Your turneasy1 of 3
A chocolate bar is cut into 10 equal pieces. Sam eats 4 of the pieces. How many pieces are left?

Comparing and Ordering Fractions

  1. How it worksHow do two bars of exactly the same length let you see which fraction covers more of it?
  2. Worked exampleCompare 2 thirds with 3 quarters by shading two bars that started out the same size.
  3. How it worksHow does asking whether a fraction beats one half sort most fractions in a heartbeat?
  4. Common mistakeWhy doesn't comparing 1 sixth with 1 fourth work the way comparing 6 with 4 does?
Your turneasy1 of 3
Which is bigger, 6 eighths or 2 eighths? Write the top number of the bigger one.

Equivalent Fractions

  1. How it worksHow does cutting each piece in two double both numbers in a fraction and change nothing?
  2. Worked exampleShow me why 3 sixths and 1 half end up shading the very same amount of the same bar.
  3. Going furtherWhat happens to 4 eighths when you glue the little pieces back together two at a time?
Your turneasy1 of 3
A bar is cut into 7 equal pieces. Then every piece is cut in two. How many pieces does the bar have now?

Adding and Subtracting Fractions

  1. How it worksHow does shading more pieces of one single bar show you what adding fractions really does?
  2. Worked exampleFind 3 eighths plus 4 eighths by shading a bar that has been cut into 8 equal pieces.
  3. Worked exampleFind 5 sixths minus 2 sixths by rubbing the shading off one piece at a time.
  4. Common mistakeWhy doesn't 1 half plus 1 half make 2 quarters when you add the tops and the bottoms?
Your turneasy1 of 3
A bar is cut into 5 equal pieces. 2 fifths are shaded, then 2 more fifths are shaded. How many fifths are shaded now?

Decimals, Tenths and Hundredths

  1. How it worksHow do the columns after the dot keep shrinking by ten with every step to the right?
  2. Worked exampleShow me 0.4 and 0.40 shaded on two grids of 100 squares and why they cover the same amount.
  3. Common mistakeWhy isn't 0.9 smaller than 0.15 when 15 is a bigger number than 9?
  4. Going furtherWhat happens to 0.3 when you rewrite it as a fraction with 10 sitting on the bottom?
Your turneasy1 of 3
A big square is cut into 100 little squares and 65 of them are coloured in. Write the coloured part as a decimal.

Ratios and Proportions

  1. How it worksHow does a mix of 2 red counters to every 3 blue ones keep its colour as the pile grows?
  2. Worked exampleFind how many cups of water 6 lemons need when 2 lemons already need 3 cups.
  3. Common mistakeWhy doesn't adding 1 to both sides of a 2 to 3 mix leave the taste alone?
Your turneasy1 of 3
A lemonade recipe uses 2 lemons and 3 cups of water. Mia makes 7 times that much. How many cups of water does she use?

Describing and Extending Patterns (4th Grade Only)

  1. How it worksHow do you catch the rule of a pattern by watching what each step adds to the one before it?
  2. Worked exampleFind the next two numbers after 3, 7, 11, 15 and say out loud what the rule is.
  3. Worked exampleFind the missing step in a stack of squares that gains one extra row every time.
  4. Going furtherWhat happens to a pattern rule when the numbers double each step instead of adding?
  5. Common mistakeWhy isn't seeing just two numbers of a pattern enough to be sure of the rule?
Your turneasy1 of 3
A pattern starts at 7 and grows by 7 every step. What is the fourth number in the pattern?

Equalities and Inequalities

  1. How it worksHow does lifting one block off one side of a scale make the whole thing tip?
  2. Worked exampleFind the missing number in 5 plus something equals 4 plus 6 by levelling out both sides.
  3. Common mistakeWhy doesn't an equals sign mean that the answer is about to come next?
  4. Going furtherWhat changes on the scale when the two sides refuse to match and you need a less-than sign?
Your turneasy1 of 3
Find the number the box stands for: 7 + box = 7 + 9.

Shapes and Their Attributes

  1. How it worksHow does counting sides and counting corners sort every flat shape into its own family?
  2. Worked exampleShow me why a shape with 4 equal sides and 4 square corners has no choice but to be a square.
  3. Going furtherWhat happens to a rectangle's name when you tilt the sides over and lose the square corners?
  4. Common mistakeWhy isn't a triangle a brand new shape just because somebody turned it upside down?
Your turneasy1 of 3
A pentagon has 5 sides and 5 corners. Ravi draws 7 pentagons. How many corners has he drawn altogether?

Solid Shapes and Their Faces

  1. How it worksHow do you count the faces, edges and corners of a box without losing track of any?
  2. Worked exampleFind how many faces a cube has by unfolding it flat into a row of squares.
  3. Going furtherWhat flat shapes fall out when you unfold a can instead of a cube?
Your turneasy1 of 3
A cube has 6 flat faces. How many faces do 7 separate cubes have altogether?

Lines, Line Segments and Symmetry

  1. How it worksHow is a line segment different from a ray and from a line that never stops going?
  2. Worked exampleFind every fold line of a square by folding it across and then corner to corner.
  3. Common mistakeWhy isn't every line that cuts a shape into two pieces a line of symmetry?
  4. Going furtherWhat happens to the number of fold lines when a shape changes from a square into a circle?
Your turnmedium1 of 3
A regular shape has 7 equal sides and 7 equal corners. How many fold lines of symmetry does it have?

Angle Measurement (4th Grade Only)

  1. How it worksHow does an angle measure how far one arm has swung away from the other one?
  2. Worked exampleFind the angle between the two hands of a clock at 3 o'clock and name what kind it is.
  3. How it worksHow do you tell a right angle, a sharp angle and a wide open angle apart at a glance?
  4. Common mistakeWhy doesn't an angle get bigger when you draw both of its arms much longer?
Your turneasy1 of 3
A clock's minute hand sweeps from the 12 round to the 8. How many degrees has it turned?

Perimeter

  1. How it worksHow does walking all the way round the outside of a shape add up to its perimeter?
  2. Worked exampleFind the perimeter of a rectangle 7 cm long and 3 cm wide by walking every side in turn.
  3. Going furtherWhat happens to the total perimeter when you shove two squares together side by side?
Your turneasy1 of 3
A rectangle is 12 cm long and 4 cm wide. What is the distance all the way round it?

Area

  1. How it worksHow does covering a rectangle in little squares turn into multiplying its two sides?
  2. Worked exampleFind the area of a rectangle 6 squares across and 4 squares down by tiling it in.
  3. Common mistakeWhy doesn't a longer fence around a shape always mean more floor inside it?
  4. Ties togetherHow do the fence and the floor of a square both change when you double every side?
Your turneasy1 of 3
A rectangle is 9 squares across and 7 squares down. How many little squares cover it?

Measuring Length, Weight and Capacity

  1. How it worksHow does lining a ruler up from its zero mark give you a length you can trust?
  2. Worked exampleFind the weight of a bag holding 3 apples when every apple weighs 150 grams.
  3. Going furtherWhat happens to the number you write down when the same water is measured in cups, then in litres?
  4. Common mistakeWhy isn't the heavier thing always the bigger thing?
Your turneasy1 of 3
A bag holds 9 apples and each apple weighs 150 grams. How many grams do the apples weigh?

Time, Temperature and Money

  1. How it worksHow do you count forward around a clock face to work out how long something lasted?
  2. Worked exampleFind how long a film runs when it starts at 2:45 and finishes at 4:20.
  3. Worked exampleFind the change from a 5 dollar bill after buying a book that costs 3 dollars and 65 cents.
  4. Going furtherWhat happens to a thermometer when the temperature falls 10 degrees starting from 5 degrees?
Your turneasy1 of 3
A film starts at 2:45 and finishes at 4:41. How many minutes does it run for?

Reading Graphs and Tables

  1. How it worksHow does each bar grow straight out of a number sitting in a table of votes?
  2. Worked exampleFind how many more children picked apples than pears when the bars reach 9 and 4.
  3. How it worksHow do you read a table by finding the row and the column that cross at your answer?
  4. Common mistakeWhy doesn't a taller row of pictures always mean more when one picture stands for 5 children?
  5. Going furtherWhat happens to every bar when the side of the graph starts counting by 2 instead of by 1?
Your turneasy1 of 3
On a bar graph the apple bar reaches 17 and the pear bar reaches 6. How many more children picked apples than pears?

Line Plots and Tallies

  1. How it worksHow does a tally mark laid across four others turn counting into counting by fives?
  2. Worked exampleFind how many children are on a plot with 3 dots at 6, 5 dots at 7 and 2 dots at 8.
  3. Going furtherWhat happens to the tallest tower when two more children of the same shoe size join in?
Your turneasy1 of 3
A line plot has 7 dots above 6, 7 dots above 7 and 2 dots above 8. How many children are on the plot?

Chance and Probability

  1. How it worksHow does spinning over and over build a tally that slowly matches the size of each slice?
  2. Worked exampleFind how likely a spinner cut into 4 equal parts with 1 green part is to stop on green.
  3. Common mistakeWhy doesn't landing on blue four times running make blue any likelier on the next spin?
  4. Going furtherWhat happens to the chance of red when one more slice of the spinner gets painted red?
Your turneasy1 of 3
A spinner is cut into 8 equal parts and 1 part is green. What is the chance of green, as a fraction of 1?

Sorting, Logic and Word Problems

  1. How it worksHow do you turn a story about 5 birds landing on a branch with 3 already there into a number sentence?
  2. Worked exampleFind how many stickers Mia has left after starting with 24 and giving 6 friends 3 each.
  3. Going furtherWhat changes about the hoops when a clue says all cats have tails but only some cats are black?
  4. Common mistakeWhy doesn't the word more in a word problem always mean you should add?
Your turneasy1 of 3
Mia starts with 51 stickers and gives 7 friends 3 stickers each. How many stickers has she left?

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