11+ Non-Verbal Reasoning: How Matrices, Analogies and Series Fit Together

Over the last few weeks we have taken matrix reasoning, analogies and shape series one at a time. On the exam paper they never arrive one at a time. They sit together in the same section, shuffled, and a child has a few seconds to work out which type is in front of them before the real thinking starts. A child who solves each type well in isolation can still lose marks in the mixed setting, because the first job is recognition.

This article puts the three types side by side. It covers how to tell them apart quickly, the single method that works for all of them, three worked examples run through that method, and a practice routine for mixed sets that a parent can run at the kitchen table.

What the three types have in common

Matrices, analogies and series all hand the child a small amount of evidence and ask them to find the rule hiding in it. The difference is how much evidence there is and how it is laid out.

A matrix gives you a grid, with a rule running across the rows and often a second rule running down the columns. An analogy gives you one pair of shapes and asks you to apply the relationship in that pair to a third shape. A series gives you a line of shapes that change step by step, and asks what comes next or what is missing in the middle.

The rules themselves come from a short list: rotation, reflection, a change in size, a change in shading, a change in how many elements there are, and a change in position. Almost every non-verbal reasoning question an 11-year-old meets is built from some combination of those six. A child who knows the list well and can name each item on it without hesitating knows the raw material for nearly every question in the topic. See the NVR overview for a fuller breakdown.

Telling the three types apart in two seconds

Recognition gets faster with practice, and it helps to give children a fixed set of cues to look for.

• A grid with one empty square is a matrix.
• Two shapes joined by an arrow or the words "is to", followed by a third shape and a gap, is an analogy.
• A row of shapes with a question mark at the end, or somewhere in the middle, is a series.

Try this with your child using a past paper. Cover the answer options and ask only one question per item: matrix, analogy or series? It takes a few seconds per question, and it trains the habit that makes everything after it quicker. Children who skip this step often hunt for a row-and-column rule in an analogy that has no rows or columns, and lose a minute they did not have.

One method for all three: describe, check, apply, eliminate

The four steps below work on every question type in this series. Learn them once and they carry across.

1. Describe. Say what changes, in words, and name every change. "It rotates a quarter turn clockwise and goes from white to black" is a complete description. "It looks different" is not.
2. Check. Test the description against all the evidence on the page. In a matrix, that means checking the rows and the columns separately. In a series, it means confirming the rule holds between the second and third steps as well as the first and second. In an analogy there is only one pair, so the check is a search for a second change you may have missed.
3. Apply. Build the answer yourself, on scrap paper or in your head, before you look at the options. Children who go straight to the options tend to accept the first one that looks close, and the options are written to make close answers tempting.
4. Eliminate. Cross out every option that breaks the rule. The right answer is the one left standing, and the elimination step is a second check on your own working.

Worked example 1: a matrix

A 2x2 grid. Top row: a small white circle, then a small black circle. Bottom row: a large white circle, then an empty square. Which shape completes the grid?

Describe. Across the top row, the shading changes from white to black and the size stays the same. Down the left column, the size changes from small to large and the shading stays the same.

Check. The row rule and the column rule are different, so both are operating. Neither rule contradicts the other.

Apply. The missing square sits at the end of the bottom row and the bottom of the right column. It needs both changes: black from the row rule, large from the column rule.

Eliminate. A large white circle has the right size and the wrong shading. A small black circle has the right shading and the wrong size.

Answer: a large black circle.

Worked example 2: an analogy

A white arrow pointing up is to a black arrow pointing right, as a white arrow pointing down is to what?

Describe. Between the first pair, the arrow turns a quarter turn clockwise and changes from white to black. That is two changes.

Check. There is only one pair to work from, so the check is a second look for anything missed. The size is the same and the shape is the same. Two changes, no more.

Apply. Take the white arrow pointing down, turn it a quarter turn clockwise so it points left, and make it black.

Eliminate. A white arrow pointing left has the turn but misses the shading. A black arrow pointing up has the shading but misses the turn.

Answer: a black arrow pointing left.

Worked example 3: a series

A row of four boxes holds dots. The first box has 2 dots, the second 4, the third 7, the fourth 11. How many dots belong in the fifth box?

Describe. The number of dots grows at each step, but the amount of growth changes. The gaps are +2, then +3, then +4.

Check. The gaps are increasing by one each time, and that holds across all three steps, not only the first two.

Apply. The next gap should be +5, so the fifth box needs 11 + 5 dots.

Eliminate. Any option showing 15 dots has assumed a constant +4. Any option showing 18 has added +7, which skips a step.

Answer: 16 dots.

Which type is it? A quick check for your child

Read these three descriptions to your child and ask them to name the type before they say anything about the rule.

1. A 3x3 grid of shapes with the bottom-right square empty.
2. A shape, an arrow, a second shape, then a third shape, an arrow, and an empty box.
3. Five shapes in a row, with a question mark in the fourth position.

The answers are matrix, analogy and series. If your child hesitates on any of them, that is the type to spend the next practice session on.

The mistakes we see most often in mixed sets

• Misreading the type. Hunting for rows and columns in an analogy, or treating a series as a single pair, sends a child down the wrong path from the first second.
• Stopping after the first change. The child spots the shading change and moves on without noticing the rotation. This is the most common error across all three types.
• Looking at the options too early. Options are written with near-misses on purpose. A child who has not built their own answer first is easy to tempt.
• Confusing rotation with reflection. For symmetrical shapes the two can look identical, and for asymmetrical shapes they give different results. A quick sketch with an arrow, which has an obvious direction, settles most arguments.
• Assuming a constant rate in a series. If the gaps between steps are themselves changing, a constant-rate guess will miss the answer, as the dot example above shows.
• Staying too long on one stubborn question. A child who is stuck after a reasonable attempt should mark it, move on, and come back. A mixed paper rewards children who collect the quick marks first.

A mixed practice routine for home

Practising each type in its own block builds skill, and mixed practice builds the recognition step that blocks do not touch. A simple week might look like this.

• Monday: one worked example of each type, talked through aloud with the four steps. No timer.
• Wednesday: six mixed questions, shuffled so the types are out of order. Before solving each one, your child names the type. Still no timer.
• Friday: the same format, with a generous time limit. Tighten the limit gradually over the following weeks instead of jumping to exam pace.
• Weekend: your child writes one question of any type for you to solve. Writing a question forces them to choose a rule and apply it cleanly, which is the same reasoning the exam asks for in reverse.

Ten to fifteen minutes per session is enough. Short, regular sessions build recognition better than a single long session, because the aim is for the cues to become automatic.

You do not need to be an NVR expert to run this. Your job is to listen for a complete description of the rule. If your child can say what changes, name every change, and explain how they checked it, the answer is usually right.