PAPER FOLDING · TACHS ABILITY

Catholic School Prep

One of 3 item types in the TACHS Ability subtest

Paper folding: a square, a fold, a punch, and where the holes are

A square of paper is folded once or twice and a hole is punched through the stack. The question is what the sheet looks like opened out again. The whole method is one sentence in the publisher’s own answer key: a punch goes through every layer under it.

Below: the directions as Riverside Assessments prints them, what its answer key says the rules turn on, and 3 real questions from the 360 of this type here — shown without their answers, because the answer comes back on the practice page after you choose.

What the directions say

In each question, look at the top row to see how a square piece of paper is folded and where holes are punched in it. Then look at the bottom row to decide which answer choice shows how the paper will look when it is completely unfolded.

Riverside AssessmentsTACHS Student Handbook, Ability sample directions

What the publisher’s answer key says the rules are

The handbook prints a handful of samples and explains them. Those explanations are the only published statement of what this item type turns on, so every question here is built to that vocabulary and nothing else.

From the answer key

Since the paper is folded in half, the holes are punched through two layers. That means there will be four holes when the paper is unfolded.

Layers times punches is the number of holes. Two layers and two punches gave four. That arithmetic is the first thing to do and the thing most wrong choices get wrong.
From the answer key

…how the paper will look when it is completely unfolded.

Completely. A choice that shows the sheet with one fold still made, or with holes copied straight across instead of mirrored, is a picture of a half-finished unfolding — and it is always among the choices.

How to work one

  1. Step 1

    Count the layers under the punch

    After each fold the stack doubles where the paper overlaps. Work out how many layers sit under the punch — one fold gives two, two folds give up to four — and multiply by the number of punches. That is how many holes to look for.

  2. Step 2

    Undo the last fold first

    Open the folds in reverse order. Each fold line is a mirror: every hole on the folded half gets a twin on the other side, the same distance from the line. Copying instead of mirroring is the classic mistake, and one wrong choice is built on it.

  3. Step 3

    Check the count, then the places

    Rule out every choice with the wrong number of holes before looking at positions. What is left usually differs by one hole being on the wrong side of a fold line.

3 real questions, easiest first

Each is an original question of ours, lettered the way the TACHS letters its answer sheet. The answers are not on this page: pick one, then find out on the practice page, where every wrong choice explains why it is wrong.

An easier oneExample 1 of 3

In each question, look at the top row to see how a square piece of paper is folded and where holes are punched in it. Then look at the bottom row to decide which answer choice shows how the paper will look when it is completely unfolded.

  1. A
  2. B
  3. C
  4. D
  5. E

What is on the page. One fold, then 2 punches. Start with the layers: after one fold, how many thicknesses of paper sit under each punch? Multiply by the 2 punches and you have the number of holes an answer has to show.

Then unfold. Open the last fold first, mirroring the holes across its line, then the one before it. Cross off every choice with the wrong number of holes, and the rest is which side of a fold line each hole sits on. The practice page marks your pick and names the mistake each wrong sheet is built on.

A middling oneExample 2 of 3

In each question, look at the top row to see how a square piece of paper is folded and where holes are punched in it. Then look at the bottom row to decide which answer choice shows how the paper will look when it is completely unfolded.

  1. A
  2. B
  3. C
  4. D
  5. E

What is on the page. 2 folds, then 2 punches. Start with the layers: after 2 folds, how many thicknesses of paper sit under each punch? Multiply by the 2 punches and you have the number of holes an answer has to show.

Then unfold. Open the last fold first, mirroring the holes across its line, then the one before it. Cross off every choice with the wrong number of holes, and the rest is which side of a fold line each hole sits on. The practice page marks your pick and names the mistake each wrong sheet is built on.

A harder oneExample 3 of 3

In each question, look at the top row to see how a square piece of paper is folded and where holes are punched in it. Then look at the bottom row to decide which answer choice shows how the paper will look when it is completely unfolded.

  1. J
  2. K
  3. L
  4. M
  5. N

What is on the page. 2 folds, then 3 punches. Start with the layers: after 2 folds, how many thicknesses of paper sit under each punch? Multiply by the 3 punches and you have the number of holes an answer has to show.

Then unfold. Open the last fold first, mirroring the holes across its line, then the one before it. Cross off every choice with the wrong number of holes, and the rest is which side of a fold line each hole sits on. The practice page marks your pick and names the mistake each wrong sheet is built on.

360

Paper folding questions here

2,280

Ability questions in all

1,140

of them free, no sign-up

3

item types in the subtest

Try ten, and see the answer after each one

The practice page deals ten Ability questions at a time — all 3 item types mixed, as the paper mixes them — marks each one the moment you choose, and says what the rule was. No sign-up and no email.

The HSPT has no Ability subtest, so this page is about the TACHS only.

Related questions

What is a paper folding test question?

The top row shows a square of paper being folded, one fold at a time, and then punched. The bottom row offers five unfolded sheets, and the child picks the one that shows where the holes really are. The whole question is how many holes there are and where each one lands once every fold is undone.

How do you work out a paper folding question?

The way Riverside Assessments’s own answer key does: count layers. A punch goes through every layer of paper stacked under it, so a sheet folded in half and punched once has two holes when it is opened, and one folded twice has four. Then undo the folds in reverse order, and each fold line mirrors the holes across it.

Are paper folding questions on the HSPT?

No. The HSPT has no Ability subtest; its five subtests are Verbal Skills, Quantitative Skills, Reading, Mathematics and Language. Paper Folding is one of the three item types in the TACHS’s Ability subtest, with Figure Classification and Figure Matrices.

How many paper folding questions are on the TACHS?

Riverside Assessments publishes no count for any item type, for the Ability subtest, or for the paper as a whole; the handbook gives samples and no more. This site has 360 original paper folding questions, each with every wrong choice explained, so the method can be practiced until counting layers is automatic.

Every quotation on this page is from the TACHS Student Handbook, which Riverside Assessments publishes. It is named here, with what it settles.