Understanding number

Understanding Number: Application of Patterns and Relationships

These questions are all concerned with the recognition and use of numerical or spatial patterns and relationships. Some questions are essentially about numbers, such as those of a given sequence or ones derived from a series of spatial configurations. Other questions are more algebraic in form, and involve the formation, use or manipulation of equations, expressions and functions.

This test now comprises 18 items: 13 items from the 12 year test, plus 5 new items from the “Mathematics 14” booklet (nferNelson). The 12 year items are unchanged from the 12 year test, except for the addition of validation rules in some cases (see table below).

For items where a calculator is required, a simple on-screen calculator should appear alongside the question, with the wording “use a calculator to work out your answer”. The on-screen calculator is provided for the benefit of twins who do not have another calculator to hand (check that the calculator is working). Some questions require typing in numbers for the answers. General validation rules: prevent from leaving blank boxes, accept only numbers (not letters or other symbols) . Generally, only whole positive numbers should be accepted (reject decimals, fractions, and negatives); the exception of question 20, which must allow decimal numbers to be entered.

Branching and discontinue rules

There are 18 items. They are divided into 3 levels of 6 items each. Each level is divided into 3 sub-levels of 2 items each. In the table above, the items are organized in increasing order of difficulty. The difficulty was judged based on UK National Curriculum (NC) level of the item and the % of the NC standardisation sample (+ % of the TEDS-12 sample where available) correctly solving the item. Within level 1 the sublevels are organised as: L.1.1 is less difficult than L.1.2; L2.1 is less difficult than L.2.3 (same for levels 2 and 3).

Item numbers	Sub-Level	Level
111, 112	L1.1	Level 1 = Easy
121, 122	L1.2
131, 132	L1.3
211, 212	L2.1	Level 2 = Medium
221, 222	L2.2
231, 232	L2.3
311, 312	L3.1	Level 3 = Difficult
321, 322	L3.2
331, 332	L3.3

Table of test items

Items dropped from the previous version are highlighted in yellow. Dropping these items has necessitated a change in the item numbering.

Item no.	Sub-Level	Source	original item no.	Response type	Correct answer	Validation rules	Calcu-lator?
-	L1.1
111		12 year test	1507	Multiple choice (click answer)	1^st option (top image)	-	-
112		12 year test	1505	Multiple choice (click answer)	2.2m (2^nd option)	-	-
-	L1.2
121		12 year test	1604	Type numbers in four boxes	0, 0, 1, 1 (in sequence)	Numbers only; no blanks	-
122		12 year test	1502	Type number in box	16	Numbers only; no blanks	-
-	L1.3
131		12 year test	1402	Multiple choice (click answer)	¼ (4^th option)	-	-
132		12 year test	1801	Type numbers in two boxes	3, 5 (in sequence)	Numbers only; no blanks	-
-	L2.1
211		Mathematics 14	Q2	Type number in box	43	Numbers only; no blanks	Yes
212		Mathematics 14	Q6	Type number in box	160	Numbers only; no blanks	Yes
-	L2.2
221		12 year test	1303	Multiple choice (click answer)	75 (4^th option)	-	-
222		12 year test	1703	Multiple choice (click two answers then click OK)	2^nd and 5^th options	Require that exactly two answers are selected	-
-	L2.3
231		12 year test	1201	Type numbers in two boxes	any one of the following: 1 + 7, 7 + 1, 3 + 5, 5 + 3	Numbers only; no blanks	-
232		12 year test	1805	Type numbers in two boxes	7, 12 (in sequence)	Numbers only; no blanks	-
-	L3.1
311		12 year test	1803	Multiple choice (click answer)	4.5 (3^rd option)	-	-
312		12 year test	1804	Type numbers in two boxes	8, 15 or 15, 8	Numbers only; no blanks	-
-	L3.2
321		12 year test	1806	Multiple choice (click answer)	y = x – 2 (2^nd option)	-	-
322		Mathematics 14	Q14	Type number in box	36	Numbers only; no blanks	Yes
-	L3.3
331		Mathematics 14	Q20	Type number in box	2.6	Numbers only; no blanks. Allow decimals.	Yes
332		Mathematics 14	Q49	Multiple choice (click answer). Four answer options: n(n + n), n² + 1, 4n - 2, n x n + n	n x n + n (4^th option)	-	-

Test rules:

· Test starts at sub-level L2.1 with item 211.

· IF both items of sub-level 2.1 are answered correctly, skip the remaining items of level 2 (CREDIT ALL LEVEL 1 ITEMS) and go to sublevel 3.1. AND:

o IF both items of sub-level L3.1 are answered incorrectly, go back to sub-level L2.2 and continue the test to the end (all remaining items) or until 2 incorrect answers in a row (not including items of sub-level L3.1).

o IF one or both items of sub-level L3.1 are answered correctly, CREDIT ALL SUB-LEVEL L2.2 AND L2.3 ITEMS and continue with the L3.2 and L3.3 sub-levels to the end (all remaining items) or until 2 incorrect answers in a row (not including items of sub-level L3.1).

· IF one item of sub-level L2.1 is answered incorrectly (and one correctly), continue with the test (sub-levels L2.2; L2.3; L3.1; L3.2; L3.3) to the end or until 2 incorrect answers in a row (not including items of sub-level L2.1). CREDIT ALL LEVEL 1 ITEMS.

· IF both questions of sub-level L2.1 are answered incorrectly, go to sublevel L1.1 and continue the test (progressing with L1.2; L1.3; L2.2; L2.3; L3.1; L3.2; L3.3) to the end or until 2 incorrect answers in a row (not including items of sub-level L2.1).

· Award 1 point for each correct answer + credited items.

The rule for discontinuing after 2 incorrect answers in a row should only apply to non-branching items, as indicated above.