I have revised the original tests below and made them a single sheet, fixed errors, and probably created new ones!, I added some probing problem solving questions.
Here they are Test 1, Test 2, Test 3, Test 4 coming, Test 5 coming. The original versions (pdf) remain below and most instructions remain relevant.

Using the LOMAS Test to Measure and Monitor Numeracy, referenced to NZC Level.

This is a really useful and fast way to measure numeracy of Year 6 to 11 students*. Aligned to the NZ Numeracy Project and NZC. Research paper on nzmaths. LINK.
* actually any age and level including adults (teachers) and The Hundred Year Old Man.

I am using this efficient test along with PAT, e-AssTTLe, Teacher OTJ's and other measures to get cohort, class and individual overtime monitoring of student achievement. I presented a workshop at the 2018 BOP Mathematics Conference all summed up in this .ppt. This is a 15mb download!
Contact me by phone or email if you have questions.

Measure and
        Monitor example

This image shows a complex time series sequence of % students v NZC Level v time 2017 and 2018 for a cohort of about 300 students. There are three variables! The colours show NZC levels and more yellow, blue and green is good. The vertical axis, height, is %students at each level. The horizontal axis, time, is Term 1, 2, 3 etc for 2017 to T2 2018. The story continued of course and the final report identified the nagging orange L2 students for whom we seem to do nothing in secondary. Another Inquiry? The pleasing thing was more blue and green.

Background of the LOMAS Test

The LOMAS test is actually the work of mainly two people, Grigor Lomas (dec) and Peter Hughes both of whom worked in the Education Faculty of Auckland University at the time. The NUMPa Numeracy Interview was a slow but very informing and detailed insight into how a young learner understood and used number reasoning. It was slow. Requests from Secondary Teachers prevailed and the two guys above responded to the need for a written test.

The result was a test which morphed into a series of parallel tests, which can be read out, or done individually if a student has reasonable literacy. Most students at any level from year 6 to Year 11 and the staff room teachers will easily cope with the literacy requirements. In practice only a few students need help with questions explanation.

My experience also shows the test is valid on an hourly, daily weekly, monthly basis. I have given the same test to a group of students in the same period, on consecutive days and weeks. It gives the same measure every time. After a few months progression will be evidenced with attendance, engagement, learning and a wise teacher all involved. 

There are 4 versions of the original test but if you are concerned about previous knowledge, teaching to the test, there is a new version for each term or different classes.

Preparation for a LOMAS Test
The test has Parts A, B, C and D. These correspond to NZC Levels 2, 3, 4 and 5 respectively. Stop and understand what this means. You only need to ask students to complete one part!

On the first use I suggest using prior knowledge or just randomly giving out Test B or C. This comment refers to mainly Year 9 classes at the start of a year and actually it does not matter what test you give them, hence random.

The second test will be much more accurate and this is one very good reason for overtime testing. Any single test is so full of variation that it is actually quite useless. Who knows what events dominated the student on the test day? Did they sleep in? Did they have morning argument? Teenagers do not argue do they? Is it in love? Have it got a new toy? A new cell phone? Another boyfriend? The test sums up all these events, none of which you know about! So please do not see a test result as an absolute truth.

For most students, by far the majority, you use Test B or Test C in each group of tests.

I do it this way, ...
I print
- a copy of the Test 1
- and from that  20 copies of Part B
- and 20 copies of Part C

- then 40 copies of the Student Response Sheet,

- and 1 copy of the Marking Sheet,

- and for reference one copy of the Instructions.

DO THE TEST B and C yourself!  Like all assessments this checks that everything is in order and will demonstrate just how clever the questions are. Writing good math questions is not an easy task so appreciate the hard work, wisdom and insights of the authors.

Test 1
Student sheet 1
Marking sheet 1

Find a math class!

Most of my classes were 28 or so Year 9 or Year 10 students. I have also used this with Year 7 and 8 students, and Year 11 or even 12 students. Certainly with new students, asap. I have tested many teachers.

Have them decide, or you guess, their math ability. Simply ask, "Are you OK with your maths?" Yes, give them Test C. No, give them Test B. It is not critical because one test on its own is a useless indicator. See above!

Instruct them to fill in the genealogical data and to record their answers in the Test B or Test C column. Keep this sheet later for use a second time.

Common error for secondary teachers whose ears and eyes are painted on. DO NOT GIVE THEM ALL TESTS OR ASK THEM TO ANSWER IN EACH TEST.

If you see a student struggling with reading, help them out by reading the question. This is not a reading test.
If you see a student struggling to record their answers, help them out. This is not a writing test.
If you see a student struggling with the problems perhaps give them a lower Test B or even Test A.

Most students take about 20minutes to complete this test and most actually seem to enjoy it. It is multi-choice and guessing is pretty obvious. NO CALCULATORS. This test is all about reasoning with numbers. It measures Strategic Thinking and Knowledge. Strategic thinking is the clever ways a student uses what they know about numbers such as "Tidy Numbers" and "Half and Double". Knowledge is what they know such as basic facts and place value ideas.

See Instructions. However, I fold the mark guide beside their answers. I simply look at the majority correct in each of the sections. Majority of Strategy and Majority of Knowledge. That is all you need. This is a measure not a diagnostic tool to inform lessons, yet. You can look in more detail later for diagnostic information but talking with the student will tell you same information as well. Talking is more about teh original NUMPA test that is still valid and available. Ask if you have questions.

This table is from the Instructions. The first table shows how the Test is related to the Numeracy Stage and the NZC Level. Know that the NZC was deeply informed by the NZ Numeracy Project and reading the AO's will clearly confirm this information.

Refer to the NZC or Numeracy Project Book 1 for deeper understanding of this table or ask me.


Test A

Test B

Test C

Test D








Stage 4

Stage 5

Stage 6

Stage 7

Stage 8




Advanced Adder




Student uses counting to solve problems

Student uses simple adding and place value

Student uses several adding strategies and derives multiplication facts.

Student uses mult factors, multiples, tables.

Student works with fractions, decimals easily


Critical Thinkers! They will say "Sir i know this!"

NCEA L1 M and E

The second table is how to make a judgement of stage.  Teachers seem to have trouble with OTJ and can dither about the correct decision. Most of my work is about improving this disposition and empowering teachers with the knowledge and skills to make informed OTJ. Progressions, deep understandings, key ideas, key skills and all that stuff.

Simply by doing this test the student probably changed. You are assessing a very dynamic event (called learning) and if the decision is WRONG the student will soon let you know and you will probably notice as well.

A student will get one of the 4 following combinations in any test.












Student is 1 or more levels lower

Student is at the correct level

Student is at the correct level

Student is 1 or more levels higher

Marking will take 20minutes per class. Pondering the results will and can take a lot longer depending on how deeply you consider and know about the data and the students. I use Excel to collate the data. Deep insights into counting, additive, multiplicative and proportional thinking is available form . Or, you contact me.

Here are all the files. All tests are parallel copies of Part A, B, C and D.
Instructions (generic)
Test 1, Student Response Sheet 1, Marking Sheet 1
Test 2, Student Response Sheet 2, Marking Sheet 2
Test 3, Student Response Sheet 3, Marking Sheet 3
Test 4, Student Response Sheet 4, Marking Sheet 4

Please do not give a student the complete TEST 1 and have them do all Parts A, B, C and D. This would only show that you do not understand the design and use of this assessment. Most students can be assessed with one Part only using one test and all using two tests NEXT TERM! Over time data is much more reliable than a single test.

You will get some interesting results and may well need to use PAT and/or AssTTLE and/or Contributing school data and/or your own knowledge and testing of a student to get a reliable estimate of current numeracy stage or use of number reasoning. This is normal. It is also just an estimate. You are measuring a dynamic (changing) variable and the variable is a complex combination of many (thousands) variables, most of which you know nothing about!

Better is when you have over time data from Term 1,2,3,4 and perhaps even a previous year so that you can see progression or time series data.

By knowing and having an emphasis on the next stage, usually multiplicative thinking for Y9 students, students will improve rapidly and be well prepared for Year 11 NCEA L1. (NZ reference)

I have written a lot about being multiplicative (see previous newsletter 2009 T3 for declaration of war on addition and 2008 T4 for details on Multiplicative thinking.

Make "Every student in this school will become a multiplicative thinker during or by the end of Year 10" the key goal for junior mathematics. This will cause a surge in mathematics achievement in your school. Believe me, it works!