Structured Maths

Lifting Maths Achievement

Tahi Maths is:

  • Structured Exploration

  • Systematic with a Scope & Sequence for Years 1-8 based on NZ Mathematics & Statistics Curriculum

  • Explicit with gradual release of responsibility

  • Diagnostic through making timely teaching points

  • Differentiated, mixed ability, whole group instruction where ākonga/learners enter in at their own, individual level

  • There is no right or wrong - justifying & explaining reasoning is the focus

  • Low cost as resources are already in NZ schools along with an exercise book which is recommended for ākonga/learners 

  • Predictable daily structure which reduces cognitive load for both teachers and children

    • day one new number is introduced

    • day two new number is revised

    • day three second number of the week is introduced

    • day four second number of the week is revised

    • day five is set aside for a practical activity of the teacher’s choosing such as a statistics investigation

  • Strands are taught in a cyclic manner with all strands in the Te Mātaiaho NZ Mathematics & Statistics Curriculum (measurement, geometry, algebra, statistics and probability) taught at least once every term

Scope & Sequence

Number Learning

"My Number Progress" is an assessment that can be used to find any gaps in numeracy skills.  

An assessment of this type is best used with Year 2 and above.

If you create an individualised doc. for every ākonga/learner in your class you can then highlight the area which each of your ākonga/learners are confident in so that the areas that are not highlighted are those they need to practise.

During Maths sessions ākonga/learners can open their doc. "My Number Learning" and write 5 equations from one of the sections that are yet to be highlighted.

Each section contains a teaching video which ākonga/learners are able to access if they need extra support.

Number Learning provides daily practise in numeracy skills at a individualised level.

Day 1

Introduce the Number

There’s no right or wrong when children have a go at writing equations using the number of the day.

Starting with the number 1 was super fun for my Year 0 & 1 ākonga/learners, every child was able to do something unique!

We learned so much from each other.

Day 1 Measurement

Ākonga/learners engaged in measuring objects around the room.

A group of ākonga/learners wanted to use the cuisenaire rods to measure the metre ruler.

This was highly engaging and fun.

Others found objects longer and shorter than the 10cm orange cuisenaire rod and took photos on Seesaw.

We ended our maths time with sharing the posts that were on Seesaw.

Day 2 Book Work

Ākonga/learned loved drawing a picture and writing equations which contained the number 1.

There’s no right or wrong!

Scope & Sequence Summary

Every year group has its own Scope & Sequence:

Year 1 - numbers to 20

Year 2 - numbers to 100

Year 3 - numbers to 1,000

Year 4 - numbers to 10,000

Year 5 - numbers to 100,000

Year 6 - numbers to 1,000,000

Every week has a Strand focus:

Week 1 Measurement - Length

Week 2 Measurement - Width

Week 3 Geometry - Reflection

Week 4 Geometry - Turns

Week 5 Statistics

Week 6 Probability

Week 7 Algebra

Week 8 Measurement - Perimeter

Week 9 Measurement - Area

Week 10 Algebra

See Think Wonder

See Think Wonder  is a thinking routine from Harvard Graduate School of Education. 

Thinking routines are tools specifically designed to help, support and guide mental processes or thinking.

Thinking routines originated from Project Zero’s Visible Thinking research initiative which included tools that teachers can use to find out more about what their children are thinking.

See Think Wonder is used daily as part of Te Tau o te Rā/Number of the day. 

On the first day ākonga are presented with a picture of something to do with a strand, such as measurement. The first time the Year 1’s do this is with a picture of three objects. One shows a square with 1 Centimeter, a thin line with 1 Millimeter, and a baseball bat with a ruler with the word Meter. Children can talk to their Maths Buddy about what they see, think or wonder about. 

As a group we talk together about the responses ākonga/learners have made. We talk about how small a millimeter is and show it on a ruler. We talk about the length of a centimeter and show it on the ruler and we bring out the meter ruler and talk about it being about the same length as a baseball bat.

On the second day ākonga/learners are presented with a picture of something to do with the number focus. The second day the Year 1’s do this it is with a picture of a grid of numbers which is an addition table where the number 1 is being added to numbers both across and down. We talk about the numbers and how the highlighted numbers on the diagonal are the same. We talk about the numbers that come next. 


Daily Structure Explained

Day 1 Number & Strand

Number Video (Year 1 & 2)

There are many videos online to choose from. The Sesame Street Count Dracula one proved to be very popular with my Year 1 class. It’s a catchy tune, simple and repetitive. Numberblocks is always a great go-to. And Jack Hartmann is fantastic for children to get up and move to the beat before settling into their maths lesson.

Calendar and Clock

When the calendar has your birthday written on it, you are interested. By looking at the calendar, many concepts in our Maths Curriculum are addressed such as “identify how the passing of time is measured in years, months, weeks, days, hours, minutes, and seconds” as well as “name and order the days of the week, and sequence events in a day using everyday language of time”. 

By looking at the clock we can identify where the hour hand is or how many more minutes until two o’clock and can practice counting by fives to work it out.


Number Visual - PV blocks, Abacus, Number Line

Starting with the tens board is a great way for ākonga/learners to consolidate their ability to subitize. The same if you look at a dice. 

Cuisenaire rods are fantastic and children can start to see relationships between the rods such as two red ones being the same as four.

Whiteboards - write number & equations

The great thing about using whiteboards is that it doesn’t matter if you make a mistake, you can rub it out. It’s a great way for the teacher to see if a child needs help with number formation, if you want to go there, or with equations.

Strand - See Think Wonder

See Think Wonder from Harvard University is a powerful way for children to enter into maths where there is no right or wrong. The images used for this can be adapted to suit the ākonga/learners in your class.

Strand Activity (eg: measure using a ruler)

Every other day there is a strand activity that is a practical, hands on activity such as measuring, working with shapes or creating patterns.

End lesson with Sharing Time 

It’s important to wrap the lesson up with some type of sharing, either sharing ākonga/learners Seesaw posts or something they have written in their maths books.

Day 2 Number Review & Book Work

Number Video (Year 1 & 2) 

A different video or the same one as the previous day, depending on the children. Jack Hartmann’s videos are excellent as they have visuals showing the different ways numbers can be represented, such as on a number line or with tally marks. 

Calendar and Clock

Having a daily routine lessens cognitive load and children love the predictable nature of knowing what they will be doing during Maths time. They know that there will be time to look at the calendar and maybe count how many more days until their birthday or another special event that is coming up.


Number Visual - PV blocks, Abacus, Number Line

Review numbers using the tens frame cards, abacus, number line, 100’s board. This is a time to subitize for the younger learners

Number Activity - draw and write equations in book (Teacher Model)

The teacher could model writing fact families or a pattern in their own maths book and ākonga/learners could do the same or make their own choice about what they write in their book.

Number Activity - draw and write equations in book

It’s empowering for ākonga/learners to choose what they will do in their books using the number of the day in their equations.


End lesson with Sharing Time

Share bookwork to show that it is valued and a way that we can all learn from each other.

REPEAT 2 DAY STRUCTURE WITH EVERY NUMBER

  • 4 days a week for Number & Strand Focus

    • 2 numbers each week

  • 1 day for Maths Investigations such as Statistics or High Ceiling, Low Floor activities

Jo Boaler Talks About Math Traumatized Kids In School

Slow it down, have children go into depths with Maths, enjoy Maths and never associate speed with Maths.

Thank you Jo Boaler for giving me permission to share this video.

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