# TEACH: Numeracy resources – Hundreds grid

This is a blank Hundreds Grid. Again, it’s a resource that would lend itself to a wide range of numeracy activities.

Here are some ideas for activities using the Hundreds Grid. You could use it for:

• Developing a visual understanding of basic fractions including half, quarters and three-quarters.
• Developing an understanding of the link from basic fractions to more complex fractions and percentages.
• Developing an understanding of decimal numbers and how they relate to percentages and fractions.

How else could you use or build from this resource?

# TEACH: Can I see an example of some planning for numeracy activity?

Here’s a different scenario and example of some planning for an activity that embeds some numeracy work into a foundation learning course with a focus on building and construction.

First, read through the scenario, learning outcome, and resources. Then have a look at the activity planned at the end.

# Scenario

You teach an entry-level Building and Construction course. Your learners need to work with metric measurement including for lengths of timber. But you also want them to learn to estimate quantities without always relying on the calculator on their phones.

# Learning outcome

Based on your mapping, diagnostic assessment and work with these learners you decided on the following as your intended learning outcome for your first attempt at embedding some numeracy into your content:

• Use strategies (including using a place value chart) to estimate and solve multiplication problems that require multiplying or dividing by 10, 100 and 1000.

# Activity

You’ve decided to walk them through some examples of how the maths works. You want them to do this mentally, but you decide to use a place value chart as a way of making it explicit to start with.

You will supply them with an example where they have to estimate and then calculate how much timber is needed.

From there, you can get the group to discuss their answers and you can go through and model the process using the place value chart.

After that, the learners can work in pairs and come up with examples for others to estimate and calculate using the same strategy.

# Resources

Here are the resources that you know you need:

• Blank place value charts that you can print out or photocopy.

# Planning

Here’s what your actual planning might look like for the guided teaching and learning sequence:

## Activity 1: Using a place value chart to estimate timber quantity

1. Draw up a place value chart on the whiteboard.
2. Provide the example: “Let’s say that you need to find out the following: What is the total amount of timber needed for 220 lengths of 87.5m?
3. Ask the learners to have a guess first, and write this down on a piece of paper.
4. Compare estimations from around the room with feedback to the board to show the range of answers.
5. Introduce the place value chart and model the estimation as follows: “Let’s simplify things… “220 lengths of 87.5 is roughly 200 lengths of 90m.”
6. Say the revised calculation: “We can calculate this quickly as two lengths of 90m times 100.”
7. Do the first part of the calculation then put this on the chart: “Two lengths of 90m is 180m.”
• Then to find 100 lengths of 180, shift the 180 two places to the left on the place value chart. This is 18 000m

8. Extension:
• Provide other examples. Ask learners to work out the answers in any way they like but without using a calculator at this stage.
• Compare answers and try working it out on a calculator.

# TEACH: Cheat sheet for number *knowledge* activities from the Learning Progressions

This is part two of two parts. Here we look at numeracy activities that relate to Number knowledge. This includes:

• Number sequence knowledge
• Place value knowledge
• Number facts knowledge

You can find numeracy activities that relate to Number Strategies on a different page.

You may already have downloaded this resource shown in the image above. If you haven’t and you want to click the link below:

These resources are filled with activities and ideas that you can use or adapt. But navigating them can be tricky. So we designed a cheat sheet.

# Cheat Sheet for Number Knowledge Activities

Here’s how to use it. Just look down the list at the second column. This tells you in one sentence what learners actually have to do in the activity.

From there, you can look at the name of the activity, find the page number in the resource, and see which progressions it lines up with.

Things to remember:

• Some activities cut across multiple progressions. This is fine. Just make sure you know what your focus is. Refer back to your learning outcomes.
• These numeracy activities are specific to certain steps. Make sure that you know what step your learners are at first.
• Not all the activities will be useful to you and your situation. If you do decide to take the time to look through these, you might want to rate them for yourself. In other words, can you use this?
• You don’t have to use these. If you have your own ideas then go with that. But remember, if you need inspiration or want to look at activities that were written by experts then look here.

You can download the cheat sheets for all three strategy progressions as a single PDF below or just read on.

## Number Sequence Knowledge Activity Cheat Sheet

#### Can I use it? Rate: ✓ ? ✗

Numbers to 100 Read and write numbers from 0 to 100; position the numbers on an empty number line. Step 2 P. 67
Understanding fractions I Order fractions with the same bottom number (denominator) by cutting, naming and ordering strips of paper. Step 3 P. 69
Understanding fractions II Order unit fractions (where the bottom number is different); understand that as the bottom number gets larger, the size of the fraction gets smaller. Step 4 P. 70
Understanding fractions III

Use fraction in division problems where the numbers do not divide evenly. Step 4 P. 71
Decimal number place value Develop their understanding of the place value system to include decimal numbers including tenths, hundredths and thousandths; name any decimal number in tenths, hundredths and thousandths. Step 5 P. 78

## Place Value Knowledge Activity Cheat Sheet

#### Can I use it? Rate: ✓ ? ✗

Introducing place value Work with a place value chart to develop their understanding that our number system is based on the number 10; Understand that the place of a digit in a number indicate its value. Step 2- 3 P. 73
Whole number place value Extend their understanding of place value by adding and subtracting 1, 10, 100 and 1000 from a given four-digit number. Step 3 P. 76
Decimal number place value Develop their understanding of the place value system to include decimal numbers including tenths, hundredths and thousandths; name any decimal number in tenths, hundredths and thousandths. Step 5 P. 78
Connecting percentages, decimals
and fractions
Explore connections between percentages, decimals and fractions; develop mental strategies for solving problems involving percentages Step 5 P. 87

## Number Facts Knowledge Activity Cheat Sheet

#### Can I use it? Rate: ✓ ? ✗

Learn strategies to remember basic addition and subtraction facts; focus on learning facts that they cannot remember quickly. Step 2 P. 80
Multiplication and division facts Learn strategies to remember basic multiplication and division facts; focus on learning facts that they cannot remember quickly. Step 3 P. 82
Understanding multiplication Identify unknown multiplication facts; Use known facts to develop recall of unknown facts.

Step 3 P.35
Deriving multiplication and division facts Use already known facts to derive and extend knowledge of multiplication facts they need for quick recall Step 3 P. 37
Estimating facts Apply basic multiplication facts to problems involving multiples of tens, hundreds, thousands in order to estimate efficiently Step 4 P. 85
Connecting percentages, decimals
and fractions
Explore connections between percentages, decimals and fractions; develop mental strategies for solving problems involving percentages Step 5 P. 87

# Teach better – What is numeracy?

### (ii) Numeracy

This next definition comes from the PIIAC study as well.

#### What’s the definition?

Numeracy is the ability to use, interpret and communicate mathematical information and ideas in order to engage in and manage the mathematical demands of a range of situations (p.4).

#### Where does this definition come from?

Ministry of Education and Ministry of Business Innovation and Employment (2016). Skills and Education: Survey of Adult Skills (PIAAC). Wellington: Ministry of Education and Ministry of Business Innovation and Employment.

#### What are some key features?

Understanding:

• Quantity
• Dimension and shapes
• Patterns
• Data and chance
• Visual displays.

#### How is this definition relevant to my teaching context?

As with the definition for literacy, this one is important because it allows us to talk about our learners, our country and other countries when it comes to numeracy.

Also, it has a practical focus on using maths for a purpose. As with literacy, numeracy shouldn’t be mindless repetition and practice. It should be about solving problems that have meaning in the context of every life and work.

This is relevant to your teaching because this isn’t about the maths that you, or your learners, got at high school. This is about how to use maths ideas and knowledge to do stuff that you need to do.

The kinds of situations that are relevant to your learners and your teaching should provide you with the kinds of maths and numeracy that you need to do. But more on that in the next definition.

# New Adult Literacy and Numeracy Standards Released for the New Qualifications

Well, it’s taken a while… but it’s finally official. Here’s what you need to know:

• We have a new suite of unit standards for adult literacy and numeracy education.
• These new standards are for the new qualifications including the New Zealand Certificate in Adult Literacy & Numeracy Education (Vocational/Workplace).
• The old standards are now expiring, but are still fit for purpose for assessment until 31 December 2018. So there is roughly a two-year transition period.
• The content for Unit Standard 21204 has been broken up.
• The new NZCALNE (Voc) will eventually replace the current NCALNE (Voc), just like the current NCALNE (Voc) replaced the original NCALE (Voc).

In terms of the new NZCALNE (Voc), there are four new standards. These are:

• Unit 29622. Describe adult literacy and numeracy education in Aotearoa New Zealand. 5 credits
• Unit 2962. Design strategies to embed adult literacy and numeracy in the delivery of a training or education programme. 10 credits
• Unit 29624. Plan and facilitate embedded adult literacy and numeracy skills development in a training or education programme. 15 credits
• Unit 2962. Use assessment to strengthen adult literacy and numeracy teaching and learning. 10 credits

A caution:

• These standards are not the roadmap to delivering the new qualification. But they do provide a clear guide to what content the new NZCALNE (Voc) should assess as part of programme delivery. It will be up to providers to determine what that delivery roadmap should look like.

The good news:

• As ALEC already has consent to assess the ALNE standards to level 6, we’ll automatically get this consent extended to the new standards.
• We submitted our course approval documentation to the NZQA months ago for delivery of the new qualification but it’s been in limbo land pending the release of these new standards. This is now underway again on the NZQA side and we’re waiting to hear on its status.
• I’ve worked on both the new qualification and the new standards as part of the subject expert group. This means any new content will incorporate the best of what ALEC has had to offer to date, as well as our most current thinking and knowledge about embedding literacy and numeracy into training.

The plan:

• Our plan is to begin delivering the new version of the qualification with the new standards as soon as we can. Hopefully, this will be by the start of the academic year in 2017. This will depend on how much longer the course approval process takes and then how quickly we can move to develop the new content required.
• We’ll keep you updated here on any progress.

Any questions? Please let me know.

# How to map the numeracy demands of your course, context or a particular calculation

This is a guest post by our numeracy expert, Janet Hogan. Thanks Janet…!

# Making Sense of Number to Solve Problems strand

1. There are six progressions in this strand. The first three are about how to do things (strategies) and the second three about what you need to know to do those things (knowledge).
2. You only need to think about the first three when you map demands. What you need to know (the second three) will sit one step behind the highest step of the first three
3. Have a look at the example above. The context mapped here is stocktaking in a warehouse. It requires addition, subtraction of whole numbers (Step 4), multiplication of whole numbers (Step 5) and finding fractions of a whole number such as ¼ of 60 (Step 4). The knowledge progressions will all be at Step 4.
4. Please note, demands will never be mapped at Step 1 and Step 2 of the additive and multiplicative strategies progressions or Step 1, 2, and 3 of the proportional reasoning progression. These are developmental stages in becoming numerate. For example Step 2 is about adding and subtracting by counting, maybe on your fingers. Learners may be at Step 2 but no demand wants people to be doing that!
5. Remember: If you know that your learners are at step 2, then you’ve got diagnostic information about your learners – not the mapped demands of the course, context, or calculation.

# Measure and Interpret Shape and Space strand

1. There are three progressions here.  Most demands require the use of some measurement – even if it is just an understanding of time – so you will probably be mapping on the measurement progression. Again Step 1, 2, and 3 are developmental so you will be mapping at Step 4 or above.
2. If your course/context or calculation does not require an understanding of distance, directions, grids and bearings, in other words how to find your way (location progression) or recognising and working with mathematical shapes (shapes and transformation progression) then do not map on these progressions – indicate that these progressions are not applicable to your context/course or calculation.

# Reason Statistically strand

1. Statistics is the branch of mathematics that deals with the collection, organisation, analysis, and interpretation of numerical data, usually with a view to making predictions. If this is not part of your courses/context or calculation, do not map your demands on the statistics strand – indicate that this stand is not applicable to your context/course or calculation.
2. Please note statistics is not about reading tables such as bus timetables, wage tables etc. Some would argue that reading tables is a literacy skill for which you might also, depending on the table, need some numeracy knowledge.