# 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?

# Word and definition matching cards

These are cards for matching up terms and definitions. Use the template for your own purposes by adding words from your programme (e.g. technical jargon or high-frequency words) on one side, and plain English explanations on the other side.

Here are some ideas for different activities that you could develop depending on your learning outcome:

• Match up the words with the definitions. This activity changes depending on whether a learner did the match-up on their own, with a partner, in a small group or as part of a whole class discussion activity.
• Use the cards to play a memory game in which all of the cards are laid face down on the table and two cards are flipped face up in each turn. The object of the game is to make matching pairs. Again, learners can play this alone (like Solitaire), or in pairs or groups depending on the number of cards and the level of difficulty.
• Create a third set of cards with either pictures that explain the words, or an example sentence showing how it’s used in context.
• Learners use the words and plain-English explanations to create crosswords, word finds and customised glossaries to practice using the words and develop their understanding.

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: Cheat sheet for number *strategies* activities from the Learning Progressions

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

• Multiplicative strategies
• Proportional reasoning strategies

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

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 Strategies 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:

• Most 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.

## Additive Strategies Activity Cheat Sheet

 Activity What do learners do? Additive strategies Where do I find it? Can I use it? Rate: ✓ ? ✗ Counting on and back Count on in ones to solve problems; Learn that you don’t have to start at number one Step 2 P. 19 Addition and subtraction strategies I Use number lines to develop addition and subtraction partitioning strategies for two-digit by one-digit problems Step 3 P. 22 Addition and subtraction strategies II Use number lines to develop addition and subtraction partitioning strategies for multi-digit problems Step 4 P. 25 Adding decimals Use strategies, traditional written methods and calculators to solve addition problems using decimals. Step 5 P. 28 Subtracting decimals Use strategies, traditional written methods and calculators to solve subtraction problems using decimals. Step 5 P. 30

## Multiplicative Strategies Activity Cheat Sheet

#### Can I use it? Rate: ✓ ? ✗

Skip counting Skip count in twos, threes, fives to solve simple problems; Begin to learn the 2, 3, and 5 times tables. Step 2 P. 32
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
Multiplication strategies Develop mental strategies for solving multiplication problems with single-digit multipliers Step 4 P. 39
Division strategies Develop mental strategies for solving division problems with single-digit divisors Step 4 P. 41
Multiplying options Use strategies, traditional written methods and calculators to solve multiplication problems. Step 5 P. 43
Dividing options Use strategies, traditional written methods and calculators to solve division problems. Step 5 P. 46
Multiplying with decimals Use estimation strategies and calculators to solve multiplication problems using decimals Step 6 P. 49
Dividing with decimals Use estimation strategies and calculators to solve division problems using decimals Step 6 P. 51

## Proportional Reasoning Strategies Activity Cheat Sheet

#### Can I use it? Rate: ✓ ? ✗

Ratios I Develop an understanding of simple ratios; learn to identify ratios for given quantities and vice versa Step 4 P. 53
Fractions of numbers I Develop an understanding of how to find a fraction of a whole number where the answer is also a whole number Step 4 P. 55
Ratios II Develop an understanding of more complex ratios Step 5 P. 58
Fractions of numbers II Develop an understanding of how to find a fraction of a whole number where the answer is also a fraction Step 5 P. 61
Rates and proportions Apply understanding of ratios to rates and proportions Step 6 P. 64

# TEACH: Cheat sheet for reading activities from the Learning Progressions

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 Read with Understanding 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:

• Most activities cut across multiple progressions. This is fine. Just make sure you know what your focus is. Refer back to your learning outcomes.
• The level of difficulty for the activity depends on how you pitch it to your learners. That’s why there’s no list of which steps a particular activity applies to. For example, if you choose a text with easy words, it’s going to be steps 1 to 3. If you choose a text with more academic or technical words, it’s going to be steps 4 to 6 depending on the words.
• 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.

#### Can I use it? Rate: ✓ ? ✗

Word sort Sort words according to features such as syllables, prefixes, suffixes or sounds Decoding and vocabulary p 29
Word building Decode unfamiliar words by identifying root words and exploring patterns Decoding and vocabulary p 30
Word maps Brainstorm words that relate to a single focus word in order to extend vocabulary Vocabulary p 31
Interactive cloze Use context clues in a sentence, paragraph or text to work out unknown words Vocabulary, language & text, comprehension strategies, reading critically p 33
Clustering Group words together into meaningful clusters Vocabulary, comprehension strategies p 35
Structured overviews Organise words into a hierarchy (e.g. like an chart describing all the roles in an organisation) Vocabulary, language & text, comprehension strategies, reading critically p 36
Clines Arrange words into a sequence that shows shades of meaning (e.g. like words expressing temperature) Vocabulary p 37
Predicting and defining new words Predict and define keywords they think will be in a text Vocabulary, comprehension strategies p 38
Concept circles Explain concepts and relationships that link related words Vocabulary, comprehension strategies p 39
Pair definitions Write a definition and someone else has to guess the original word Vocabulary p 40
Word and definition barrier activity Match words with definitions verbally Vocabulary, comprehension strategies p 42
Identifying key words Locate keywords in a text and work out their meanings from context. Vocabulary, comprehension strategies p 43
Navigating a text Skim and scan a text to identify its structure, key ideas and relevant details. Language and text, comprehension strategies, reading critically p 44
Surveying language and text structure Scan a text to get an overview of how it’s organised and predict its content Language and text, comprehension strategies, reading critically p 45
Brainstorming Activate prior knowledge about a topic before reading a text Vocabulary, comprehension strategies p 46
KWL activity Activate prior knowledge about a topic and create a purpose for reading Comprehension strategies p 47
Previewing and predicting text content Preview a text in order to predict its content Language and text, comprehension strategies, reading critically p 48
Skimming and scanning Skim a text to get a general idea and then scan for relevant information Language and text, comprehension strategies, p 50
Identifying main ideas Match sentences that summarise the main ideas in a text with paragraphs from a text Comprehension strategies p 51
Using ‘comment codes’ Mark up a text using comment codes to show their response or the kind of content Comprehension strategies, reading critically p 52
Selecting relevant information Sort statements about a text depending on how relevant they are to purpose or question Comprehension strategies, reading critically p 54
Using three-level thinking guides Read a text for meaning on three different levels including literal, interpretative and evaluative Comprehension strategies, reading critically p 55-56
Reciprocal teaching of reading Discuss a reading text in a small group using different roles to predict, clarify, question and summarise Comprehension strategies, reading critically p 57-58
Shared-reading Practice reading comprehension strategies Decoding, vocabulary, language and text, comprehension strategies, reading critically p 59, 118
Teaching-decoding A selection of activity ideas across the steps in the decoding progression Decoding p 119-121

# More Maths and Numeracy Jigsaw Puzzles – Multiplication and Division

I’ve posted our ALEC subtraction jigsaw puzzles here if you want to download and print, or if you want to tinker with them yourself you can also download the original word doc files as well.

Here’s the rest of them below… they’re all based around the standard 10 x 10 multiplication and division tables. You can get your learners to work them out alone or in pairs or groups.

One great thing about them is that there is only one way to solve them, but what happens is that as your learners get better they will most likely focus more on solving the problems and less on the shapes of what fits. But you’ve got the advantage of working with the shapes if you need the support.

• Just a note: These work best if you print on thick card A3 size

# Blue – 9 x

If these are useful, or you turn them into something cool for your own training then give us a shout out in the comments.