SLR NCEA L1 Numeracy Portfolios -‐ 2017
10 STEPS
1. When to Use the Numeracy Portfolio ................................................................................................................................... 1 2. Why Use the Numeracy Unit Standards? ............................................................................................................................... 1 3. Getting to Know Each Unit Standard ...................................................................................................................................... 3 4. Getting to Know Numeracy Skill Required Within Each Unit Standard .................................................................................. 4 5. Planning Your Numeracy Portfolio Programme .................................................................................................................... 5 6. Delivering A Thematic Numeracy Portfolio Programme .................................................................................................... 6-‐7 7. Delivering the Key Numeracy Tasks ...................................................................................................................................... 8 8. Breaking Down Each Numeracy Unit Standard ...................................................................................................................... 9 -‐
Us 26623 – Use Numbers to Solve Problems ........................................................................................................ 9-‐11
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Us 26626 – Interpret Statistical Information for A Purpose ................................................................................. 12-‐14
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Us 26627 – Use Measurement to Solve Problems ............................................................................................... 15-‐17
9. Marking, Verification and Moderation ........................................................................................................................... 18-‐19 10. Putting It All Together ......................................................................................................................................................... 19
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1. WHEN TO USE THE NUMERACY PORTFOLIO?
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With students who will struggle with your numeracy/maths achievement standards. With students who need alternative material in a more naturally occurring context. With students who would enjoy practical, applied, every day numeracy tasks. With students who may be working in smaller groups or on numeracy outside of maths. It could be for students on an extended numeracy programme.
2. WHY USE THE NUMERACY UNIT STANDARDS?
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Students have told us they find them more “practical” and “less intense”. The themes and tasks have been designed with students. The themes reflect areas of interest for students. The programmes flows from prior learning skills to themes that introduce key numeracy tasks. The numeracy portfolios have flexibility to deliver which can be adapted to meet each student. As unit standards, a student focuses on showing they CAN do the skill, not worrying about merit or excellence which means more targeted learning programmes.
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3. GETTING TO KNOW EACH NUMERACY NCEA L1 UNIT STANDARD
• Using the SLR Teacher Guidelines booklet (.pdf (4) or (5)), read through each unit standard carefully -‐ US 26623 – Use number to solve problems (4 credits) -‐ US 26626 – Interpret statistical information for a purpose (3 credits) -‐ US 26627 – Use measurement to solve problems (3 credits) • Highlight the key numeracy skills covered in each standard • Highlight the evidence requirement for each unit standard • Note how many examples are needed, when a conclusion is needed, when to observe a skill etc. • It is the teacher’s responsibility to make sure they have the skills to deliver the unit standards to the level required.
** Do this for each unit standard until you are confident in what is being asked of a student.
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4. GET TO KNOW EACH NUMERACY SKILL REQUIRED WITHIN EACH UNIT STANDARD
• Each unit standard has different evidence requirements for a student to prove they are working at the appropriate numeracy level. • Use can see the breakdown of the skills within the unit standard. • To start a numeracy programme, you could deliver the Numbers Making Sense booklet (.pdf 2a & 2b) -‐ the introduction to NCEA L1 numeracy skills that quickly goes through each skill. • This booklet helps introduce each skill, and can be a diagnostic for where a student is at before starting the numeracy portfolio. • This could also give you the opportunity to build in additional learning tasks for a key skill to build confidence and improve their ability level. • Note: the Numbers Making Sense booklet is optional. If you feel confident that a student is aware of the NCEA L1 skills, you could move onto the programme you choose, or just select key numeracy skills from the booklet to work on before starting. • If more time is needed on a skill, look for practical examples and simple worksheets
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5. PLANNING YOUR NUMERACY PORTFOLIO PROGRAMME
• Each SLR theme has a suggested Scheme of Work (SOW) to show how a numeracy programme can be naturally occurring within themes and build evidence towards a numeracy portfolio. • The SLR SOW planning sheet (.pdf (1)) for each theme is a ‘suggestion-‐only’ teaching and learning programme and you should adapt it to meet your current student’s needs, requirements and interests, as well as the resources available. • Don’t rush the numeracy portfolio programme. It is designed to be done over time and could be started, then stopped, then started again. • The SOW reflects the order of learning tasks in the Student Workbooklet for each theme (.pdf (3)) – see next section.
• Look at your existing programmes to make use of relevant and engaging ideas and activities you currently incorporate or resources you have from previous years or professional development. • Again, if a student is struggling, build more learning opportunities into your SOW • You can choose to complete the programme in different sessions/subjects, or support each student in one longer programme. Some tasks may require Internet, research, special equipment or visits off-‐site so ensure you have looked ahead and pre-‐planned your programme.
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6. DELIVERING A THEMATIC NUMERACY PROGRAMME
• The numeracy tasks are completed throughout a programme of learning rather than as a summative assessment at the end. Some programmes are all on one theme like Fun Fitness or Masterchef Madness, while the General programme has a range of mini-‐themes. • SLR offer a student workbooklet that builds learning around a theme and then introduces or embeds a key numeracy task sheet that will be used as evidence in a student portfolio. • The contextual tasks around the numeracy are flexible and you could adapt, change, miss out or add depth to any of them before attempting the key numeracy task.
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6. DELIVERING A THEMATIC NUMERACY PROGRAMME (continued) … • As you move through the student learning booklet, you will come across tasks in red boxes. These are key numeracy tasks that will be used to build the NCEA L1 Numeracy Portfolio for each unit standard.
• Each key numeracy task has a separate instruction sheet (within the (3a-‐c) .pdf’s in your folder) that further explains the task in the red box.
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7. DELIVERING THE KEY NUMERACY TASKS
• The key numeracy tasks are embedded throughout the programme if delivering thematically. • So, for example, in Fun Fitness, students will do learning and numeracy tasks around fitness, recreation, health, well-‐being, sports careers etc. • In Masterchef Madness students will do learning tasks and numeracy tasks around food safety, hygiene, menus, budgeting, planning, careers, recipes, cooking, serving, eating out etc. • In the General theme, there are mini-‐themes with tasks that cover food, fitness, social, well-‐being, design and building to offer short, focused projects that with learning that engages students. • For example, tasks in the General theme US 26623 -‐ number to solve problem tasks are: -‐ • Lunch #1 -‐ Costs • Leisure #1 -‐ Pick a Sport
• Lunch #1 -‐ Timings • Leisure #2 -‐ Time Management
• Scoring a Sports Job • Building Materials
• Planning a Party
• For example, tasks in the General theme US 26626 – statistical interpretation for a purpose are: • Shopping survey • A Career in Sports • Friends Going Out #1 • Friends Going Out #2 • Preparing Awards • Summer Holiday Options
• Building a House
• For example, tasks in the General theme US 26627 – measurement to solve problem tasks are: • Food for Health • Seasonal Goodness • Fitness Plan • Safe Sports • Party Settings #1 -‐ Layout • Party Settings #2 -‐ Design • Finding the Celebration • Design Plans • Our Flagpole • After a red box, key numeracy task has been completed, go back to the student workbooklet and carry on with contextual tasks about the theme that will lead into the next key numeracy task. • As a student works through each key numeracy task, you should check the key numeracy skills are being used and at the right level (refer to the unit standard evidence requirements). • As a student works on conclusions or solutions for a key numeracy task, start by discussing what they have found out, selecting the most relevant evidence and building an answer using the evidence. It may take several drafts or discussions to be comprehensive.
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8. BREAKING DOWN EACH NUMERACY UNIT STANDARD … US 26623 – Use number to solve problems (4 credits)
The best way to make sure you understand each unit standard is to do all the key unit standard tasks BEFORE delivering any material. That way you can check your own knowledge, check instructions, check answers and check where each task fits in your programme. a) Make sure you cover: -‐ -‐ Using all the different number functions to solve problems -‐ Using real-‐world problems as a context to solve -‐ Using effective strategies and pathways to solve problems -‐ Using one-‐step solutions for: addition, subtraction, multiplication, division -‐ When solving problems use of integers (whole numbers), percentages, decimals, fractions b) Understand the evidence required: -‐ -‐ Evidence has come from at least THREE separate activities to solve problems. See Outcome 1 in US 26623 for clarification. You should be teaching these skills prior to these worksheets to ensure a student is confident on all. -‐ Evidence of at least THREE instances in total for addition, subtraction, multiplication and division in solving problems. -‐ Evidence of the use of integers, percentages, decimals, fractions (see Outcome 1 in US 26623 for clarification. -‐ Students should decide how to use numbers to solve the problem.
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c) Creating Solutions for A Number Problem …
We often find students are good at doing the basic number functions to work towards a problem (adding, subtracting, multiplying etc.), but then may not select and give enough evidence to actually SOLVE the problem. To create a solution to a problem (or dictate it to someone writing it down), a student may need to: • Work out the pathway needed to solve each problem • Select the number method (addition, subtraction, multiplication, division) to use to solve each problem (make sure they use at least THREE of each) • Show all working and calculations • Make sure they also show evidence of integers (whole numbers), percentages, decimals, fractions when solving each problem • Use extra paper to show workings if necessary • Double check all calculations • Do it twice or three times if necessary to make sure they are correct Check sample conclusions to solve problem at the back of the SLR Teacher/Assessor booklet in your files: -‐ Lunch #2 -‐ Timings Drawing conclusions – use evidence. Written or discuss answer to solve problems. If discussed, assessor takes notes. Sample conclusion: While most of the time is spent prepping (20mins) and cooking (45 mins) which is a total of 65 mins, it is not a hard recipe and some of it could be spent doing other things while cooking. Because 120mins was set aside, it leaves 35 mins to eat (or more if you are quicker doing prep) and only 12.5% time on cleaning up which is a good meal for busy people. Scoring a Sports Job Sample conclusion: The most expensive jobs are being a personal trainer which totals $230 + 499.99 ($729.99) just to start and then has expensive $130 a week travel costs, but maybe you get paid more? Some of the lower cost jobs like rugby coaching are affordable, but the equipment cost is expensive. The most affordable is a pool attendant which costs per week 12.25 and the training costs are only $60.95. The holiday programme looks cheaper, but the on-‐going transport costs of $72 a week for maybe 8 weeks a year adds up to $576 which is steep. Building Material Sample conclusion: Yes, I am able to buy all the wooden rows, posts and chicken wire if my friend claims the GST of 15%. This would make the total go down from $1122 to $953.70 which is within the $1000 he has to spend.
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d) Before finishing the numbers unit standard US 26623… • Check all key numeracy tasks have been completed. • Check answers are correct, working and calculations have been shown. • Check enough evidence has been used when drawing conclusions. • Check the range of evidence has been used to meet the standard. • Add extra numeracy tasks if a student has not done the above. • Use the cross-‐reference table to make sure a student has completed tasks to the level required.
Division
Integers
Addition
US26623
Fractions
of each*: Decimals
of each throughout portfolio*: Percentages
At least one piece of evidence
Multiplication
At least three pieces of evidence
Subtraction
Lunch #1 – Costs
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Lunch #2 -‐ Timings
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Leisure #1 – pick a sport
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Leisure #2 – time manage
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Scoring a Sports Job
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Planning A Party
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Building Material
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Using numbers to solve problems
You could add tasks to show additional numbers to solve problems
• Refer to judgement statements/checklist, cover sheets or US26623 version 3
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US 26626 – Interpret statistical information for a purpose (3 credits) The best way to make sure you understand each unit standard is to do all the key unit standard tasks BEFORE delivering any material. That way you can check your own knowledge, check instructions, check answers and check where each task fits in your programme. a) Make sure you cover: -‐ For each problem, a student must use one of the following to work towards a conclusion: -‐ Mean, Median, Mode -‐ Spread – Range, Trends and extreme values -‐ Drawing conclusions b) Understand the evidence required: -‐ -‐ Evidence of at least FOUR different general statistical features is required when drawing conclusions. -‐ A student should choose a different feature for each conclusion (or make sure these use FOUR minimum) choosing from: -‐ -‐ Mean, median, mode, spread, trends, unusual features (extreme values) etc. See ER 1.3 in US 26626 for clarification. -‐ You should be teaching these skills prior to these worksheets to ensure a student is confident on all the different general statistical features. -‐ At least THREE different purposes are required (so one purpose could use TWO different general features such as Friends Going Out).
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c) Drawing Conclusions using Statistical Interpretation … -‐ Decide on a general statistical feature to base conclusions around. Many students will opt for the simpler MEAN, but note they must use different methods to show they can use the other statistical features too. Encourage them to select a different focus for drawing a conclusion. -‐ Use evidence of the general feature to support the conclusion. -‐ Conclusions must be appropriate and reasonable in terms of the information provided and what the purpose of the statistics was that was provided. -‐ Conclusions can be done orally, visually or written. Or orally and then a TA or similar writing up the oral conclusion. -‐ Check sample conclusions at the back of the SLR Teacher/Assessor booklet in your files: -‐
Friends Going Out #1 Sample conclusion if using TREND as general feature (and also mean and median): -‐ Males go out more in our local area with 14 + 22 + 14 from Fri-‐Sun compared to 16 + 12 + 8 for females Fri-‐ Sun. There is almost as many people in total (male and female) that go out Mon-‐Thurs with 25 going out, compared to 22 males on a Saturday. The average per day isn’t much different with 8 males going out a day (61/7) compared to 7 females (50/7) but the most go out on a Saturday, with the median day for going out being a Thursday for males. A Career in Sport Sample conclusion if using RANGE as general feature: -‐ Yes, there are suitable positions as there are three jobs that need no prior experience with hourly wages that range from $11.91 (food prep in a sports café) to $18.99 (holiday sports programme). This is also in line with some of the starting wages for 16-‐17 yo that range from $11.85 (the lowest) to $18.99 the highest (but the holiday programme may be high because it is only short term). If young people wanted to get some qualifications, their wages could then range from $11.91 to as high as $75 an hour as a personal trainer (with the average being $26.37). Building a House Sample conclusion for: Comparing the two regions, how accurate is the company policy of completing the house build in 120 days? The company policy is more accurate for building houses within the 120 promise in Region B where the average house is built in 118.6 days (Region B average for each month: March 113.5 days, April 120.6 days, May 122.3 days, June 118 days) and 70% of their houses fill the promise and the three that don’t were only slightly over. While the average for Region A shows that 66% of their house builds were over the 120 days and didn’t meet the promise. The average house build in March, May and June were all over 120 days (123 days, 130.5 days, 125.5 days). The time to build in region A ranged from 117 days to 142 days while Region B was 108 to 129 days. The trend line on the graphs also show that both Regions were trending towards increasing the days to build. w: www.supportedlearning.com t: 021 100 1342 e: info@supportedlearning.com
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d) Before finishing the statistical interpretation unit standard US 26626… • Check all key numeracy tasks have been completed. • Check answers are correct, working and calculations have been shown. • Check enough evidence has been used when drawing conclusions. • Check the range of evidence has been used to meet the standard. • Add extra numeracy tasks if a student has not done the above. • Use the cross-‐reference table to make sure a student has completed tasks to the level required. Uses at least FOUR general features to underpin the conclusions: (a student needs to select features to use and you need to tick to check FOUR have been used with evidence to justify)
Must draw THREE valid conclusions – each with different purpose
Mode
Spread -‐ range
Trends
Unusual features
Conclusions appropriate & reasonable
Conclusion reasoned (statistically valid)
statistical
Median
Interpreting
Mean
US26626
information for a purpose Shopping Survey A Career in Sports Friends Going Out #1 Friends Going Out #2 Preparing Awards Building a House Summer Holiday Options You could add task to show additional interpretation of statistics
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US 26627 – Use measurement to solve problems (3 credits)
The best way to make sure you understand each unit standard is to do all the key unit standard tasks BEFORE delivering any material. That way you can check your own knowledge, check instructions, check answers and check where each task fits in your programme. a) Make sure you cover: -‐ -‐ Taking measurements to solve problems and using measurement tools -‐ Using appropriate units of measurement to solve problems -‐ Measurements: Length, capacity or volume, mass, angle, temperature, time -‐ Also evidence of: Conversion – within the metric system, estimation, location – compass directions or bearings and formal distances -‐ Reaching reasoned solutions b) Understand the evidence required: -‐ • Evidence of using at least FOUR different problems to solve choosing from: Length, capacity or volume, mass, angle, temperature, time etc. See Outcome 1 in US 26627 for clarification. You should be teaching these skills prior to these worksheets to ensure a student is confident on all the using measurement. • Evidence of at least FOUR measurements used. • Evidence of FOUR calculations from the measurements. • Evidence of the use of conversion, estimation and location (see Outcome 1 in US 26627 for clarification). • Measurement tools/devices and units of measurements used are appropriate to the problems being solved.
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c) Creating Solutions for A Measurement Problem …
We often find students are good at doing the basic number functions to work towards a problem (adding, subtracting, multiplying etc.), but then may not select and give enough evidence to actually SOLVE the problem. • Students should decide the pathway using measurements to solve the problem. • The solution reached for each problem is reasonable in relation to the problem. • Conclusions can be done orally, visually or written. Or orally and then a TA or similar writing up the oral solution. • Check samples at the back of the SLR Teacher/Assessor booklet in your files.
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d) Before finishing the measurement unit standard US 26627 … • Check all key numeracy tasks have been completed. • Check answers are correct, working and calculations have been shown. • Check enough evidence has been used when drawing conclusions or reaching solutions. • Check the range of evidence has been used to meet the standard. • Add extra numeracy tasks if a student has not done the above. • Use the cross-‐reference table to make sure a student has completed tasks to the level required.
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Fitness Plan
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Safe Sports
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Seasonal Goodness
Party Settings #1 – Layout Party Settings #1 – Designs Finding the Celebration Design Plans
Location
Food for Health
Conversion
solve problems
Estimation
Time
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measurement to
Length
Temperature
evidence in each problem:
Use
Uses at least ONE piece of
Angle
US26627
Capacity or mass
Evidence of problems involving FOUR of the following and including FOUR measurements taken and FOUR calculation to solve a problem*:
For this numeracy task you need to cross reference the model they choose to design/draw/adapt with the skills identified above. Ask them to add in additional information if necessary to meet more of the skills.
Our Flagpole
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Additional tasks
• Refer to judgement statements/checklist, cover sheets or US26627 version 3 w: www.supportedlearning.com t: 021 100 1342 e: info@supportedlearning.com
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9. MARKING, VERIFICATION AND MODERATION …
a) Marking … • A student’s answer will either meet the standard or it won’t as these are unit standards. • When marking look for answers that use the numeracy skills and answer problems or draw conclusions. • If a student has not provided enough evidence, get them to add depth, re-‐do the task, or attempt another similar one to prove their skills. • When drawing conclusions, look for the numeracy skill being used, and details to back up points. • When drawing conclusions, a student could write or discuss answers. If discussed, an assessor or teacher could take notes to transcribe their evidence/conclusions. • Use the Judgement statements/checklists and cover sheets and fill in the details for each unit standard.
Continued next page ….
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b) Verification … • The work and folder has to be verified by a registered teacher other than the assessor and the correct cover sheet put on each unit standard ready for NZQA moderation if called upon. • Once you have completed these steps, the student’s achievement can be uploaded onto their NZQA Record of Learning with their enrolling school. • Once all of this has been done, file it safely so it can be easily found it needed for NZQA moderation. c) NZQA moderation … • NZQA may call for samples for one or more of the numeracy unit standards. • It is a school’s responsibility to select the samples and make sure all steps have been taken, all paperwork fill in, work marked and verified to the standard, all cover sheets, judgement statements, observations etc. are true and accurate. • Make sure all work is complete and signed off by the assessor (marker) and the verifier. • If you are unsure a student has met the standard, discuss with a numeracy specialist and allow the student more opportunities to provide evidence. 10. PUTTING IT ALL TOGETHER … • By the end of the student workbooklet (.pdf (3)), a student will also have completed ALL the key numeracy tasks (in .pdf’s (3a-‐3c)) and should have enough evidence to meet each unit standard to make up their Numeracy Portfolio. • It is now your job to put it all together: -‐ -‐ Collect all the key numeracy tasks and put them together under each unit standard. We suggest using folders and divisions for each unit standard. -‐ Check all key numeracy tasks are complete and marked -‐ use Teacher/Assessor guide .pdf (4). -‐ Check each answer meets the outcomes and requirements for each standard. -‐ Fill in or check the cross-‐reference table to ensure you meet each standard evidence requirements. -‐ Make a judgement for each unit standard – Achieved or Not Achieved. -‐ If not achieved, more tasks are needed as evidence to meet the standard.
More information and all the latest versions for these standards can be found at NZQA Literacy and Numeracy unit standard resources on the NZQA website. w: www.supportedlearning.com t: 021 100 1342 e: info@supportedlearning.com
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