# Numeracy - annotated exemplars level 1 us 26627

## Use measurement to solve problems

This annotated exemplar is intended for teacher use only. The student work shown does not always represent a complete sample of what is required. Selected extracts are used, focused on the grade boundaries, in order to assist assessors to make judgements at the national standard.

### Meets Performance Criteria 1.1 and 1.2

Commentary
Student work extract

Learner 1 (PDF, 345KB)

#### Cutting down a tree

This sample of learner evidence contributes to a portfolio of naturally occurring evidence generated over an acceptable period of time to meet the requirements of Guidance Information (GI) 2 and GI3. The evidence reflects skills described by step 5 of the Measure and Interpret Shape and Space strand of the Learning Progressions for Adult Numeracy (GI4).

Solving this real world problem (1) contributes evidence towards Outcome 1. The learner has made a reasonable estimation of the tree height (2) and taken appropriate and accurate measurements of length (3) and angle (4) (using a clinometer app on an iphone). The learner has then used these measurements in calculations to find the height of the tree (5). Note: using the clinometer app is acceptable, see GI5 and Performance Criteria (PC) 1.2, because it still requires the learner to take a measurement. The app must be calibrated to zero, positioned correctly at eye level, and read accurately.

The measuring tool and units used are appropriate to the problem and context (PC1.1). Although useful formula are provided, the learner has independently chosen the measurements to take, formulae to use, and calculations to make to reach an acceptable solution (as required by GI7, PC1.1 and PC1.2). The signed attestation by the supervisor (6) provides the information necessary to verify that these PCs have been met.

This sample provides acceptable evidence for four of the seven range items required to meet Outcome 1: length, angle, estimation (2) and conversion (7).

### Meets Performance Criteria 1.1 and 1.2

Commentary
Student work extract

Learner 2 (PDF, 293KB)

Painting a room

This sample of learner evidence contributes to a portfolio of naturally occurring evidence generated over an acceptable period of time to meet the requirements of Guidance Information (GIs) 2 and 3. The evidence reflects skills described by step 5 of the Measure and Interpret Shape and Space strand of the Learning Progressions for Adult Numeracy (GI4).

The problem (1) has a useful, real life purpose, which meets GI1 and the intent of the standard.

Taking measurements of length and using them in calculations to solve a capacity problem contributes evidence towards Outcome 1. The learner has measured the room’s dimensions (2) and used them to calculate the total area to be painted (3) to solve the problem of the amount of paint required (4). The learner has independently selected an effective method to solve the problem, see GI7 and Performance Criteria (PC) 1.2, and checked the reasonableness of the answer (5). The accuracy of the measurements taken has been attested to by the assessor (6) to meet PC1.1.

This sample provides acceptable evidence for solving a problem involving both length and capacity (two of the possible range items of Outcome 1).

### Meets Performance Criteria 1.1 and 1.2

Commentary
Student work extract

Learner 3 (PDF, 634KB)

Grass seed

This sample of learner evidence contributes to of a portfolio of naturally occurring evidence generated within the context of an agricultural training course and over an acceptable time period (as required by Guidance Information (GI) 2 and GI3. The evidence reflects skills described by step 5 of the Measure and Interpret Shape and Space strand of the Learning Progressions for Adult Numeracy (GI4).

Taking measurements of length and making calculations to solve the problem of how much grass seed is needed (1) contributes evidence towards Outcome 1. The learner has used an informal measurement of length by pacing out the dimensions of the area to be sown. The assessor has recorded what the learner actually did (2) and how the learner checked the accuracy of the informal measurements by measuring the length of his pace (3).

Using informal measurement (such as paces) can be acceptable depending on the context and the level of accuracy required for the problem. In this instance the assessor has noted that a high degree of accuracy is not required (4). The learner has calculated the total area using sensible rounding (6), and the amount of grass seed required (7) to solve the problem. The assessor has signed and dated the observation sheet (5).

This sample provides acceptable evidence of three of the seven range items required to meet Outcome 1: solving problems involving length and mass and conversion within the metric system (8).

### Meets Performance Criteria 1.1 and 1.2

Commentary
Student work extract

Learner 4 (PDF, 282KB)

Ramp 1

This sample of learner work contributes to a portfolio of evidence generated over an acceptable period of time, see Guidance Information (GI) 3. The evidence presented is naturally occurring, from an assessment of standard 5236 (GI 2). The evidence meets (or exceeds) the level of demand described by step 5 of the Measure and Interpret Shape and Space strand of the Learning Progressions for Adult Numeracy (GI4).

The problem to be solved (1) is applied and relevant to the learner’s work and training context. The NZ Building Code regulations (Resource A) has been provided for reference.

The learner has taken appropriate and accurate measurements of length (2) and used them in calculations (3) to find the angle of the ramp (4). This solves the problem of whether the ramp meets the building code (5), and contributes evidence towards Outcome 1.

The measuring tool and the units used are appropriate to the problem and context (PC1.1). The signed attestation by the supervisor (6) provides the information necessary to verify that PC1.1 and PC1.2 have been met.

This sample provides acceptable evidence for two of the seven range items required to meet Outcome 1: solving problems involving length and angle.

### Meets Performance Criteria 1.1 and 1.2

Commentary
Student work extract

Learner 5 (PDF, 682KB)

Ramp 2

This sample of learner work contributes to a portfolio of evidence generated over an acceptable period of time GI3. The evidence presented is naturally occurring, from an assessment of standard 5236 as part of a Trades Block course (GI 2). The evidence meets (or exceeds) the level of demand described by step 5 of the Measure and Interpret Shape and Space strand of the Learning Progressions for Adult Numeracy (GI4).

The problem to be solved (1) is applied and relevant to the learner’s work and training context. The NZ Building Code regulations (Resource A) has been provided for reference.

As required by Outcome 1, the learner has taken an appropriate and accurate measurement of length (2) and used it in calculations (3) to find the length of the ramp (4) and the horizontal distance from the landing (5). This solves the problem of building a ramp that meets the building code (1). The measuring tool and the units used are appropriate to the problem and context (PC1.1) and the signed attestation by the supervisor (6) provides the information necessary to verify that PC1.1 and PC1.2 have been met.

This sample provides acceptable evidence for two of the seven range items required to meet Outcome 1: solving problems involving length and angle.

### Meets Performance Criteria 1.1 and 1.2

Commentary
Student work extract

Learner 6 (PDF, 452KB)

This sample of learner evidence contributes to a portfolio of naturally occurring evidence generated within the context of a learning programme and over an acceptable period of time to meet the requirements of Guidance Information (GI) 2 and GI3. The evidence reflects skills described by step 5 of the Measure and Interpret Shape and Space strand of the Learning Progressions for Adult Numeracy (GI4). The activity meets the intent of the standard that the problems posed are in a real context and relevant to learners and/or everyday life.

The learner has taken measurements of mass (1) and capacity (2) and used them in calculations (3) (4) to solve problems (5) (6) contributing evidence towards Outcome 1. The learner has selected and used appropriate and effective methods to reach a reasonable solution, see GI7 and Performance Criteria (PC) 1.2.

By completing and signing the attestation on the learner work (7) the assessor has verified that the learner has taken accurate measurements without assistance, using appropriate measuring tools and units of measurement (PC1.1).

This sample provides acceptable evidence of four of the seven range items required to meet Outcome 1: solving problems involving mass and capacity, as well as estimation (8) and conversion within the metric system (9).

### Meets Performance Criteria 1.1 and 1.2

Commentary
Student work extract

Learner 7 (PDF, 195KB)

Peeling the spuds

This sample of learner evidence contributes to a portfolio of naturally occurring evidence generated within the context of a foundation learning programme and over an acceptable period of time to meet the requirements of Guidance Information (GIs) 2 and 3. The evidence reflects skills described by step 5 of the Measure and Interpret Shape and Space strand of the Learning Progressions for Adult Numeracy (GI4). The activity meets the intent of the standard that the problems posed are in a real context and relevant to learners and/or everyday life.

Measurements of mass (1) and time (2) have been taken and used in calculations (3) to solve the problems posed (4), thereby contributing evidence towards Outcome 1. The learner has independently chosen effective methods to use to reach a solution, see GI7 and Performance Criteria (PC) 1.2.

The assessor has verified (5) that the learner has taken measurements (to an acceptable degree of accuracy), using appropriate measuring tools and units of measurement (PC1.1), and has judged the solutions to be reasonable (6).

This sample provides acceptable evidence for three of the seven range items required to meet Outcome 1: solving problems involving mass and time, as well as conversion within the metric system (7).

### Meets Requirements of Guidance Information 2, 3 and 4

Commentary
Student work extract

Learner 8 (PDF, 3.7MB)

This sample of learner evidence contributes to a portfolio of naturally occurring evidence generated over an acceptable period of time to meet the requirements of Guidance Information (GI) 2 and GI3. The evidence reflects skills described by step 5 of the Measure and Interpret Shape and Space strand of the Learning Progressions for Adult Numeracy (GI4).

This sample provides acceptable evidence for location as the learner has shown an understanding of location in terms of direction and distance in marking the sections of the ride on the map (1) in order to determine the finish point for the ride (2).

### Meets Requirements of Guidance Information 2, 3 and 4

Commentary
Student work extract

Learner 9 (PDF, 732KB)

This sample of learner evidence contributes to a portfolio of naturally occurring evidence generated over an acceptable period of time to meet the requirements of Explanatory Notes (GIs) 2 and 3. The evidence reflects skills described by step 5 of the Measure and Interpret Shape and Space strand of the Learning Progressions for Adult Numeracy (GI4).

This sample provides acceptable evidence for location as the learner has described the distance and direction of each section of the course (1). Directions have been described using bearings and the 8 point compass.