Intro to Measurement (five steps)

Role of estimation

It is important that children estimate when measuring: • Helps focus on the measurement attribute • Poor estimates indicate lack of understanding • Provides intrinsic motivation • Helps develop familiarity with standard units • An approximation serves as a rough check of the accuracy of a measurement

Sequence of Instruction for Teaching Measurement (Length, Weight, Capacity, Area)

Step 1: Number-free comparison activities

Step 2: Develop and use non-standard units

Step 3:Develop need for a standard unit

Step 4:Introduce a standard unit of measurement

Step 5:Establish need for smaller and larger units of measurement

Step 1: Number-free Comparison

Activities •Comparing two quantities and seeing a relationship between them

•Maintain a focus on informal and formal mathematical language

•What language will you use when comparing length? weight? capacity? area?

• Focus on the attribute e.g. ‘longer than’, ‘holds more than’, ‘is heavier than’ • Avoid ‘more than’, ‘bigger than’

•Strategies for comparing

• Direct comparison

• Indirect comparison (if not possible to compare directly)

Activities Direct Comparison: Length

• Comparing two lengths and seeing a relationship between them • How will you check which pencil case is longer/shorter?

Direct Comparison: Capacity

• Comparing the capacity if two containers • How will you check which holds more/less?

: Weight • Comparing the weight of fruit e.g. an orange and a banana. • Get children to estimate first • Hand weigh to support your estimate • How can the children check which weighs more or less? • How do they know which is heavier/lighter? •What would be an interesting context to justify comparing the weight of fruit?

Length • Comparing the lengths of 2 items which cannot be brought together e.g.comparing the length of two rooms/areas •We can’t bring them side by side! • How could we work it out?

Indirect Comparison: Capacity • Comparing the volume of liquid in 2 different containers • How could we work out which container holds more/less liquid?

Step 1: Number-free Comparison Activities Progress from Comparing to Ordering •Capacity: holds least to holds most • Longest: shortest to longest •Weight: lightest to heaviest, etc.

Step 2: Develop and use non-standard units

Create a need for a ‘non-standard’ unit of measurement •When comparison is not possible/effective

•When a number is required to communicate the measurement more effectively

Non-standard units are everyday units (e.g. blocks, marbles, spoons) which can be used to measure an item. They support children in focusing on the attribute being measured because:

• Using non-standard units is fun.

• Non-standard units support understanding using iteration of units and the use of numbers to describe the measurement that matches the children’s number understandings

• The focus is on children’s rationale for their selection of non-standard unit-what is important in measuring? what worked well? What was difficult? Would they use them next time?

• Non-standard units provide a good rationale for standard units.

The limitations of non-standard units must be uncovered.

A discussion of the need for a standard unit can have more meaning after groups in your class have measured the same objects with their own units and arrived at different answers.

Step 2: Develop and use non-standard units

Provide children opportunities to measure using non-standard units

•What non-standard units could children use for measuring Capacity

Weight

*Area Children should have opportunities to:

•Select the unit that is most appropriate

•Estimate the number of units required to match, balance, fill, cover

•Measure by iterating the unit selected Brainteaser: For which measures is it difficult/impossible to measure with a single unit?

Length •What non-standard units could you use to find the length of the room? The table? Your pen? Your A4 page? •When choosing the non-standard unit what things do you need to consider?

Measure using multiple identical non-standard units:

• place it •mark it • place it •mark it • repeat • count S

Benefits of Creating Instruments: Opportunities to create instruments using the ‘unit’ allows the child to understand how the instrument measures. Note: see the required reading for Week 2 (create instruments using the ‘ladybird’ as the unit of measurement)

Step 3: Develop need for a standard unit

Help children discover the unreliability of the non standard unit. How could you help children to discover the unreliability of the non-standard unit?

•Think back to the measurements using non-standard units for length

Step 3: Develop need for a standard unit

•By highlighting issues with non-standard units e.g. different lengths of keys/different capacities of mugs/different weight blocks, we can make children aware that using non-standard units can cause confusion. •

The issue is with communication –as everyone has different length keys, then the tablecloth could be too long or short. •So, we need a measurement unit where there is less potential for confusion.

• The standard unit assures a basis for communication the world over.

Topics

Measures • Teaching Length • Teaching Area • Teaching Weight • Teaching Capacity & Volume • Teaching Time Shape and Space • Spatial Awareness • Symmetry • 2D Shapes • 3D Shapes • Lines and Angles

Step 4: Introduce the standard unit of measurement

•Advantages of the standard unit:

• Standard • Familiar • Reliable •Widely applicable

• In the Irish education system, we use metric standard units: • length (m) • area (cm2) •weight (kg) • capacity (litre)

Step 4: Introduce the standard unit of measurement

Provide children opportunities to measure using standard units.

Allow children to:

• Select the unit that is most appropriate e.g. metre

• Estimate

•Measure using • a unit e.g. metre strip/string (use a single iteration or as many copies of the unit as needed)

• the appropriate instrument e.g. trundle wheel • Discuss the advantages and disadvantages of both approaches

Step 5: Establish need for smaller and larger units of measurement

How would you establish the need for larger or smaller units of length?

• The desire for more precision creates the need for a smaller unit of measurement e.g. cm/mm, ml, g/mg

• The need to measure longer, heavier etc. creates the need for a larger unit of measurement e.g. km, tonne, hectare etc. What have we learned…

With the person beside you: •Choose one of the following concepts: length, weight, capacity, area • Identify two suitable not standard-units that could be used to measure your chosen concept • Identify the metric units for your chosen concept •Describe two steps of the sequence of instruction for teaching measure for your chosen concep