# Great grams

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Purpose

This unit comprises 4 stations which develop students' concept of, and "feel for", a gram. The stations may be taken as whole class activities or they may be set up as activities that groups of students use throughout the week.

Achievement Objectives
GM2-1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.
Specific Learning Outcomes
• Recognise a 100 gram mass.
• Record measurements in kg and g using whole numbers.
• Accurately measure specific amounts of materials.
Description of Mathematics

When students can measure objects effectively using non-standard units, they are ready to move to the use of standard units. The motivation for moving to this stage often arises from experiences in which students have used different non-standard units for the same mass, and have subsequently realised that the use of consistent units allows for easier, and more accurate, communication of mass measures.

Students’ measurement experiences must enable them to:

• develop an understanding of the size of the standard unit
• estimate and measure using the unit

It is sensible to begin with the kilogram as the gram is too small to "feel". An appreciation for the feel of a kilogram needs to be built up with lots of examples of 1 kilogram mass. For example, 1 kilogram bags of stones, polystyrene, sand, butter and nails. Students should compare a standard 1 kilogram mass with other objects, first by holding them, and then by using a balance scale.

The usual sequence is then to divide the kilogram into smaller parts, for example, ½ a kilogram (500 grams), ¼ of a kilogram (250 grams) and 1/10 of a kilogram (100 grams). If appropriate to the knowledge of your students, you might record these numbers and a relevant expression (e.g. 500 is 1/2 of 1000) alongside the measurement of different items.

Next, students should have opportunities to explore the size of the gram. This can be done by investigating the mass of very light objects, with 10g used as a starting point.

Metric measurements, and their position as a decimal system, lend themselves well to opportunities for revisiting and reinforcing ideas related to place value. E.g. If this object has a mass of 100g how many will it take to make 1000g or 1 kg?

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

• placing items in individual plastic bags so it is easier for children to compare the mass of one object with another
• varying the use of scales when measuring different masses. For example, different types of kitchen scales, luggage scales, balance scales. You might discuss which type is easiest/most efficient to use
• asking predictive questions to encourage students to think beyond what is visible (e.g. which items do you think will weigh less?)
• providing opportunities for students to work in a range of flexible groupings to encourage peer learning, scaffolding, and extension
• providing opportunities for students, who are ready for extension, to write gram and kilogram measurements as decimals
• modelling the measurement of different items, and the comparing and recording of their mass
• substituting packages for blocks of different masses and have children sort them from lightest to heaviest.

The context for this unit can be adapted to suit the interests and experiences of your students. For example:

• Students might make kono (small flax food baskets) and kete (carrying bag) and use these to estimate the mass of bags of items, in reference to a 100 g personal benchmark.
• Students can estimate and compare the weight of a pumice (size of a child’s palm) or other objects that are similar in length, height, width or shape to their hands, feet, heads, arms etc.

Te reo Māori kupu such as ine (measure), grams, kilogram, and tatau (count) could be introduced in this unit and used throughout other mathematical learning.

You could also encourage students, who speak a language other than English at home, to share the words related to measurement that they use at home.

Required Resource Materials
• Station 1: Ingredients for Chocolate Bubble Cakes, Kitchen scales with at least 10 gram gradations, paper patty cases.
• Station 2: 10 g, kitchen scales with 10g gradations, light objects eg feathers, calculators.
• Station 3: 10 g and 50 g weights, paperclips, cm cubes, drawing pins.
• Station 4: 1 kg, 500 g, and 100 g bags of sand, rocks, counters etc., Ziplock bags, classroom objects such as counters, small blocks etc.
Activity

#### Station 1: Chocolate Bubble Cakes

In this station we use the scales to measure and make Chocolate Bubble Cakes. We suggest that you carry out this station as a whole class (as it involves cooking over heat and the use of edible ingredients). Alternatively, this could be done in small groups if you have a lot of available adult or very responsible student helpers available. Print off the instructions below for each group. If you feel the food context is not appropriate for your classroom, you could make a different, non-food item (e.g. slime or play dough).

Ingredients for chocolate bubble cake

250 grams vegetable shortening
100 grams icing sugar
25 grams cocoa
100 grams rice bubbles
100 grams coconut

Method for making chocolate bubble cake

1. Put vegetable shortening in a saucepan.
2. Cook over a low heat until melted.
3. Sift icing sugar and cocoa together.
4. Add sifted ingredients, rice bubbles and coconut to saucepan, stirring until well combined.
5. Spoon mixture evenly into paper patty cases.
6. Chill until firm.

Whilst the cakes chill, discuss the process with the students:

• How many cakes did you make?
• How heavy do you think each cake is? What about all of the cakes together?
• Explore and develop a "feel" for 1 kilogram and 500 grams by passing around the 1 kg and 500 g bags. Have students compare, in pairs, and as a class, which items are heavier and which are lighter. Help them to discover that two of the 500 g items weigh the same as the 1 kg item by comparing and using scales.
• Mass is a word we use to describe how heavy something is. Show the students the bag of the leftover ingredients and use a "think aloud" to estimate its mass (e.g. I can feel that this bag is heavy, I think its mass might be about 500g).
• Ask your students to pass around the bag of ingredients and write down an estimate of its mass (e.g. on sticky notes, small whiteboards). If students' estimations are way off, spend some time developing personal benchmarks of the comparative "heaviness" and mass of some classroom objects.
• Model how to use and read the measuring scales, and how to record the mass of the classroom objects. Have students repeat this process with a variety of classroom objects. You might have them record their estimations and measurements in a table.

Once the cakes have chilled, have students estimate the mass of one cake. Support them to weigh it. As a class, discuss the following questions:

• Is there a find a way to find the total mass of all of the cakes?
• If we had 20 cakes, what would the approximate mass of coconut be in each cake?
If we wanted to make 100 patty cakes how much cocoa would we need?

#### Station 2: As Light as a Feather

In this station we use kitchen scales and 10 gram weights to figure out the mass of very light objects.

Ask the students to find objects in the class they think will weigh about 10 grams and compare these to the weights. Then they need to weigh the object on the kitchen scales and record the working done to get the answer. Students ready for extension could be asked to find, measure, and record different combinations of classroom objects that have a mass of 10g, 20g, 30g etc. (i.e. different multiples of 10).

#### Station 3: Light Challenges

In this station we use the "feel" of 10 grams to make some guesses about light objects. We are not allowed to use any measuring scales to help with our guesses.

Present students with a variety of light objects in different, closed containers (e.g. paper clips, counters, drawing pins, cm cubes). Make memo pad paper and pencils available to students. Pass around the objects, or arrange them in the middle of a class circle. Have students feel the objects, and write their name and an estimate of the mass of each object on a piece of paper. This task could be repeated throughout the week with different objects. At the end of the unit, have students reveal their guesses to a partner or group, and then reveal, as the teacher, the mass of each item.

Students ready for extension could investigate the following questions:

• How many paper clips in 10 grams?
• How many drawing pins in 20 grams?
• How many cm cubes in 50 grams?

#### Station 4: Gram Challenges

Present students with the 100 g, 500 g and 1 kg items. Tell them we would need 10 of an item weighing 10 grams to make the same mass as the 100 g item, and 100 of them to make the 1 kg item. You might explore this using diagrams, arrays, and/or expressions (e.g. 1 eraser = 10 g. 100 erasers = 1000 g or 1 kg).

Challenge students to find objects in the classroom that they estimate, when combined, have a mass of 100 g, 500 g, or 1 kg. Students should put them them into a Ziplock bag, and swap their bag with a partner. Together, pairs of students should weigh their bags and record the findings.