# Rice, Rice, Rice

### Task 88 ... Years 4 - 8

#### Summary

Set in a story shell, the challenge is to estimate grains of rice without actually counting their number. This is equivalent to the problems faced by many people in practical employment - for example a bricklayer estimating the number of bricks to order to clad a house. Such problems are often guided by 'rules of thumb'. In this task students are experimenting with possibilities so there is no right or wrong answer. However, asking the mathematician's question:
• Can I check this another way?
will result in discussion about the accuracy of the two methods used.

#### Materials

• Container of rice and some spare rice
• Spoon and small cups

#### Content

• estimating number
• counting
• basic arithmetic operations
• volume and mass measurement
• informal experience with proportion
• problem solving

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

There are no right or wrong answers in this task. The focus is on the range of methods that could be used and the calculations associated with them. Students could:

• carefully count out a small number of grains, say 200, weigh this amount and multiply up to find an estimate for the number of grains in 500 grams.
• carefully measure a smaller mass, say 100 grams, count the grains and multiply up to find an estimate for the number of grains in 500 grams.
• take a digital photo of the top of the container, as suggested in the photo above and estimate the grains in one layer. They could then estimate the number of layers - again a digital photo might be useful - and calculate the number of grains in 500 grams.
• ...
What happens if you are allowed to open the container. Would you be able to calculate the number of grains a different way? How about pouring grains to make a closely packed single layer inside a 5cm square, counting those grains, then checking how much mass has been removed from the container.

Extensions
Rule: One grain of rice represents one person.

• Calculate the mass of rice you would need to display the population of Australia.
• Do the same for the population of Tibet.
• Work out the population density for each of these countries, ie: the number of people on average per square kilometre.
• Count out the correct number of grains to show these population densities and make a display.
Prepare a 'Guess the Number of Lollies in the Jar' competition with a sealed jar. Discuss methods for estimating the number and give every student a chance to make an estimate. Agree that if there is more than one correct answer the lollies will be shared. Raise money for social service by requiring the students to pay to register their guess.

#### Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

Prepare a sealed container with 500 grams or 1 kilogram of rice. You will also need a smaller amount of rice per group and a variety of measuring equipment. A vacuum cleaner might be a useful tool at the end of the lesson. Set the challenge for each group to devise two ways to estimate the number of grains of rice in your container and allow them time to do so. Record and discuss the variations across the class. Come to an agreement on the most likely result.

Develop the extensions above. Also set related challenges such as:

• How many bricks did it take to build our school?
• Find out how a builder calculates the number of bricks to order when building a house.

At this stage Rice, Rice, Rice does not have a matching lesson on Maths300.

#### Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

Rice, Rice, Rice is not in any MWA kit. However it can be used to enrich the Chance & Measurement kit at Years 5/6.