10 of these is equal to one of those:
- 10 ones are equal to a unit of 1 ten
- 10 tens are equal to a unit of 1 hundred
Whole class
Lolly Shop PowerPoint
Each group
A large quantity of Unifix or interlocking cubes (ideally 2cm). Each group of 2-3 students needs at least 120 cubes.
Each student
Rolls and boxes Student sheet
Task
Use Lolly Shop PowerPoint to continue the story of Ms Fizz’s Lolly Shop:
Ms Fizz decides to use units of 10 to organise the lollies in her shop. She creates rolls of 10 lollies. She then puts 10 rolls of 10 lollies into a box.
Ms Fizz has a special record chart. When she has finished packing all the lollies, she records on her chart the number of full boxes, the number of extra rolls not in boxes, and then the number of loose lollies that are not in rolls. She then records the total number of lollies in her collection.
Pose the task: Pack your lollies into rolls and boxes to go into Ms Fizz’s Lolly Shop. When you finish packing your lollies, record the number of boxes, rolls, and loose lollies you have, and the total number of lollies.
Differentiation
Differentiate this task by carefully choosing the size of the collections that groups of students are asked to count. Some groups may count smaller collections and other groups may count larger collections. Differentiating the task in this way gives all students the opportunity to engage in the main mathematical activity of the task and contribute to the collective learning of the class.
Differentiate this task by carefully choosing the size of the collections that groups of students are asked to count. Some groups may count smaller collections and other groups may count larger collections. Differentiating the task in this way gives all students the opportunity to engage in the main mathematical activity of the task and contribute to the collective learning of the class.
Provide groups of 2-3 students with a large quantity of Unifix or interlocking cubes (at least 120 cubes). Ask students to create rolls of 10 lollies by stacking 10 Unifix cubes and then create a box by grouping 10 stacks of cubes.
Provide students with Rolls and boxes Student sheet, which shows Ms Fizz’s Record Chart. Ask students to create a diagram of their lollies in rolls and boxes and to record their results on their student sheet.
- How did you organise your count in the previous task (Task 1)? How was your previous strategy similar to organising the lollies like Ms Fizz? How was your previous strategy different? Which do you prefer and why?
- It is likely that both strategies involved equal-sized groups. The size of the group may have differed.
Ask students: How many lollies do you have in your collection? How do you know?
Take note of how the students determine the total in their collection. Do they:
- Make tens but count in ones - If students count in ones, ask them to consider how the rolls and boxes might help them determine the total in the collection.
- Use the groups of tens and hundreds to count - Students trust the group structure and use it to facilitate efficient counting. You might ask students how many lollies there would be if another 5 rolls were added to their collection.
- Use the groups of tens and hundreds to name the number - Students recognise the place value pattern that emerges when making tens and hundreds. This is investigated in the next phase of the task. Again, you might ask students how many lollies there would be if another 5 rolls were added to their collection.
Representation
Base 10 blocks are commonly used in primary classrooms to model the base 10 structure of our number system. But students won’t necessarily just ‘see’ the mathematics in the models. It is helpful for them to construct the models themselves.
In the reSolve Lolly Shop, students build base 10 blocks for themselves as they make rolls and boxes of lollies; 10 lollies go into a roll and 10 rolls make a box which forms the hundreds, tens, and ones base 10 blocks.
Create a class version of Ms Fizz's Record Chart (you can use the slide provided in the Lolly Shop PowerPoint). Record data on how many boxes, rolls and loose lollies students had in their collection, and the total number of lollies in their collection. Don’t correct errors at this stage.
| Total number of lollies | Boxes | Rolls | Loose lollies |
| 178 | 1 | 7 | 8 |
| 235 | 2 | 3 | 5 |
| 308 | 3 | 0 | 8 |
| 146 | 1 | 4 | 6 |
Discuss: What do you notice about the data that we have collected for Ms Fizz? Students may notice that the number of boxes, rolls and loose lollies are represented by each digit in the total number of lollies.
Pose the question: Will this pattern always occur?
Invite students to explore these patterns using different collections of cubes. This further exploration time is also a chance to revisit any incorrect counts. Students should continue to record their results on their student sheet.
Gather students together again and add the new data to the class chart. Look at how the pattern continues, regardless of the numbers that are used.
Discuss that three-digit numbers are made up of hundreds, tens, and ones, and that the value of a digit is determined by its place in a number.
Connect phase
Focus this Connect phase on the fact that 10 ones are equal to a unit of 1 ten and that 10 tens are equal to a unit of 1 hundred. These powerful ideas help us understand structure of two- and three-digit numbers.
Students may quickly notice the tens and ones pattern that is formed in Ms Fizz’s Record Chart, but this noticing does not mean they fully understand that the place value pattern that is present. The additional explore time in this Connect phase provides the opportunity to explore and make sense of this pattern.
Focus this Connect phase on the fact that 10 ones are equal to a unit of 1 ten and that 10 tens are equal to a unit of 1 hundred. These powerful ideas help us understand structure of two- and three-digit numbers.
Students may quickly notice the tens and ones pattern that is formed in Ms Fizz’s Record Chart, but this noticing does not mean they fully understand that the place value pattern that is present. The additional explore time in this Connect phase provides the opportunity to explore and make sense of this pattern.
Ms Fizz's Record Chart
Ms Fizz’s Record Chart highlights the place value pattern of hundreds, tens and ones. Rather than simply observing the pattern, students are given time to explore and work out if the pattern will always occur. Exploring the pattern is an important step in forming generalisations.
As you collect data, don’t correct students’ mistakes. These mistakes provide a valuable context to explore whether the place value pattern is always present.
Ms Fizz’s Record Chart highlights the place value pattern of hundreds, tens and ones. Rather than simply observing the pattern, students are given time to explore and work out if the pattern will always occur. Exploring the pattern is an important step in forming generalisations.
As you collect data, don’t correct students’ mistakes. These mistakes provide a valuable context to explore whether the place value pattern is always present.
Class dataset
All students contribute their data to the class version of Ms Fizz’s Record Chart. A large collection of data is needed to see and test the patterns that emerge. This communicates to the class that all students’ contributions are important and that all contribute to the shared learning of the class.
Errors that may be present in some data become a powerful opportunity to explore the pattern to determine if it always occurs.
All students contribute their data to the class version of Ms Fizz’s Record Chart. A large collection of data is needed to see and test the patterns that emerge. This communicates to the class that all students’ contributions are important and that all contribute to the shared learning of the class.
Errors that may be present in some data become a powerful opportunity to explore the pattern to determine if it always occurs.