Place Value: reSolve Garden
View Sequence overview10 ones can be grouped to form a unit of 1 ten. This idea is central to the structure of two-digit numbers.
Whole class
reSolve Garden PowerPoint
Each group
At least 10 10-cell seed punnets and/or ten frames to represent seed punnets
Each student
Filled ‘seed packets’ from Task 2. Students should use a different seed packet to the one they filled in Task 2.
Planting seeds Student sheet
Task
Using the reSolve Garden PowerPoint, continue the story of the reSolve Garden:
Mr Sprout is planting his seeds. He plants them into seed punnets that look like this.
Show students a 10-cell seed punnet, or the picture of the punnet in the PowerPoint. Note the 10 cells for planting 10 individual seeds.
Mr Sprout has a special record chart. Before he starts planting, Mr Sprout records his total number of seeds. Then Mr Sprout plants his seeds by putting one seed into each cell of the punnet. When every cell has a seed in it, he moves on to the next punnet. The last punnet might not get completely filled.
When he finishes planting all the seeds, he writes on his record chart the number of full punnets and the number of extra seeds in the last punnet.
Pose the task: Help Mr Sprout by planting your seeds. Make sure you keep an accurate record for Mr Sprout.
Provide groups of students with at least 10 seed punnets, or ten-frames to model the punnets. Provide each student in each group with a seed packet. As they will be creating groups of ten again, it is preferable that they have a different numbered packet to the previous task.
Provide students with Planting seeds Student sheet, which shows Mr Sprout's Record Chart. Invite students to take turns planting their seeds into the punnets and working out how many full punnets and extra seeds they have. Each student in the group should record the results from all group members on their student sheet.
- How is this task similar to the previous task? How is it different to the previous task?
- Both tasks involve making equal-sized groups of ten. However, in this task, the groups of ten are organised using a ten-frame structure.
Representations
The reSolve Garden sequence uses different representations to build students’ understanding that 10 ones are equal to 1 ten.
Students start by arranging a collection so that it is easy to count. They choose how they group, such as using 2s or 5s. As they arrange their collections students recognise the power of using groups.
Grouping in 10s is introduced to students through Mr Sprout the Gardener. Students create groups of ten in any way that they choose.
As students plant their seeds, a structure for ten is introduced, and the ten-frame emerges out of their mathematical activity. The ten-frame helps students see the place value structure of two-digit numbers.
Multiple representations have been used up to this point in the sequence. Understanding is built as students make connections between these different representations. Watch this video to learn more.
Create a class version of Mr Sprout's Record Chart (one is provided in reSolve Garden PowerPoint). Record students’ results on the chart. 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.
Mr Sprout’s Record Chart
| Total number of seeds | Full punnets | Extra seeds |
| 26 | 2 | 6 |
| 72 | 7 | 2 |
| 64 | 6 | 4 |
| 51 | 5 | 1 |
| 19 | 1 | 9 |
Discuss: What do you notice about the data that we have collected for Mr Sprout? Students will likely notice that the pattern of tens and ones represents the digits in the total number of seeds.
Pose the question: Will this pattern always occur?
Redistribute the seed packets amongst the groups so that each student and group has new seed packets. Invite students to explore the pattern and see if it continues. Students should continue to record their results on their student sheet.
Exploring patterns
The powerful mathematical idea that “10 of these is 1 of those” is highlighted in the tens and ones pattern evident in Mr Sprout’s Record Chart. The fact that 10 ones can be grouped to form a unit of 1 ten helps us to understand the structure of two-digit numbers.
Students may quickly notice the patterns in the chart, but noticing does not mean they fully understand that this pattern is based on the key idea that 10 ones are equal to 1 ten. The additional time to explore in this Connect phase is critical. It provides students with the opportunity to explore and make sense of this pattern with different numbers. Exploring the pattern is an important step in forming generalisations.
The powerful mathematical idea that “10 of these is 1 of those” is highlighted in the tens and ones pattern evident in Mr Sprout’s Record Chart. The fact that 10 ones can be grouped to form a unit of 1 ten helps us to understand the structure of two-digit numbers.
Students may quickly notice the patterns in the chart, but noticing does not mean they fully understand that this pattern is based on the key idea that 10 ones are equal to 1 ten. The additional time to explore in this Connect phase is critical. It provides students with the opportunity to explore and make sense of this pattern with different numbers. Exploring the pattern is an important step in forming generalisations.
After more results have been collected, gather students together again and add the data to the class version of Mr Sprout’s Record Chart. Look at how the pattern continues regardless of the numbers that are used.
Explain: Two-digit numbers are made up of tens and ones. The first digit in a two-digit number represents the total number of tens and the second digit represents the number of ones.