We can trust that a unit of 1 ten will always contain 10 ones. This idea is central to the structure of two-digit numbers.
Whole class
reSolve Garden PowerPoint
A large collection of seeds (e.g. counters or dried beans) and 10-cell seed punnets (ten-frames) for students to use if they need
Each student
At least one empty ‘seed packet’ (for example: snap lock bags, brown paper bags, or envelopes). Each packet should be labelled with a different number between 25 and 99.
2 copies of Planting more seeds Student sheet
Task
Using the reSolve Garden PowerPoint, continue the story of the reSolve Garden:
Mr Sprout continues to plant his seeds. When he picks up a packet of seeds, he knows exactly how many full seed punnets he will have and how many extra seeds there will be.
Tell the students that they are going to continue to help Mr Sprout today by planting seeds.
Explain that today they will be given a seed packet with a number clearly printed on the front, but there will be no seeds in the packet.
Pose the task: How many full punnets will you have and how many extra seeds will there be? Show your thinking on your student sheet.
Provide each student with:
- an empty seed packet with a number printed on the front
- one copy of Planting more seeds Student sheet
Ask students to record on their student sheet how many punnets and extra seeds they will have when all their seeds are planted, and to show their thinking.
Have seeds and punnets available for students who choose to use them.
- Can you predict how many full punnets you might have and how many extra seeds you might have?
- Asking students to predict gives you a chance to see if they are developing a generalised understanding of the value of digits in a number.
- Do you need to see all the seeds to know how many full punnets and extra seeds there will be when all the seeds are planted?
- If you recognise the value of digits in a number, it is not necessary to see all the seeds.
All seeds represented – Some students may continue to use concrete materials and/or draw all the seeds to determine how many full punnets and extra seeds there will be when their seeds are planted. Prompt these students to consider whether they need to see all the seeds to know how many full punnets there will be.
Not all seeds represented – Do students recognise the connection between the punnets and extra seeds and the tens and ones digits in a two-digit number? Students may trust the fact that there are 10 in a punnet and choose to represent the number of tens as punnet without showing all 10 seeds contained in that punnet. Prompt these students to think about how many seeds they would have if they had another 5 full punnets, or if they had another 10 full punnets.
Key mathematical ideas
Look at how these students have represented how many full punnets and how many extra seeds there will be.
Discuss with colleagues: What do these students know and what have they shown that they can do? Give evidence from the work samples for your statements.
Look at how these students have represented how many full punnets and how many extra seeds there will be.
Discuss with colleagues: What do these students know and what have they shown that they can do? Give evidence from the work samples for your statements.
Show students the three different representations of punnets and seeds in reSolve Garden PowerPoint.
Discuss:
- Which representation is most like yours? Why?
- How are each of these representations similar? How are they different?
- Each representation is similar in that they illustrate punnets of ten seeds and then a final punnet that is not completely full.
- Each representation shows the collection of ten seeds in a different way. The final representation does not illustrate all the seeds. It uses a punnet to represent collections of 10, reinforcing the idea that ten of these is equal to one of those.
- Is it possible to represent the total number of seeds without drawing all the seeds?
- Use the last representation to see how a punnet can be used to represent 10 seeds.
Redistribute the seed packets so that every student has a new packet, and provide students with another copy of Planting more seeds Student sheet. Ask students to once again record on their student sheet how many punnets and extra seeds they will have when all their seeds are planted, and to show their thinking.
Connect phase
The focus of this Connect discussion is the key idea that a unit of 1 ten will always contain 10 ones, even if we cannot see the ones. This key mathematical idea underpins the place value structure of two-digit numbers.
We have carefully chosen three different representations to present to students. In this instance, the difference between the representations highlights the fact that we do not need to see the individual ones to trust that there is always 10 ones in a unit of 1 ten.
The focus of this Connect discussion is the key idea that a unit of 1 ten will always contain 10 ones, even if we cannot see the ones. This key mathematical idea underpins the place value structure of two-digit numbers.
We have carefully chosen three different representations to present to students. In this instance, the difference between the representations highlights the fact that we do not need to see the individual ones to trust that there is always 10 ones in a unit of 1 ten.
Whole class discussion
Watch this video of a whole class discussion from this Connect phase.
Watch this video of a whole class discussion from this Connect phase.