### Place Value: reSolve Garden

View Sequence overview10 ones can be grouped together to form a unit of 1 ten.

### Whole class

**reSolve Garden PowerPoint**

### Each group

A large quantity of items to represent ‘seeds’ (for example: counters or dried beans)

### Each student

At least one ‘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.

**Making tens Student sheet**

### Task

Using the **reSolve Garden PowerPoint**, continue the story of the reSolve Garden:

Mr Sprout the gardener is putting his seeds into packets. Each packet has a number of seeds clearly written on the front. He needs to make sure that he puts exactly the right number of seeds in each packet.

Mr Sprout decides to make groups of ten to help him count. He makes a smaller group with the seeds that are left over at the end.

Provide each student with loose seeds and a seed packet. Explain that the number written on each packet represents the number of seeds that need to be placed into that packet.

**Pose the task:** *Count your seeds like Mr Sprout to make sure you have exactly the right number in your packet.*

#### Differentiation

Differentiate this task by carefully choosing the number of seeds that different students are asked to count. Some students may count smaller collections and others may count larger collections.

Differentiating 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 number of seeds that different students are asked to count. Some students may count smaller collections and others may count larger collections.

Differentiating 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.

Allow students time to count and organise their seeds using groups of ten like Mr Sprout.

Once students have organised their seeds, ask them to use **Making tens Student sheet** to make a poster showing how they organised and counted their seeds. Explain that the poster should make it clear how they counted and how many seeds are in their collection.

*How did you group your count in the previous task*(Task 2)*? How was your previous strategy similar to counting in tens like Mr Sprout? How was your previous strategy different? Which do you prefer and why?*- It is likely that both strategies involve equal-sized groups. The size of the group is what differs.

**Do students create equal groups of ten?**

**Ask students: ***Can you explain to me how your counting is like Mr Sprout's?*

**Not creating equal groups of ten:**Prompt students to think about how they might arrange the seeds in each group, so that they can see at a glance that each group contains ten.**Creating equal groups of ten:**Prompt students to think about how they might arrange the seeds in each group so they see at a glance that there are ten in each group. Also, notice how the students are counting. Do they skip count the total in tens, or do they still determine the total by counting in ones (not utilising the group structure)? Prompt students‘ inquiry by asking them to think about how the group structure can support efficient counting.**Organised groups:**Organising the groups of ten makes it easy to see the number of seeds in each group. For example, students might use subitisable patterns to arrange their seeds. As students count the total number of seeds to go into the packet, they may end up with some seeds that do not form a complete group. Prompt students' inquiry by asking them to think about how they might deal with these seeds.

**How do the students use the group of ten to count the total number of seeds?**

**Ask students: ***Do you have the right number of seeds to go into your seed packet? How do you know that you do?*

**Make tens but count the total in 1s, 2s or 5s:**Prompt students' thinking about how they might use the ten structure to facilitate their counting.**Count in tens:**Students trust the group structure and use the 10 structure to facilitate their counting.

#### Key mathematical idea

Look at how these students have represented the way they have used equal-sized groups of 10.

**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.

#### Making posters

We suggest printing the **Making tens Student sheet** on A3 paper and asking students to make a poster of their work. Using a poster-sized recording will be useful for the class gallery walk in the Connect phase of this task. Keep these posters on display for a period of time so students can come back to them and continue to reflect on their learning.

We suggest printing the **Making tens Student sheet** on A3 paper and asking students to make a poster of their work. Using a poster-sized recording will be useful for the class gallery walk in the Connect phase of this task. Keep these posters on display for a period of time so students can come back to them and continue to reflect on their learning.

Ask students to display their student sheet next to their seeds.

Review the task that was posed (*Count your seeds like Mr Sprout*) and ask students to think about what they expect to see as they complete the gallery walk. Ask students to consider the following questions as they look at others’ work:

*What do you notice that is the same?**What do you notice that is different?*

Conduct the class gallery walk.

At the end of the class gallery walk, allow students time to read and reflect on any post-it notes left by other students.

#### Looking at the work of others

We have used a gallery walk at this point in the task so students can critically view and review the work of others in the class. We want them to notice same-ness and difference as they look at and make sense of others’ work.

*Same-ness* is seen in every student using groups of ten and having some left-over ones. *Difference* is seen in the number of tens and ones in each count. Noticing that all numbers can be represented using tens and ones supports the generalisation that 10 ones can be grouped together to form a unit of 1 ten, and that this idea underpins the structure of 2-digit numbers.

We have used a gallery walk at this point in the task so students can critically view and review the work of others in the class. We want them to notice same-ness and difference as they look at and make sense of others’ work.

*Same-ness* is seen in every student using groups of ten and having some left-over ones. *Difference* is seen in the number of tens and ones in each count. Noticing that all numbers can be represented using tens and ones supports the generalisation that 10 ones can be grouped together to form a unit of 1 ten, and that this idea underpins the structure of 2-digit numbers.

#### Gallery walk

In a gallery walk, students display their mathematical work as posters on the wall or as physical displays on tables or the floor. Everyone then moves around the classroom like they are in an art gallery, in silence or whispering with a partner. Tell students to take their time to look at and make sense of other students’ solutions.

As students move around the classroom, they can stick post-it notes next to other students’ work to give feedback or to ask questions about the mathematics they see. Students can use symbols instead of words. For example, students can leave a post-it note with a tick or smiley face along with their name or initials to indicate they really like a strategy, or they might leave a question mark with their name or initials to communicate they have a question to ask. Make sure you allow time at the end of the gallery walk for students to look at their post-it notes and to ask any questions they may have. It is also good to provide students with the time to add to or adjust their work based on what they have seen.

In a gallery walk, students display their mathematical work as posters on the wall or as physical displays on tables or the floor. Everyone then moves around the classroom like they are in an art gallery, in silence or whispering with a partner. Tell students to take their time to look at and make sense of other students’ solutions.

As students move around the classroom, they can stick post-it notes next to other students’ work to give feedback or to ask questions about the mathematics they see. Students can use symbols instead of words. For example, students can leave a post-it note with a tick or smiley face along with their name or initials to indicate they really like a strategy, or they might leave a question mark with their name or initials to communicate they have a question to ask. Make sure you allow time at the end of the gallery walk for students to look at their post-it notes and to ask any questions they may have. It is also good to provide students with the time to add to or adjust their work based on what they have seen.

After the gallery walk, come together for a whole class discussion.

**Discuss:**

*What were some of your noticings during the gallery walk?*- Students may comment on how some collections arranged their groups of ten to make counting easier, or the different ways of recording that were used.
- Students may notice the place value pattern that occurs when grouping in tens. Allow students to share this noticing, but don’t focus on it as it will be explored in the next task
*.*

*What did you notice that was the same?*- Everyone made groups of ten seeds and had some left-over seeds.

*What did you notice that was different?*- Everyone had a different number of tens and left-over ones, because they all had to count out a different number of seeds.

#### Connect Phase

Focus this Connect phase on the idea that 10 ones can be grouped to form a unit of 1 ten. The number of units of ten that can be made will differ in different students’ collections of seeds, but the size of the units that they make will always be “10”.

#### Similarity and difference

Asking “what is the same and what is different?” is a powerful prompt to guide students’ inquiry. In mathematics, when we find *same-ness *we can make generalisations. *Difference* shows us how generalisations can be applied to specific examples.

In this task, we see same-ness in everyone using groups of ten and having some left-over ones. Difference is seen in the number of tens and left-over ones in each count. This is a powerful idea that will be built on in the following tasks.

Asking “what is the same and what is different?” is a powerful prompt to guide students’ inquiry. In mathematics, when we find *same-ness *we can make generalisations. *Difference* shows us how generalisations can be applied to specific examples.

In this task, we see same-ness in everyone using groups of ten and having some left-over ones. Difference is seen in the number of tens and left-over ones in each count. This is a powerful idea that will be built on in the following tasks.

Discuss with the students how using tens made it easier to see how many seeds there were. Ask students to reflect on the counting strategies that they used in the first task, and why ten may be a more helpful unit for counting.

**Explain:** *When we group 10 ones, we make a unit of 1 ten. Counting in tens is an efficient way to count a large collection.*