Place value: What’s in a number?
View Sequence overviewThe position of a digit in a number gives it its unit value.
A digit represents the number of units in a place value position.
A number is the sum of its unit values.
Whole class
What’s in a number? PowerPoint
Each student
Sorting using place value Student sheet printed on A3 paper
Task
Revise: We can sort numbers into different groups using place value. The place of a digit in a number gives it value. The same digit has different values in different positions in a number. We add the place value parts to find the whole number.
Show slide 25 of What’s in a number? PowerPoint. Ask students to work out what numbers might go in the two circles, based on the number in the intersection.
Draw students’ attention to the difference between this task and the Place value sort game played in the previous task—not only must students think of place value rules that apply to the number in the intersection, they will need to think of a place value rule for each of the Venn diagram circles and generate the numbers that belong in each circle.
Students should:
- label each circle with a property.
- be able to explain why the number in the intersection belongs there.
Discuss the clues that are in the number that will help them to decide what place value properties they might use to label each circle.
Pose the task: You are going to work on your own to decide which numbers belong in the circles. Remember to use place value thinking to label each circle.
Students work independently on this task, which may be used as an assessment.
Provide each student with Sorting using place value Student sheet.
The Student sheet includes three different Venn diagram sorting activities. Students should select and fill out at least one Venn diagram sort. They may complete a second and third if they have time.
- What can you tell me about the number in the middle of the circles?
- What do you know about the digits in the number that could help you to label each circle?
- Talk to me about the numbers you have placed in the circles. How can you describe what is the same about these numbers? How are they different?
- What other numbers might fit here?
- How could you explain your sorting to someone who did not do this learning today?
Strategically select work samples from students which demonstrate a range of thinking, including samples that show ‘nearly there’ levels of understanding to prompt critical thinking.
Task variation
Varying the task complexity and requirements allows students to think critically, make connections between the important ideas in the task, deepen their understanding, and apply their learning to solve novel problems. Students have moved throughout this sequence from simple sorting to demonstrating similarities in numbers using sorting tools (such as the Venn diagrams).
In this task we extend students’ understanding of place value concepts and the generalisations they have made to communicate commonalities and differences between groups of numbers. The open-ended nature of this task provides the opportunity for students to work at a level that is challenging but achievable. This task allows students to think critically and creatively when suggesting numbers and how they might fit a predetermined rule.
Students are provided with a choice of Venn diagrams to select which Venn diagram sort they want to complete. This allows students to choose the complexity of the task they want to complete to demonstrate their thinking. This allows the teacher to assess the sophistication of their understanding of using place value properties to sort numbers.
This task may be used as an assessment task, however, ensure that students work independently if you choose to use it in this way.
Varying the task complexity and requirements allows students to think critically, make connections between the important ideas in the task, deepen their understanding, and apply their learning to solve novel problems. Students have moved throughout this sequence from simple sorting to demonstrating similarities in numbers using sorting tools (such as the Venn diagrams).
In this task we extend students’ understanding of place value concepts and the generalisations they have made to communicate commonalities and differences between groups of numbers. The open-ended nature of this task provides the opportunity for students to work at a level that is challenging but achievable. This task allows students to think critically and creatively when suggesting numbers and how they might fit a predetermined rule.
Students are provided with a choice of Venn diagrams to select which Venn diagram sort they want to complete. This allows students to choose the complexity of the task they want to complete to demonstrate their thinking. This allows the teacher to assess the sophistication of their understanding of using place value properties to sort numbers.
This task may be used as an assessment task, however, ensure that students work independently if you choose to use it in this way.
Discuss and share student work samples, focusing the discussion on:
- What place value clues does the number in the overlap give about the numbers chosen to go in each circle?
- What other numbers could you think of that would fit in the overlap?
- What other numbers could belong in the circles and why?
The goal of these questions is to encourage students to justify their understanding of the generalisations they have made.
You may choose to show any of slides 25-28 to generate further discussion about the number in the intersection and what properties numbers would need to have in order to fit in the groups.
Bring the learning together by highlighting the idea that mathematics has a special language to talk about numbers.
Explain: The place of a digit in a number gives its value as one, or ten, or a hundred. The digit tells us how many hundreds, tens or ones there are in the whole number. When a digit is moved to a different place in a number this changes the value of the whole number.
Ask students for examples of numbers with the same digits in a different place in the number. Invite them to explain and justify their thinking.
You may want to highlight the idea that 1 ten is the same as 10 ones, and that 10 tens is the same as 1 hundred. This makes it more efficient for us to count collections.
You may also want to encourage students to represent their ideas using models (tens frames, bundled pop sticks, unifix etc.) of the concrete quantity next to a number.