Grade 4: "How Much Water?"
(Adapted from: Marian Small, "Good Questions" / NRICH Math / #scdsbmath)This lesson may span over the course of several days.
Embedded Files
This lesson may span over the course of several days.
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Content
Content
Big Idea: Compare, estimate and determine measurements in various contexts.
Big Idea: Compare, estimate and determine measurements in various contexts.
Expectations:
Expectations:
E2.1 explain the relationships between grams and kilograms as metric units of mass, and between litres and millilitres as metric units of capacity, and use benchmarks for these units to estimate mass and capacity
E2.2 use metric prefixes to describe the relative size of different metric units, and choose appropriate units and tools to measure length, mass, and capacity
C.4 apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations
Learning Goals
Learning Goals
We want students to...
We want students to...
Compare and describe relationships between litres and millilitres as metric units of capacity
Problem solve using prior knowledge of fractional language
Apply the process of mathematical modelling to explore the idea of water consumption in their school
Learn to communicate effectively with each other in order to better understand mathematical ideas and concepts
Success Criteria
Success Criteria
I can make connections between the math we are doing and other math concepts, the real world, and other subjects.
I can express my thinking
I listen to the ideas of others
I use my ideas and the ideas of others to help solve challenging problems
I can explore relationships between litres and millilitres
Materials
Materials
Knowledgehook Diagnostic Link
Cylinders image to project on Smartboard or Zoom screen share
Oh Harry Resource Sheet
Jamboard link for Minds On
Mathematical Modelling Student Guide
Mathematical Modelling Rubric
Vocabulary
Vocabulary
Litre (L)
Millilitre (mL)
Measurement
Cylinders
Thousand
Three-quarters
Half
teacher background
teacher background
E2.1:
Millilitres and litres are standard metric units of capacity. Grams and kilograms are metric units of mass:
1 kilogram (kg) is equivalent to 1000 grams (g)
1 litre (L) is equivalent to 1000 millilitres (mL)
1 mL of water has a mass of 1 g
1 mL of liquid occupies the space of a 1 cm cube
Although standard and non-standard units are equally accurate for measuring (provided the measurement itself is carried out accurately), standard units allow people to communicate distances and lengths in ways that are consistently understood.
E2.2:
The metric system parallels the base ten number system. One system can reinforce and help with visualizing the other system.
The same set of metric prefixes is used for all attributes (except time) and describes the relationship between the units. For any given unit, the next largest unit is 10 times its size, and the next smallest unit is one-tenth its size.
Conversions within the metric system rely on understanding the relative size of the metric units and the multiplicative relationships in the place-value system.
Pedagogy
Pedagogy
Minds On
Minds On
(From: Marian Small Good Questions)
Action!
Action!
PART 1: Pose the following problem for the students:
PART 1: Pose the following problem for the students:
(From: NRICH Maths- https://nrich.maths.org/5979)
A group of eight children in Class 6 were measuring water using measuring cylinders. They coloured the water to make reading the scales easier.
They lined up the cylinders in two neat rows, each labelled with a child's name and the amount they had measured out.
Then Harry opened the window and the wind blew most of the labels onto the floor! "Oh! Harry!" they all wailed. Can you re-label the cylinders for them?
Ahmed had measured out just a thousand millilitres and Belinda twice as much as Ahmed.
Grace had measured out three-quarters of the amount that Belinda had done and Freddie had half the amount that Ahmed had measured out.
Which were their cylinders?
Callum had coloured his water blue. How much did he measure out?
Ellie had coloured her water pink and Dan coloured his orange. How much did they measure out?
Harry accidentally stretched his hand out and he knocked over his red liquid. "Oh! Harry!" they all wailed again. How much was left in Harry's cylinder after the accident?
Student Resource Sheet: https://nrich.maths.org/content/id/5979/Oh%20Harry%20resource.pdf
Early Finishers can explore:
Consolidation Questions:
What understanding about millilitres and litres did you need to help you make decisions?
What questions did you have about the problem?
What assumptions did you need to make about the situation?
What math did you use?
Part 2: Mathematical Modelling
Part 2: Mathematical Modelling
Focus Question: How much water does our school use in a year?
Mathematical modelling is not simply using a graph, chart, equation or physical model to represent a concept, but rather the process of engaging in a multistep, iterative process in which students use mathematics to make sense of a real-world context. It's a creative process, involving making assumptions and decisions, in order to understand something new and relevant and make informed choices based on that learning.
- Starting from a real-life situation: How much water does our school use in a year?
What real-life questions and wonderings are meaningful to your students, in your context? How might students’ cultural contexts / interests / community help frame the problem? How can math help us solve this problem?
Does the problem allow for several different possible solutions and pathways?
Consider how this question might be used as a student learning opportunity to engage in mathematical modelling?
What might you be hearing, introducing, prompting as the students engage in this discussion? What teacher moves will support the process of mathematical modelling? Allow students to begin brainstorming.
Teacher moves:
Anticipate questions ahead of time.
Be prepared to be flexible based on student responses.
Ensure students are provided with enough time to come up with ideas and think time / discussion time.
Listen for opportunities to mathematize what they are hearing.
Listen for connections across the stands.
- Analyze the situation: Based on the brainstorming, students will start to think about assumptions and variables and more questions will bubble up, thus illustrating how this process is cyclical.
What might this component sound like in the classroom?
Introduce the Mathematical Modelling Student Guide for students to record their thinking along the way.
- Begin to create a mathematical model: Have students identify and use possible representations, tools, technologies or strategies to help create a model to determine and show how much water the school uses in a year.
Consolidation Of Learning
Consolidation Of Learning
4. Analyze and assess their models: Pose questions to the students to analyze their model.
4. Analyze and assess their models: Pose questions to the students to analyze their model.
Teacher moves:
How does classroom discourse promote communicating, reasoning and proving, reflecting and connecting?
What different points of view might I consider? Are all voices heard? Does the solution make sense?
How can the assumptions made be revised according to what was learned in the first solution and translate them into a new or modified mathematical problem that can be solved?
Independent Task / Assessment Opportunities
Independent Task / Assessment Opportunities
Technology
Technology
Knowledgehook
Knowledgehook
Gizmos
Gizmos
Jamboard (Mind's On)
Jamboard (Mind's On)
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