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https://learn.makemathmoments.com/task/take-a-chance/#

Number - Fractions, Decimals and Percentages

Equivalence (including Fractions, Decimals and Percentages)

• Showing the graph;

• asking students to guess what it represents

• slowly revealing more information to make it possible for the students to guess.

Could be extended to ask students to find their own data set and create their own slow reveal presentation.

Prompt:

“How many marshmallows are in the image? How do you know?”

Low Floor - Entry Points for All Learners:

1. Notice & Wonder:

• “What do you notice about the arrangement of the marshmallows?”

• “What do you wonder?”

2. Estimating:

• “Can you make a quick guess without counting?”

• “Is there a way to estimate a reasonable number?”

Middle Phase - Encouraging Deeper Thinking:

3. Finding Structure:

• “Can you see a pattern in how they are arranged?”

• “Could you group them to make counting easier?”

4. Different Strategies:

• “What are different ways to count them?”

• “Could we count in rows, columns, or groups?”

High Ceiling - Extending the Thinking:

5. Generalizing the Pattern:

• “If we added another row, how many would there be?”

• “If we doubled the number, what strategy would help count them efficiently?”

6. Applying to a New Context:

• “Imagine stacking them in layers—how would you count a 3D arrangement?”

• “What if we had a different shape instead of rows? Would your strategy still work?”

Why This Works as Low Floor, High Ceiling:

• Everyone can start (even by estimating or noticing).

• Different strategies emerge as students explore patterns.

• More advanced students can generalize and extend to bigger ideas like multiplication, area models, and combinatorial thinking.

Would you like any refinements based on a specific grade level?

1. Find a set of 3 numbers such that the mean is 7 and the median is 7.

2. Find a different set of 3 numbers such that the mean is 7 and the median is 7.

3. Find a different set of 3 numbers such that the mean is 7 and the median is 7.

Challenge 2

Find a set of 3 numbers such that…

1. The mean is 6 and the median is 5.

2. The mean is 5 and the median is 7.

3. The mean is 4, the median is 2, and the mode is 2.

Challenge 3

Find a set of 3 numbers such that…

1. The mean is 2 and the range is 2.

2. The mean is 8 and a single number is the mode.

3. The mean is 6, the median is 8, and there is no mode.

Challenge 4

A set of 6 numbers includes 2, 3, 6, 7, ⬜, ⬜. 

Find the two missing numbers such that…

1. The mean is 5 and the median is 5.

2. The mean is 3 and a single number is the mode.

3. The mean is 4 and the range is 6.

Challenge 5

Find a set of 4 numbers such that…

1. The mean is 5, the mode is 4, and the range is 6.

2. The median is 7 and the mean is 2.

3. The mode is 9, the median is 9, and the mean is 7.

Step 1:Give 4 sine/cosine graphs without a coordinate grid.

"What are you able to say about each graph?" "Is there a way that you can compare and/or contrast the graphs?"

Step 2: Share the graphs with x-y axis lines, but no relative scaling on it.

"What are you now able to say about each graph?" "Have any of your assumptions changed?"

Step 3: Add the scaling of the x-axis

"What are you now able to determine?" "Are you able to write an equation to represent each graph?" "What would be missing from each equation?"

Step 4: Give them the complete graph with y scaling included.

"What is everything that you are now able to say about each graph?" "Which of your initial assumptions were correct or incorrect?"

Grade 10 MYP 5 – Mathematics

Learning Objective:

Students will recognize, describe, and extend an arithmetic sequence, developing an understanding of its structure and deriving a general rule.

Task Progression (Thin-Sliced Steps)

Step 1: Noticing the Pattern (Observation & Recognition)

• Display the sequence:
  4, 9, 14, 19, 24, …

• Ask: What do you notice?

• Students share observations (e.g., numbers increase, a consistent pattern in changes).

Step 2: Identifying the Rule (Structuring)

• Ask: How do you get from one term to the next?

  • Guide students to recognize the common difference: +5

• Introduce key vocabulary: first term (a1a_1a1​), common difference (ddd).

Step 3: Extending the Pattern (Application)

• Ask: What are the next two terms?

• Have students justify their answers based on the pattern.

Step 4: Generalizing the Rule (Algebraic Expression)

• Introduce the arithmetic sequence formula: a_n=a₁+(n−1)d

• Guide students in forming the specific formula for this sequence: a_n=4+(n−1)×5

Step 5: Reflecting on the Pattern (Connecting & Justifying)

• Ask: How can we find the 50th term without listing all values?

• Challenge students to check if 100 is in the sequence by solving for nnn.

Differentiation Options:

🔹 Support: Provide scaffolded examples of simpler arithmetic sequences.
🔹 Extension: Introduce sum of an arithmetic series and real-world applications.

Magic School

For Grade 9 MYP year 3 - Right Angled Trig

Prompt: Please create a Thin Sliced task for Grade 9 IB MYP maths student who is learning about angles of elevation and depression. Please make the first task with a low floor and base it on the principles of Building Thinking Classroom with an extension component. The task should be about 20 mins.

Thin Sliced Task: Angles of Elevation and Depression for Grade 9 IB MYP Maths

Task Title: Exploring Angles of Elevation and Depression

Objective:
Students will apply the concepts of angles of elevation and depression in a collaborative setting, promoting critical thinking and problem-solving skills.

Duration: Approximately 20 minutes

Scenario:
A bird is perched on a tree, and a person is standing on the ground looking up at the bird.

Given Information:

1. The height of the tree is 10 meters.

2. The angle of elevation from the person to the bird is 45^\circ.

Tasks:

1. Group Discussion (5 minutes):

   • In small groups, discuss what you know about angles of elevation and depression. Share examples from real life where these concepts might be useful.

2. Identify the Angle (2 minutes):

   • Individually, write down what the angle of elevation from the person to the top of the tree is. (Answer: 45^\circ)

3. Draw a Diagram (5 minutes):

   • As a group, create a clear and labeled diagram showing the tree, the person, and the angle of elevation. Use large paper or a whiteboard to facilitate collaboration.

4. Calculate the Distance from the Person to the Base of the Tree (5 minutes):

   • Using the angle of elevation, as a group, determine how far the person is from the base of the tree.

   • Hint: Use the tangent function:
     \(
     \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
     \)

5. Reflection and Share Out (3 minutes):

   • Each group shares one insight from their discussion about the importance of understanding angles of elevation and depression in everyday life.

Extension Activity (Optional):
Task Title: Exploring Real-World Applications

Duration: 10-15 minutes

1. Research and Present (10-15 minutes):

   • Choose a real-world scenario where angles of elevation or depression are crucial (e.g., architecture, aviation, or gaming). Research the scenario and prepare a brief presentation or poster explaining how these angles are used in that context.

   • Include any relevant calculations or diagrams in your presentation.

Instructions:

• Collaborate with your group members, ensuring everyone's ideas are heard.

• Use clear labels in your diagram and show all work in calculations.

Assessment Criteria:

• Participation in group discussion.

• Clarity and accuracy in the diagram.

• Correct calculation of the distance.

• Insightfulness of the shared reflection.

• Creativity and depth of research in the extension activity.

This extension activity encourages students to explore real-world applications of angles of elevation and depression, reinforcing their understanding and promoting critical thinking. If you need further adjustments or additional resources, feel free to ask!

Co-pilot

For Grade 9 MYP year 3 - Right Angled Trig

Prompt: Please create a Thin Sliced task for Grade 9 IB MYP maths student who is learning about angles of elevation and depression. Please make the first task with a low floor and base it on the principles of Building Thinking Classroom with an extension component. The task should be about 20 mins.

Sure! Here's a thin-sliced task for a Grade 9 IB MYP math student focusing on angles of elevation and depression, designed with a low floor and an extension component, based on the principles of Building Thinking Classroom.

Task: Angles of Elevation and Depression

Part 1: Low Floor Task

1. Understanding the Basics:

   • Question: What is the angle of elevation? What is the angle of depression? Draw a simple diagram to illustrate each concept.

   • Activity: Use a protractor to measure and draw an angle of elevation and an angle of depression on a piece of paper.

Part 2: Problem-Solving

2. Problem 1: A person standing 30 meters away from a flagpole observes the top of the flagpole at an angle of elevation of 20°. Find the height of the flagpole.

   • Hint: Use the tangent ratio, where (\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}).

Part 3: Extension Component

3. Problem 2: A person standing on a 25-meter-high cliff observes a boat at an angle of depression of 15°. Find the distance from the base of the cliff to the boat.

   • Hint: Draw a right-angled triangle and use the tangent ratio to find the horizontal distance.

4. Problem 3: A drone is flying at a height of 50 meters. It observes a car on the ground at an angle of depression of 30°. Find the horizontal distance between the drone and the car.

   • Hint: Use the tangent ratio and consider the height of the drone as the opposite side of the triangle.

Instructions:

• Draw diagrams for each problem to help visualize the situation.

• Use trigonometric ratios (sine, cosine, tangent) to solve the problems.

• Show all your workings clearly.

• Use a calculator where necessary.

• Round your answers to two decimal places where appropriate.

Extension Activity:

• Challenge: Create your own problem involving angles of elevation or depression. Swap problems with a classmate and solve each other's problems.

This task should take about 20 minutes to complete. Feel free to ask if you need any help with these problems!

(4+2i) + (5+7i) =

(4-2i) + (-5+7i) =

(4-2i) + (9) =

2 (4+i) =

i (8-3i) =

4i (-5-10i) =

(4-2i) * (-10) =

(4+i) * (3+2i) =

(5-2i) * (-5+6i) =

(-3+4i) * (-2i) =

(7+3i) * (7-3i) =

• Quadrant 1: Key Concepts

• Quadrant 2: Problem Solving Process (i.e. Worked Example)

• Quadrant 3: Applications and Real-life Connections

• Quadrant 4: Reflection and Questions

Co-pilot

• Quadrant 1: Key Concepts and Definitions

• Quadrant 2: Visual Representations

• Quadrant 3: Examples and Practice Problems

• Quadrant 4: Reflections and Questions

Magic School

• Quadrant 1: What I Know (Individual Reflection)

• Quadrant 2: What I Learned (Worked Examples and Problems)

• Quadrant 3: What I Still Wonder (Questions and Reflections)

• Quadrant 4: How I Can Apply It (i.e. Where is this used?)