Differentiated Instruction in the Primary Mathematics Classroom J. Silva

Differentiation Strategies

ContentProcessProduct According to Students’ Readiness Interest Learning Profile Teachers Can Differentiate Adapted from The Differentiated Classroom: Responding to the Needs of All Learners (Tomlinson, 1999) Environment

Differentiated Instruction Structures and Strategies Strategies Anticipation Guide Anticipation Guide Think-Pair-Share Think-Pair-Share Exit Cards Exit Cards Venn Diagrams Venn Diagrams Mind Maps Mind Maps Concept Maps Concept Maps Metaphors/Analogies Metaphors/Analogies Jigsaw JigsawStructures Cubing Cubing Menus Menus Choice Boards Choice Boards RAFTs RAFTs Tiering Tiering Learning Centers Learning Centers Learning Contracts Learning Contracts Open Questions Open Questions Parallel Tasks Parallel Tasks

Cube Journal Prompts Face 1: I understand… Face 2: I don’t understand… Face 3: I find it easy to… Face 4: I find it difficult to… Face 5: I learned… Face 6: I still want to know…

Cube Geometry Compare and Contrast

Cube Probability Prompts IMPOSSIBLE LIKELY CERTAIN Describe probability as a measure of the likelihood that an event will occur, using mathematical language

Appetizer (Everyone): What is a pattern? What is a pattern? Main dish (Choose 1): Create a repeating pattern using pattern blocks. Create a repeating pattern using pattern blocks. Create a growing pattern using pattern blocks? Create a growing pattern using pattern blocks? Side dishes (Choose 2): Describe a pattern that results from repeating an action. Describe a pattern that results from repeating an action. Describe a pattern that results from repeating an operation. Describe a pattern that results from repeating an operation. Describe a pattern that results from using a transformation. Describe a pattern that results from using a transformation. Dessert(if you wish) Create a growing pattern. How is it the same as a repeating pattern? How is it different? Create a growing pattern. How is it the same as a repeating pattern? How is it different? Menu Patterning

Use base ten materials to decompose 327 Use base ten materials to show that the 3 in 324 represents 3 hundreds Use base ten materials to represent the relationship between a decade and a century Show 60 in as many different ways as you can Show $1 in as many different ways as you can Describe the number 18 in as many different ways as you can Use counters to show that 3 groups of 2 is equal to Draw a picture to show that 3 groups of 2 is equal to 3 x 2 Give a real-life example of when you might need to know that 3 groups of 2 is 3 x 2 Choice Board Number Sense and Numeration

ROLEAUDIENCEFORMATTOPIC lengthTeacherPictures How I help you find the perimeter of a square heightPrincipalWords How I help you find the perimeter of a rectangle distanceStudentNumbers How I help you find the perimeter of a circle R.A.F.T.

Station 1: Simple “rectangular” or cylinder shape activities Station 2: Prisms of various sorts Station 3: Composite shapes involving only prisms Station 4: Composite shapes involving prisms and cylinders Station 5: More complex shapes requiring invented strategies Learning Centers Surface Area

Open Learning Tasks have a specific mathematical purpose are built on a big idea allow students at different levels to participate Open-Ended Learning Tasks:

Open Learning Task Choose a type of shape. Tell as many things about it as you can.

Open Learning Tasks What makes the task open? The mathematical purpose The mathematical purpose To reveal what students understand about attributes or properties of the shape. Big idea Big idea Shapes of different dimensions and their properties can be described mathematically. Student Readiness Student Readiness It allows students to tell whatever they know about a shape, whether it is 2D or 3D.

Some “Opening Up Strategies” Start with the answer instead of the question. Start with the answer instead of the question. Ask for similarities and differences. Ask for similarities and differences. Leave the values in the problem somewhat open. Leave the values in the problem somewhat open.

Start with the Answer The answer is 42. What is the question? The answer is 42. What is the question? Number Sense & Numeration

Start with the Answer A triangle has a perimeter of 10. Make as many different triangles as you can. What are the side lengths. A triangle has a perimeter of 10. Make as many different triangles as you can. What are the side lengths. Geometry & Spatial Sense

Start with the Answer A container holds about 4litres. Describe its size in other ways. A container holds about 4litres. Describe its size in other ways. Measurement

This balance shows that This balance shows that = How could you move the blocks to show other equations that are true? Start with the Answer Patterning & Algebra

Start with the Answer Work in pairs to decide what this graph might be about. Work in pairs to decide what this graph might be about. Data Management & Probability

How are the numbers 10 and 15 alike? How are they different? How are the numbers 10 and 15 alike? How are they different? Number Sense & Numeration Similarities and Differences

How are these shapes alike? How are they different? How are these shapes alike? How are they different? Similarities and Differences Geometry & Spatial Sense

Two shapes are the same size. What could they be? How are they different? Two shapes are the same size. What could they be? How are they different? Measurement Similarities and Differences

Jane made the pattern below. Make a pattern that you think is like this. Jane made the pattern below. Make a pattern that you think is like this. Tell how the patterns are alike. Tell how they are different. Tell how the patterns are alike. Tell how they are different. Patterning & Algebra Similarities and Differences

How are these graphs alike and how are they different. How are these graphs alike and how are they different. Similarities and Differences Data Management & Probability

Choose a number for the second mark on the number line. Choose a number for the second mark on the number line. Mark a third point on the line. Tell what the number name it should have and why. Number Sense & Numeration Leaving Values Open

Draw a design or shape made up of three shapes. The design should have symmetry. Draw a design or shape made up of three shapes. The design should have symmetry. Choose two objects in the room. Think about their locations. Tell how to get from location to the other. Choose two objects in the room. Think about their locations. Tell how to get from location to the other. Geometry & Spatial Sense Leaving Values Open

Pick a length between 5cm and 10cm. Draw a pencil that is ___cm long. Pick a length between 5cm and 10cm. Draw a pencil that is ___cm long. Measurement Leaving Values Open

The fourth picture in a pattern consists of five squares as shown: The fourth picture in a pattern consists of five squares as shown: What could the first, second, third, and fifth pictures look like. Leaving Values Open Patterning & Algebra ????

Think of something that might be true about most of the students in the class. Conduct a survey to find out if you are correct. Display your data. Think of something that might be true about most of the students in the class. Conduct a survey to find out if you are correct. Display your data. Leaving Values Open Data Management & Probability

Let’s Open Up Questions Find a closed question. Create an open question using one of the “Opening-up Strategies”: Start with the answer instead of the question Ask for similarities and differences Leave the values in the problem somewhat open

Resource “Opening-up Strategy”  Start with the answer  Ask for similarities and differences  Leave the values in the problem somewhat open Original Question New Question Let’s Open Up Questions

Parallel Learning Tasks Parallel learning tasks are two or more different tasks that: differ in sophistication possess the same big idea focus have a common set of consolidation questions

Parallel Tasks Choose a way to sort so that one bar of your graphs is much longer than all of the other bars. Sort the items the teacher has provided. Create a bar graph to describe the number in each group after you have sorted them. Choose a way to sort so that the bars are all about the same size.

Consolidation Questions How did you sort your items? How did you sort your items? Why was your sorting rule an appropriate one for these items? Why was your sorting rule an appropriate one for these items? Where would this object go (hold up another object) if we used your sorting rule? Where would this object go (hold up another object) if we used your sorting rule? How does your graph describe the items? How does your graph describe the items? What can you tell about the number of different types of items by looking at the graph? What can you tell about the number of different types of items by looking at the graph?

Asking the Right Questions What consolidation questions could we ask for each parallel task? They must apply equally to both tasks and the big idea we want to address.

Parallel tasks: Number Sense & Numeration What is the big idea? There are many ways to represent numbers. What consolidation questions would you ask? What number did you represent? How do you know that that number is one that was okay to choose? What are some of the different ways you represented that number? Choose a number between 1 and 10. Show that number is as many ways as you can. Choose a number between 20 and 30. Show that number is as many ways as you can.

Parallel tasks: Geometry Choose 2D shapes to make two different creatures. Describe the two creatures you made. Choose 3D shapes to make two different creatures. Describe the two creatures you made. What is the big idea? Shapes of different dimensions and their properties can be described mathematically. What consolidation questions would you ask? What are the names of the shapes you used? How many of each did you use? Why did you decide those would be good shapes to use?

Parallel tasks: Measurement A rectangle has sides that are whole numbers of centimetres. The perimeter is 44cm. Draw five possible shapes. A polygon has a perimeter that is 44cm. Draw five possible shapes. What is the big idea? The same object can be described using different measurements. What consolidation questions would you ask? What does it mean to know that the perimeter of a shape is 44cm? How did you select your first shape? How do you know that your perimeter is 44cm?

Parallel tasks: Patterning & Algebra Create a repeating pattern that begins with 3, 5,… Create an increasing pattern that begins with 3, 5,… What is the big idea? A group of items form a pattern only if there is an element of repetition, or regularity, that can be described with a pattern rule. What consolidation questions would you ask? What is your pattern? What makes it a pattern? What would be your 10 th number?

Parallel tasks: Data Management & Probability You have these two bags: You pick one cube from one of the bags and it is blue. You return the cube and pick again from the same bag and it is blue, the one after that is yellow. Which bag do you think you have? Explain. You have these three bags: You pick one cube from one of the bags and it is blue. You return the cube and pick again from the same bag and it is blue, the one after that is yellow. Which bag do you think you have? Explain.

Parallel tasks: Data Management & Probability Which bag do you think you have? Explain. What is the big idea? In probability situations, one can never be sure what will happen next. This is different from most other mathematical situations. What consolidation questions would you ask? What colour do you think will be picked on the fourth try? Why do you think that? Can you be sure?

Some Math Find different ways to make 120

Hunting on the Hundreds Chart Find three numbers on the Hundreds chart that form an I and add to give 150. Record your thinking/strategy on chart paper to share later. Can you find other letters that will give your sum? Show your work. Find an L on the Hundreds chart where the numbers add to give 308.

Consolidation Questions With your table group, come up with a few consolidation questions you could ask that would be appropriate for either task.

The Three Part Lesson Minds On Action After 5-10 minutes minutes minutes Ways to make 120? Summing numbers to make “I” and “L”. Consolidation, Highlight Key Ideas, Misconceptions, Practice, Next Steps...