DIFFERENTIATION
In any class, there will be a range of maths understanding.
Because maths is conceptually based, and understanding of one level of a concept is needed to understand the next level and related concepts, differentiation is essential!
Check out the research at the end of this document to deepen your understanding about differentiation!
The Teaching Resources at A Learning Place A Teaching Place have been designed to allow you to differentiate!
First, we’ll need to know what level of understanding each child currently has!
For this we need Formative assessment!
Assessing current understanding of Addition, Subtraction, Multiplication and Division is simple!
If children are used to using playing cards to generate the numbers that they are ready to investigate, they may do this.
If children are not used to using playing cards to generate the numbers are ready to investigate, record some number sentences on the board and allow children to select the level they feel ready to start from.
The following table displays samples from each level of understanding:
Children record the number sentence and their solution strategy.
The levels on the Addition and Subtraction Concept Page will allow you to identify each child’s level of understanding in Addition and Subtraction.
DIFFERENTIATING ADDITION AND SUBTRACTION
1. Identify the levels of understanding of the children in your class, for example,
2. Select the Teaching Plan for each level of the concepts that children are ready to investigate, for example,
3. Select the segment of each Teaching Plan to include in the Explicit Teaching segment of the lesson, for example,
You may decide you’d like to use the Teaching Plan PowerPoint. If you do, you could create your own PowerPoint by selecting and joining the segments from the Teaching Plans, for example,
4. Start at the lowest level, and explicitly teach each level to the whole class using the Teaching Plan or the segment from the Teaching Video, for example,
Addition and Subtraction 4 – select cards to make a teen number and a single-digit number, subtract counting by 1s.
Addition and Subtraction 7 – using the same cards and numbers, subtract using place value, partitioning and friends of 10.
Place Value 9 – place 20 counters onto two 10 frames, subtract the same single-digit number of counters, recording friends of 20.
Place Value 13 – use the card as a tens number, make a tower of blocks naming each block 10, partition.
Place Value 16 – select cards to make a three-digit number, count forwards by 10s on a number line.
Place Value 19 – select cards to make a five-digit number, describe using standard and non-standard place value.
Children may identify the level and concept that they are ready to investigate, or you may tell them.
5. Each child then uses playing cards to engages in the Investigation described 
at the end of the Teaching segment, for example,
Children could be sitting next to a child who is investigating a different level of the same concept, or a different concept. Children stop every now and then to explain what they are investigating to the person next to them.
This leaves you free to walk around, observe children, ask questions, scaffold learning just enough to allow children to continue investigating.
The levels on the Multiplication and Division Concept Page will allow you to identify each child’s level of understanding in Multiplication and Division.
DIFFERENTIATING MULTIPLICATION AND DIVISION
1. Identify the levels of understanding of the children in your class, for example,
2. Select the Teaching Plan for each level of the concepts that children are ready to investigate, for example,
3. Select the segment of each Teaching Plan to include in the Explicit Teaching segment of the lesson, for example,
You may decide you’d like to use the Teaching Plan PowerPoint. If you do, you could create your own PowerPoint by selecting and joining the segments from the Teaching Plans, for example,
4. Start at the lowest level, and explicitly teach each level to the whole class using the Teaching Plan or the segment from the Teaching Video, for example,
Multiplication and Division 9 – select cards to make a number, multiply by 10 using place value.
Multiplication and Division 11 – select cards to make a number, divide by 4 using properties and relationships.
Multiplication and Division 12 – select cards to make a number, multiply by 3 using the distributive property.
Multiplication and Division 13 – select cards to make a number, divide by 5 using properties and relationships.
Multiplication and Division 25 – select cards to make a decimal number, multiply by 10 or a whole number using the distributive property and place value.
Children may identify the level and concept that they are ready to investigate, or you may tell them.
5. Each child then uses playing cards to engages in the Investigation described at the end of the Teaching segment, for example,
Children could be sitting next to a child who is investigating a different level of the same concept, or a different concept. Children stop every now and then to explain what they are investigating to the person next to them.
This leaves you free to walk around, observe children, ask questions, scaffold learning just enough to allow children to continue investigating.
Current Learning Research on Differentiation
Carol Ann Tomlinson University of Virginia cat3y@virginia.edu
Differentiation and the Brain: How Neuroscience Supports the Learner Friendly Classroom
SGIS Conference Zug, Switzerland March 9-10, 2012
Carol Ann Tomlinson, Catherine Brighton, Holly Hertberg, Carolyn M. Callahan, Tonya R. Moon, Kay Brimijoin, Lynda A. Conover, & Timothy Reynolds Differentiating Instruction in Response to Student Readiness, Interest, and Learning Profile in Academically Diverse Classrooms: A Review of Literature
Pearl Subban Monash University pearlsubban@iprimus.com.au Differentiated instruction: A research basis