FREE RESOURCE: Whole-class incremental rehearsal for addition and subtraction facts
Download this resource to help your class learn addition and subtraction facts bit-by-bit. These slides are the sibling resource for the incremental rehearsal slides for times tables available in a previous post.
In an earlier post, I made the case for why students need to memorise addition and subtraction facts. In another post, I proposed 3 important steps to help students memorise these facts:
Strategy instruction - The goal is for students to learn a mental strategy that can be applied to a set of facts.
Strategy practice and retrieval practice - The goal is to develop accurate responding to the relevant set of facts.
Fluency practice - The goal is to develop fluent responding and long-term retention.
These slides are designed for that second step. Like the slides for times tables shared in an earlier post, they have been designed for teachers to lead their whole class in practising addition and subtraction facts using the principles of incremental rehearsal. Traditionally, incremental rehearsal is an intensive one-to-one flashcard intervention in which one new fact is introduced at a time. A session involves the new fact being retrieved by the student several times, each retrieval being spaced further and further apart by retrieval of facts that have been previously learned until a ratio of 9 learned facts to 1 new fact are being practised.
How does whole-class incremental rehearsal work?
Each lesson involves 3 parts:
Practising a strategy
Saying the new facts
Fluency practice
In the above Strategy slide, students are given two facts to derive using a taught strategy. Scaffolds are provided but faded out over subsequent lessons. Students then turn and talk to discuss how the strategy is applied. The teacher can then call on students to respond. Discussing strategies is not part of incremental rehearsal, but this step has been added to encourage connections between students’ conceptual understanding of these facts and the ability to know these facts implicitly without having to think hard.
This New Facts slide presents the problem and answer for all students to say as a whole: 12 minus 6 is 6. 14 minus 7 is 7. The focus has shifted from applying a strategy to direct recall.
This Fact Fluency slide is animated with each row appearing separately. At first, only two facts are practised, the same two facts from the previous slide. The teacher says the problem and the students say the answer in a back-and-forth manner. Next, the students practise 3 facts, then 4 facts and so on. The facts in red are the new facts from the previous slide. The facts in black were learned in previous lessons. An important way to differentiate instruction here is to call on individual students at the end of each row to demonstrate. Checking that weaker students are successful at the start, middle and end of the sequence ensures everyone is learning.
How do I implement it successfully?
These slides are designed to follow on from explicit instruction in strategies students use to derive multiplication facts, so teach the strategies first. The strategies referenced in this resource include:
Using materials
Counting on (e.g. 6 + 1 or 2 + 9)
Counting back (e.g. 8 - 2 or 11 - 3)
Doubles and near doubles (e.g. 6 + 6 or 7 + 8)
Using related facts for subtraction (e.g. 12 - 6 where 6 + 6 is known)
Bridging 10 (e.g. 9 + 6 or 4 + 7)
Subtraction from 10 (e.g. 13 - 5 or 11 - 4)*
*This strategy involves partitioning the larger number into 10 and ones, subtracting from the 10, then adding the ones back. For example, 13 - 5 = 10 - 5 + 3. For this set of facts, the bridging 10 strategy can also be used (e.g. 13 - 5 = 13 - 3 - 2).
These slides are a useful bridge from acquisition to fluency, but fluency needs to be maintained. So, follow up with activities to maintain fluency. This might include timed practice or games. You can use the blue box in the right-hand corner to include notes about activities that students can engage with at different points in the sequence. I’ve added example notes about relevant activities in Times Tables Rock Stars at the end of each set, but you can and should add your own notes.
How can I adapt the resource?
The slides are editable, so if you use slightly different language to explain strategies, use different visual supports or teach different strategies, it’s easy to adapt the resources to better align with the instruction used in your context.
How fast should I progress through the lessons?
It is best to confirm students have achieved fluency with a set before moving to the next set. When teaching a set, a pace of one lesson a day is about right. Once a set has been taught, pause the introduction of new strategies and facts and focus on using fluency practice to consolidate learning. Once you have confirmed that students have an adequate level of fluency, teach a new strategy and a new set of facts. The main point is to let the pace of instruction be informed by your students’ performance.
In a future post, I’ll be sharing a diagnostic assessment you can use to assess student fluency in basic addition and subtraction facts. In the meantime…
Download the resources here
And if your school is looking to upskill in Retrieval and Fluency in Maths, you can book me to run a full-day workshop. More info here.
