**Foundation Concepts**- is what we now believe to be the core deficit in math difficulties. It is an awareness of quantity and quantity relationships.**Numeracy**- According to research the human brain can recognize quantities up to four but over that, the quantity needs to be in a pattern. (See the research of Stanislas Dehaene and the work of Brian Butterworth.)
- After mastering quantity patterns of all addends up to and including the ordered pairs of ten (1+9, 2+8, 3+7, 4+6 & 5+5) the student can apply those patterns and relationships across place value to reason mathematically.
- When students are learning numeracy patterns, they should do so using multisensory methods and not just use numbers and flash cards. They should construct and deconstruct patterns with many different representations: Unifix or linking cubes, ten frames, dice & domino patterns, sets of objects. They should apply the facts in problem solving.
- Adding and subtracting with visual patterns in memory can aid LD students to work with numbers between 10 and 20 by using construction & deconstruction of quantity with a "Go To The Ten" strategy.
- After mastering quantity patterns, students can apply those patterns across place value to begin really reasoning in math.
- Avoid accommodation strategies which can inhibit numeracy acquisition. These may include too early use of calculators or touching & counting strategies. Students can be wedded to these compensations and be discouraged from really every learning facts or developing fluency with them.
- Every attempt should be made to develop a strong sense of quantity independent of language retrieval without meaning.
- The Multisensory Math Program is dedicated to developing real comprehension of number quantities and using mastery to apply quantity relationships across place value to reason mathematically.

For a hierarchy of essential skills by grade level, see the Achieve the Core Math Focus by Grade website:

https://achievethecore.org/category/774/mathematics-focus-by-grade-level

This website offers a simple, clear view of what is expected of students at each grade level.

https://achievethecore.org/category/774/mathematics-focus-by-grade-level

This website offers a simple, clear view of what is expected of students at each grade level.