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Teaches students how to count to solve sums to 12, mapping solution with animated manipulatives and on a number line. Counting from zero and counting on from the greater quantity to combine quantities is explicitly taught.

Sometimes called “fact families,” this lesson briefly teaches students how to solve for a missing number in any position in sums to 20 and subtraction 0-20 problems. This skill requires students to understand the conceptual relationship between addition and subtraction.

A lesson teaching students how to understand multiplication as repeated addition, to count on an array model or map on a number line to solve.

A lesson teaching division 0-9 as solving for an unknown factor.

Sometimes called “fact families,” this lesson teaches students how to solve for the missing number in any position in multiplication and division fact problems 0-12. This skill requires students to understand the conceptual relationship between multiplication and division.

Teaches students how to correctly solve multi-digit addition with and without regrouping, using the algorithm and expanded notation and demonstrates solutions on a number line.

Teaches students how to correctly solve multi-digit subtraction with and without regrouping, using the algorithm and expanded notation, with demonstration of solutions on a number line.

Teaches students how to correctly solve multi-digit multiplication with regrouping, using the algorithm and expanded notation and demonstrates solutions on a number line.

Teaches the concepts of prime and non-prime numbers and how to find the missing factor in a factor pair to create equivalent multiplication expressions. This skill is an important precursor to finding factors to convert fraction quantities to different base units and to simplify fractions.

Fractions are often very confusing to students because things they thought they understood, like numbers later in the counting sequence always represent greater quantities, are no longer necessarily true. Teaches students how to understand fraction quantities (including the concept that two fraction quantities can be equal but contain totally different numbers), how to convert fractions with different denominators to share the same fraction base unit to allow for comparing quantities and adding and subtracting with fractions. Fractions are taught using number lines and the lesson explicitly teaches how to follow specific procedures (and why) to find the least common multiple and then to convert fractions to share a least common denominator.

Teaches students how to simplify fractions for which the denominator is divisible by the numerator. Greatest common factor is taught and students are taught how to factor denominators to find the greatest common factor and then to simplify the fraction. Number lines are used to map quantities and students learn that the same fraction quantity can be represented by fractions with different numbers. There are two additional “levels” to this skill in SpringMath and this one is the entry skill for simplifying fractions.

Teaches students how to simplify improper fractions to create a mixed number using what they understand about division with remainders and mapping the operation and quantity on number lines to find the unknown factor plus missing addend (the new numerator) and maintain the fraction base unit.