Intervention: Explicit Instruction in Single-digit Multiplication
Grade 3 - Operations and Algebraic Thinking
Cluster: Represent and solve problems involving multiplication and division and Multiply and
divide within 100.
Activity: Developing the meaning of multiplication through visual models and stories utilizing
the Concrete  Representational Abstract Instructional strategy.
Start by assigning a number to the group that has several factors - for example, 12, 18, 24, 30 or
36.
1. With counters, students attempt to find a way to separate the counters into equal
subsets.
2. Have students find multiplication expressions for their assigned number.
3. With arrays, (perhaps made from square tiles or cubes or drawn on grid paper),
students build rectangles that have the given number of squares.
4. For each such arrangement of sets or appropriate rectangles, both an addition and a
multiplication equation should be written.
5. Students record their equal groups, expressions, equations, and stories on paper.
6. Have students tell a multiplication story for the equal subsets they created.
Example:
1. Target number: 12
Students separate counters into equal subsets. e.g., 2 groups of 6, 6 groups of 2, 4
groups of 3, and 3 groups of 4.
2. Model and push students to use “groups of” language with precision as they describe
their subsets.
3. Model writing addition and multiplication expressions that match their manipulative
models, e.g., 2 groups of 6. Addition expression 6 + 6 Multiplication expression 2 x 6. Ask
students how the expression match the manipulative models. Place expressions on
notecards below or next to the manipulative model.
4. Students next use square tiles to create arrays that match their expressions, e.g., 2 x 6 is
represented by creating a 2 by 6 array (2 rows of 6)
5. Model writing equations that match the subsets created with the manipulatives.
2 rows of 6 x 6 + 6 = 12 2 x 6 = 12
6. Students tell a story for each equation, e.g., There were 2 rows of apples on the shelf.
Each row had 6 apples. How apples were on the shelf? The story is also recorded along
with the drawings, expressions, and equations.
Repeat this same process numerous times with other numbers and their factor pairs gradually
increasing independence.
8/14/13.mh
Howard County Public Schools
https://grade3commoncoremath.wikispaces.hcpss.org