Primary Standards:
MAFS.4.NBT.2.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on a place value and the properties of operations. Illustrate and explain calculations by using equations, rectangular arrays, and/or area models.
Content Knowledge:
In 3rd grade, students were introduced to multiplication and division. They created models to show the operations, explored properties, and worked to master basic facts. In this Unit, students will extend their understanding of multiplication by working with larger numbers. The use of the standard multiplication algorithm is NOT the goal of the 4th grade standard.
Students will build on previous knowledge of multiplication as equal groups to explore multiplication with a 2-digit number. By using place value and the Distributive Property students will learn they can multiply by breaking apart the 2-digit (and later 3- and 4-digit) factors, for example in 4 × 26, one could multiply 4 groups of 20, and 4 groups of 6, then add together the partial products. By using concrete (base-ten blocks) or area models (grid paper, open area) students begin to develop the important understanding that each digit in a multi-digit factor must be multiplied by the other factor.
As the factors get larger, the open area/rectangular model becomes more manageable than using grid paper or base-ten blocks. As students explore multiplying a 1-digit factor by 2-, 3-, and 4-digit factors they are able to visualize the process, seeing the connections to place value concepts and the Distributive Property.
After using models, students should be able to multiply without them, using their understanding of expanded form to decompose factors, multiply by each place value part, and then add the partial products to find the total. They can again extend this understanding to multiply two 2-digit numbers.
GCG 1 – Learning Goal: As a mathematician, I can Use patterns to multiply by 10s, 100s, and 1000s
- Step 1: Use base ten blocks to model multiplication of single-digit factors by multiples of 10, 100, and 1,000
- Step 2: Apply place value patterns to multiply single-digit factors by multiples of 10, 100, and 1,000
GCG 2 – Learning Goal: As a mathematician, I can Multiply a single-digit factor by a multi-digit factor using area models
- Step 1: Estimate products and assess the reasonableness of solutions
- Step 2: Use base-ten blocks to build arrays representing 1-digit by multi-digit factors
- Step 3: Connect concrete area models of single digit factors multiplied by a multi-digit factor to array models
- Step 4: Extend work with area models to record array models and determine partial products
GCG 3 – Learning Goal: As a mathematician, I can Use strategies and models to multiply 2-digit by 2-digit factors
- Step 1: Extend understanding of area models to represent 2 -digit by 2-digit multiplication using base ten blocks
- Step 2: Connect concrete area models of 2-digit by 2-digit factors to grid paper representations
- Step 3: Extend work with area models to record open area models and determine partial products