Primary Standards:
MAFS.4.NBT.2.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Connecting Standards:
MAFS.4.OA.1.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Content Knowledge:
In 3rd grade students were introduced to the operation of division and explored basic division facts. In this Unit, students extend their understanding of division beyond these basic facts to include multi-digit dividends. The emphasis is developing strategies that are based on an understanding of place value, properties, and the relationship between multiplication and division. These strategies provide the foundation for the standard algorithm of division, which is not a goal of the standards until 6th grade.
Though this standard will not be assessed on FSA in context, posing word problems helps students to build an understanding of the division process as well as when and why we divide. Problems (both contextual and not) may include remainders. When context is used, students should make sense of and interpret the role the remainder plays in the solution. In this Unit, students should experience work with concrete models, such as partitioning base-ten blocks into equal groups, or using diagrams with squares, sticks, and dots/circles to show the quantities being divided. These concepts will help students to better understand the concept of remainders as well. These concrete and visual experiences can transition to partial-quotient strategies. By thinking about multiplication as the inverse of division, students find different ways to determine groups that can be subtracted from the total, until there are no parts left over (or a remainder).
GCG 1 Learning Goal: Use context to determine what to do with a remainder in a division problem
- Step 1: Use models to represent division scenarios where a remainder may occur (2-digit dividends)
- Step 2: Solve division problems and interpret the remainder based on the context of the scenario (2-digit dividends)
GCG 2 Learning Goal: Model equal groups with concrete models, drawings, and place value
- Step 1: Estimate quotients involving division by multiples of 10 and 100
- Step 2: Use compatible numbers to estimate quotients with greater dividends
- Step 3: Use concrete models to extend understanding of division as equal groups to work with greater dividends
- Step 4: Use quick pictures and place value strategies to divide with 1-digit divisors
GCG 3 Learning Goal: Use number sense to decompose a dividend to divide
- Step 1: Estimate quotients of greater dividends
- Step 2: Connect prior work with multiplication and area models to use open array models to divide by determining missing factors
- Step 3: Use open array models to decompose greater dividends (up to 4-digits)
- Step 4: Connect prior modeling strategies to use partial quotients to divide