Mathematics 12. Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with one-digit divisors and up to four-digit dividends.
a. Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.
Unpacked Content
Evidence Of Student Attainment:
Students:
When given division problems with one-digit divisors and up to four-digit dividends,
Find quotients with remainders using strategies based on place value, properties of operations, and the relationship between multiplication and division.
Illustrate quotients using a rectangular array and/or area model, and explain the connection of the visual model to the equation. Teacher Vocabulary:
Quotient
Dividend
Divisor
Divide
Multiply
Multiple
Equation
Remainder
Area model
Greatest multiple
Decompose
Compose
Array
Properties of operations
Unknown factor
Partial quotient Knowledge:
Students know:
How to decompose and compose numbers in a variety of ways using place value and the properties of operations to demonstrate a variety of strategies for division.
Division can be described as an unknown factor problem.
A variety of contextual situations can be represented with a division equation. Skills:
Students are able to:
Use strategies based on place value to find whole number quotients and remainders.
Use the properties of operations to find whole number quotients and remainders.
Use arrays and area models to find whole number quotients and remainders.
Illustrate division situations with rectangular arrays and area models.
Write an equation to represent a division situation. Understanding:
Students understand that:
Division expressions represent
The number of objects in each group when the total number is partitioned evenly into a given number of groups. The number of groups when the total number is partitioned into groups that each contain a given number. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.4.12.1: Define fraction, numerator and denominator.
M.4.12.2: Recognize fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.
M.4.12.3: Identify the parts of a fraction a/b as the quantity formed by a parts and size 1/b.
M.4.12.4: Recognize fractions as numerals that may represent division problems.
M.4.12.5: Label numerator, denominator, and fraction bar.
M.4.12.6: Identify parts of a whole with two, three, or four equal parts.
M.4.12.7: Recognize that equal shares of identical wholes need not have the same shape.
M.4.12.8: Distinguish between equal and non-equal parts.
Prior Knowledge Skills:
Recognize fractions as lengths from zero to one.
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
Identify a number line.
Recognize whole numbers as lengths from zero to one.
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
Identify a number line.
Label the fractions on a pre-made number line diagram.
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
Recognize a number line diagram with equally spaced points.
Compare length using non standard units to determine which is longer.
