ALEX Classroom Resource

Students:
When given multi step word problems,

• Solve a variety of multistep word problems involving all four operations on whole numbers including problems where remainders must be interpreted.
• Explain and justify solutions using connections between the problem and related equations involving a single (letter) unknown.
• Evaluate the reasonableness of solutions using estimation strategies.

Note: Multi step problems must have at least 3 steps.

Students know:

• Context situations represented by the four operations.
• How to calculate sums, differences, products, and quotients.
• Estimation strategies to justify solutions as reasonable.

Students are able to:

• Solve multi-step word situations using the four operations.
• Represent quantities and operations physically, pictorially, or symbolically.
• Write equations to represent the word problem and use symbols to represent unknown quantities.
• Use context and reasoning to interpret remainders.
• Use estimation strategies to assess reasonableness of answers by comparing actual answers to estimates.

Students understand that:

• Using problem solving strategies will help them determine which operation to use to solve a problem.
• Remainders must be interpreted based on the context, and remainders are sometimes ignored, rounded up, or partitioned.

Learning Objectives:
M.4.3.1: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
M.4.3.2: Solve single-step word problems.
M.4.3.3: Recognize key terms to solve word problems.
Examples: in all, how much, how many, in each.
M.4.3.4: Solve division problems without remainders.
M.4.3.5: Recall basic addition, subtraction, and multiplication facts.

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.

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.

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.

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.

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.

Students:

• Choose strategies based on place value, partial quotients, properties of operations, or the relationship between multiplication and division to find whole number quotients and remainders.
• Solve word problem situations involving division.
• Justify solution path for quotients using equations, arrays or area models.
Note: Standard algorithm for division is not an expectation at grade 5.

Students know:

• Efficient strategies to find a whole number quotient when a multi-digit number (up to 4-digit dividend) is divided by a single-digit divisor.
• How to justify quotients using an illustration or the relationship between multiplication and division.

Students are able to:

• Find whole number quotients and remainders using a variety of strategies based on place value and properties of operations.
• Illustrate and explain the calculation using equations, arrays, and area models.

Students understand that:

• Strategies for division by a one-digit divisor are extended to two-digit divisors.
• Visual models are used to illustrate division.
• Remainders may be written as a fraction or decimal and interpreted based on context of the problem situation.

Learning Objectives:
M.5.7.1: Construct a division equation with an example of the division algorithm.
M.5.7.2: Illustrate the division algorithm using a one-digit divisor and a 2-digit dividend.
M.5.7.3: Identify the place value of a division problem.
M.5.7.4: Restate the inverse process of division as multiplication.
M.5.7.5: Recall basic multiplication facts.