ALEX Classroom Resource

Students:

• When given a multiplication equation, create and explain a corresponding verbal multiplicative comparison statement.
  Example: interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 35 is 7 times as many as 5.
• When given a verbal (written or oral) representation of a multiplicative comparison, write and solve the related multiplication equation.

Example: Sue has 7 cards and Joe has 5 times as many cards as Sue. The student will write 5 x 7 and accurately find the number of cards Joe has to be 35.

Students know:

• How to write an equation to represent a word situation.
• Which quantity is being multiplied and which factor is telling how many times.
• Varied language that describes multiplicative comparisons.

Students are able to:

• Interpret equations for multiplicative comparisons.
• Write equations for multiplicative comparisons.

Students understand that:

• Multiplicative comparisons relate the size of two quantities and a scale factor.
• Factors in multiplication problems have different roles from each other in the context of comparison problems.
• Explanations and drawings show ways multiplicative comparisons are similar to and different from equal groups and arrays.

Learning Objectives:
M.4.1.1: Use arrays to show equal groups in multiplication.
M.4.1.2: Recall basic multiplication facts.
M.4.1.4: Demonstrate computational fluency, including quick recall of addition and subtraction facts.
M.4.1.5: Recognize multiplication as repeated addition.

Students:

• When given word problems involving multiplicative comparison, will solve using concrete, pictorial representations, and write related equations involving a single unknown.

Example: There are 12 children and 3 adults at the playground. How many times as many children are at the playground than adults? Represent the situation with the equation 12 = n × 3 and a tape diagram with a total of 12 and groups of 3, repeating each group 4 times to solve.

Students know:

• how to find products and quotients.
• Recognize situations represented by multiplicative comparison.
• Distinguish between multiplicative comparison and additive comparison.

Students are able to:

• Solve word problems involving multiplicative comparison.
• Write equations using a symbol for the unknown to represent word problems involving multiplicative comparison.
• Use drawings to represent the word situation involving multiplicative comparison.

Students understand that:

• additive comparison focuses on the difference between two quantities and multiplicative comparison focuses on one quantity being some number times larger than another.

Learning Objectives:
M.4.2.1: 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.4.2.2: Recognize key terms to solve word problems.
Examples: in all, how much, how many, in each.
M.4.2.3: Apply properties of operations as strategies to add.
M.4.2.4: Recall basic multiplication facts.
M.4.2.5: Demonstrate computational fluency, including quick recall of addition and subtraction facts.

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:

• Use strategies based on place value, properties of operations, rectangular arrays, area models, and equations to illustrate and explain the product of two factors (up to four digits by a one-digit number and two two-digit numbers).

Note: Standard algorithm is not an expectation for grade 4.

Students know:

• How to compose and decompose numbers in a variety of ways using place value and the properties of operations.
• How to represent the product of two factors using an area model.
• Use strategies based on place value (partial products), the properties of operations, arrays and area models to represent a two digit factor times a two digit factor.

Students are able to:

• Use strategies based on place value and the properties of operations to find products.
• Illustrate the product of two factors using rectangular arrays and area models.
• Explain the product of two factors using equations.
• Make connections between models and equations.

Students understand that:

• arrays, area models, place value strategies, and the properties of operations can be used to find products of a single digit factor by a multi-digit factor and products of two two-digit factors.

Learning Objectives:
M.4.11.1: Divide within 100, using strategies such as the relationship between multiplication and division (e.g. knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8).
M.4.11.2: Divide within 100, using strategies such as properties of operations.
M.4.11.3: Multiply within 100, using strategies such as properties of operations.
M.4.11.4: Multiply within 100, using strategies such as the relationship between multiplication and division (e.g. knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8).
M.4.11.5: Recall products of two one-digit numbers.
M.4.11.6: Name the first 10 multiples of each one-digit natural number.
Example: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.
M.4.11.7: Recall basic addition, subtraction, and multiplication facts.