Students begin Topic A by investigating the formulas for area and perimeter. In Lesson 1, they use those formulas to solve for area and perimeter and to find the measurements of unknown lengths and widths. In Lessons 2 and 3, students use their understanding of the area and perimeter formulas to solve multiplicative comparison problems including the language of times as much as with a focus on problems using area and perimeter as a context (e.g., A field is 9 feet wide. It is 4 times as long as it is wide. What is the perimeter of the field?) (4.OA.2, 4.MD.3). Students create diagrams to represent these problems as well as write equations with symbols for the unknown quantities.

Content Standard(s):

Mathematics MA2019 (2019) Grade: 4

2. Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.

Unpacked Content

Evidence Of Student Attainment:

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.

Teacher Vocabulary:

Multiplicative comparison

Times as many

Product

Factor

Multiplication

Equation

Symbol

Additive comparison

Tape diagram

Unknown

Knowledge:

Students know:

how to find products and quotients.

Recognize situations represented by multiplicative comparison.

Distinguish between multiplicative comparison and additive comparison.

Skills:

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.

Understanding:

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.

Diverse Learning Needs:

Essential Skills:

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.

Prior Knowledge Skills:

Demonstrate computational understanding of multiplication and division by solving authentic problems with multiple representations using drawings, words, and/or numbers.

Identify key vocabulary words to solve multiplication and division word problems.
Examples: times, every, at this rate, each, per, equal/equally, in all, total.

Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Recall basic multiplication facts.

Add and subtract within 20.

Represent repeated addition, subtraction, and equal groups using manipulatives.

Distinguish between rows and columns.

Use repeated addition to solve problems with multiple addends.

Count forward in multiples from a given number.
Examples: 3, 6, 9, 12; 4, 8, 12, 16.

Recall doubles addition facts.

Model written method for composing equations.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.4.1 Solve one-step word problems involving real-life situations using the four operations within 100 without regrouping and select the appropriate method of computation when problem solving.

Mathematics MA2019 (2019) Grade: 4

23. Apply area and perimeter formulas for rectangles in real-world and mathematical situations.

Unpacked Content

Evidence Of Student Attainment:

Students: When given real-world situations involving area and perimeter will,

Apply area formula to find the area of rectangles.

Find one missing dimension of the rectangle if one dimension is known.

Apply perimeter formula to find perimeter of rectangles.

Find one missing dimension of the rectangle if one dimension is known.

Teacher Vocabulary:

Area

Perimeter

Formula

Equation

Dimension

Length

Width

Knowledge:

Students know:

The relationship of area to the operations of multiplication and addition.

The relationship of three whole numbers in a multiplication or division equation.

How to distinguish between linear and area measures.

Skills:

Students are able to:

Apply area formula for rectangles given real-world situations.

Apply perimeter formula for rectangles given real-world situations.

Understanding:

Students understand that: Given real-world situations involving rectangles,

Area formula represents the region inside a rectangle and is used to calculate area, or calculate one missing dimension if one side length is known.

Perimeter formula represents the distance around the rectangle and is used to calculate the perimeter, or calculate one missing dimension if one side length is known.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.4.23.1: Recall the formula for area (L × W).
M.4.23.2: Recognize that unit squares are equal.
M.4.23.3: Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).
M.4.23.4: Recall basic addition and multiplication facts.

Prior Knowledge Skills:

Define perimeter.

Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).

Recall basic addition and multiplication facts.

Build and draw shapes to possess defining attributes.

Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

Describe measurable attributes of objects such as length or weight.

Define rows, columns, and total.

Identify rectangle.

Count to 20 by ones.

Trace partitions in a rectangle.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.4.23 Determine the area of a square or rectangle by counting units of measurement (e.g., unit squares).

Tags:

area, divide, multiplicative comparison, multiply, perimeter, rectangle, word problems