Fourth Grade - MATH
5: Math
Unit 1: Place Value to 1,000,000
Lesson 1
Numbers to 10,000 Review
Students are given a "Perimeter and Area Review" that defines area of a rectangle and shows the procedure: multiply a rectangle's length and width to find area, with a worked example 6 × 9 = 54 sq in. The Basic Skills Review also includes multiplication practice problems (e.g., 7 × 10 = 70, 5 × 9 = 45) which reinforce the computation used in area calculations. Perimeter is defined and calculated by adding side lengths or multiplying for regular polygons, so students practice related measurement concepts.
Lesson 8
Rounding to Estimate
The Basic Skills Review #3 includes an item asking students to "Circle the perimeter: 54 m or 30 m" with an image of a rectangle labeled with side lengths (4 m, 6 m, 9 m, 6 m), which requires students to compute perimeter from given side lengths. The worksheet item 6 therefore has students use side measurements to determine the perimeter value and choose the correct total.
Unit 2: The Four Operations
Lesson 9
Extending Factors and Prime Numbers
Students are shown a rectangle labeled 4 inches by 5 inches and asked to compute its area (20 sq. in.) and which operation to use, linking area to multiplication. Students are told that the side lengths (4 and 5) are factors that multiply to make the area and are directed to an interactive 'Factorize' tool where they create rectangles with side lengths that multiply to a given target number and record factor pairs. Students complete activities using division and multiplication tables to identify factors of given numbers, reinforcing the connection between rectangular arrays and factor pairs.
Lesson 11
Working With Equations
Students solve equations with unknown factors in word problems (for example, Renata puts $2 every day and solves 2·x = 20 to find x). Students practice solving multiplication and division equations with variables (examples include 28 ÷ y = 4 and other missing-factor problems). Students compute area of a rectangle when given both dimensions (a worksheet asks for the area of a 10 in. by 7 in. rectangle and expects 70 sq. in.).
Unit 3: Geometry
Lesson 6
Playing with Angles
The Basic Skills Review includes a rectangle labeled 7 in. by 9 in. and an answer key states the area is 63 sq. in., so students compute area by multiplying side lengths. The "My Own Flags" activity uses rectangular flag spaces that require students to draw and reason about rectangular shapes, giving an opportunity to consider rectangle dimensions.
Unit 4: Multi-Digit Multiplication
Lesson 5
The Area Model
Students draw rectangles and label sides to represent multiplication problems (e.g., 64 by 72) and break each side into place-value parts (60+4 and 70+2). Students compute partial areas for each smaller rectangle (e.g., 60x70=4200, 4x70=280, 60x2=120, 4x2=8) and add them to find the whole product. Students complete word problems by multiplying quantities (e.g., offices per floor, players per team) and use the rectangle/area model to compute products. Students also practice solving for an unknown factor in an equation on the basic skills review (700 x N = 2100).
Lesson 8
Unit Test
Students are asked to use visual multiplication methods: prompts include "Use an array to find the product: 19 × 6" and "Use an area model to find the product: 34 × 18," and several problems require students to show work with arrays, area models, or expanded form. The materials instruct students to use a laminated grid or whiteboard to construct arrays and area models and include multiple problems where students compute products using these visual/rectangular representations.
Final Project
Multiplication Contract
Students are asked to teach two multiplication strategies, including an "Area Model" and "Arrays," and to create a product (video or poster) that explains those strategies. The evaluation rubric requires examples using multi-digit numbers (such as 25 x 32) and at least one word problem involving a real-world use of multi-digit multiplication. Students plan, draft, and present their chosen strategies and real-world examples to an audience, and must include words and illustrations for one strategy.
Unit 5: Fractions
Lesson 6
Adding Fractions
The Basic Skills Review #15 includes a real-world problem asking for the area of Pat's yard given its length (110 ft) and width (80 ft), with the answer shown as 8,800 square feet. The problem requires students to multiply two side lengths to produce an area, demonstrating use of the area formula for rectangles in a contextual problem.
Lesson 10
Adding Mixed Numbers
Students solve a perimeter problem: the Basic Skills Review answer key lists "Kent's yard is 90 feet long and 80 feet wide. What is the perimeter of his yard? (340 feet)." The student activity page asks a similar question: "Kent's yard is 40 feet long and 80 feet wide. What is the perimeter of his yard?" Students also practice multiplication and solving for a variable in problems such as "4000 x N = 360,000," which builds fluency with multiplication used in area calculations.
Lesson 12
Multiplying Fractions and Whole Numbers
The Basic Skills Review includes a real-world perimeter problem: "Cat's yard is 120 feet long and 85 feet wide. What is the perimeter of her yard? (410 feet)." Students are expected to compute the perimeter of a rectangle given its length and width, showing application of the perimeter formula in a context.
Unit 8: Measurement
Lesson 7
Reviewing Perimeter and Area
Students read the definitions and the formula 'The area of a rectangle is its length times its width' and practice computing area and perimeter for given rectangles (e.g., rectangle labeled 6 ft by 4 ft with P = 20 ft and A = 24 sq ft). Students solve multiple real-world word problems that use perimeter and area (Mr. Sampson garden/patio perimeter comparison and Mrs. Hamilton rooms for flooring). One task asks students to change the garden width so the perimeter becomes 66 ft, requiring them to solve a perimeter equation for an unknown width.
Lesson 8
Working With Perimeter and Area
Students are shown how to use perimeter by finding missing sides of a rectangle (example: given length 15 in and perimeter 42 in students subtract known sides and divide to find the short side of 6 in). Students are shown how to use area to find a missing side (example: given width 5 m and area 35 m^2 students divide 35 by 5 to get length 7 m). Activities and answer keys ("What's Missing?", Mr. Harmon and Ms. Scott problems, area-with-pool patio problems, and Creating Rectangles tasks) require students to compute perimeter and area and to find unknown side lengths using division and subtraction in real-world and mathematical contexts.
Lesson 9
Connecting Perimeter and Area
Students draw and label rectangles with a given area (e.g., area = 16 and area = 36) and compute each rectangle's perimeter, comparing results. Students create rectangles with a given perimeter (e.g., perimeter = 16 or 12) and compute each rectangle's area. The Perimeter and Area Problem Solving activity explicitly asks students to fill in missing side lengths using a given area and equal perimeters, and the example steps instruct students to "calculate the length of the unknown side using the area" and then use perimeter values to solve for missing dimensions.
Lesson 10
More Practice and Problem Solving
The lesson answer key explicitly compares areas and perimeters of rectangles (e.g., "A of a 4 (x) 5 rectangle < A of a 6 (x) 6 rectangle" and "P of a 6 (x) 6 rectangle < P of a 6 (x) 8 rectangle"). The Student Activity Page includes items that ask students to compare rectangle measurements (items referencing 3 x 6 and 6 x 6 rectangles), implying students compute area or perimeter values to make comparisons.
Lesson 11
Unit Test
Students are asked to compute areas and perimeters of rectangles in multiple places: the Student Activity Pages include a Length x Width = Area table with worked examples (e.g., 14 m x 20 m = 280 sq m) and problems that ask "What is the area of the shaded shape?" and "What is the perimeter of the whole shape?". Answer keys list numerical area and perimeter results for rectangular diagrams (e.g., area = 30 sq cm, area = 35 sq in, perimeter = 42 in). The materials also link to an interactive 'Area Blocks' game for additional practice with area.
Final Project
Measurement Think-Tac-Toe
The lesson lists the skill "Apply the area and perimeter formulas for rectangles in real world and mathematical problems." Students are given a "Perimeter and Area With Everyday Objects" task where they create a table listing measured perimeters and areas of objects and round measurements. The materials include a "Perimeter and Area Worksheet" that requires creating 12 problems "focusing on perimeter and area" and explicitly mentions including missing lengths or side measurements, and a "Perimeter and Area Design a Room" activity where students mark perimeter and area on a grid with each square representing one square foot.
Unit 9: Skills Review
Lesson 4
Measurement
Students complete Activity 2 "Review: Perimeter and Area," filling a table that asks them to compute perimeter and area for given rectangle dimensions and to supply missing values (for example, a row gives Length = 10 miles and Perimeter = 32 miles, and another gives Length = 9 inches and Area = 81 square inches). Students find areas of shaded rectangular shapes from given side lengths (e.g., rectangles with dimensions labeled in inches and meters) and are instructed to use correct square units. The activity requires students to use the area and perimeter formulas repeatedly to compute and label numeric answers.
