Ready-to-teach lesson
WHERE THIS FITS IN YOUR YEAR
Around It, or Across It: Perimeter and Area
Grade 4 · Mathematics · Iowa
NATURAL UNIT
Grade 4 measurement: distinguishing perimeter and area through concrete, pictorial, and numerical representations.
TEACHER-FACING PLACEMENT
Use this unit during the Grade 4 measurement work on perimeter and area, after students can multiply whole numbers and measure side lengths reliably. Lessons 1–4 deliberately place two measures on the same rectangle. Students trace or walk the boundary, add side lengths to find perimeter, tile the interior, organize tiles in rows, and connect the count to multiplication and an area formula. This sequence is useful when students know procedures but still confuse which measure a question is asking for.
The strongest Iowa fit is the rectangle work in Lessons 2–4. Students calculate perimeter and area, attach the appropriate linear or square unit, and check a numerical result against a concrete or pictorial model. Lesson 5 then builds four copies of an area and asks students to distinguish four times as much from four more. That makes the unit a useful bridge from measurement into multiplicative-comparison language.
Lessons 6–7 ask students to read the relationship before choosing an operation and to restate a comparison in the reverse direction. Keep those lessons as reinforcement rather than treating shared vocabulary as proof of complete curriculum coverage. Where the Iowa expectation requires composite figures, unknown dimensions, estimation, construction, conversions, or other representations that the unit does not explicitly require, add that work through the district's core materials and assessment routines.
STRONGEST CURRICULUM CONNECTIONS - OUR SUMMARY
Teaches: 4.MD.A.3 - Apply area and perimeter formulas for rectangles in real-world and mathematical problems.
Reinforces: 4.OA.A.1 - Interpret a multiplication equation as a comparison and represent verbal multiplicative comparisons as equations.
Limitation: The unit practices interpreting multiplicative-comparison language in Lessons 5–7, but does not provide the breadth of comparison situations and equation representation required for this expectation.
TEACHER MUST ADD
Use locally required units, problem types, representations, and assessment conventions alongside this conceptual unit. Add any required work named in a limitation above that is not explicitly required in the TumbleTA core.
Placement note: careful curriculum placement, not a claim that the complete unit fully covers every requirement in a curriculum expectation.
MATH UNIT
Around it, or across it: perimeter and area
Grade 4 7 lessons 7 x 30 minutes 3 source books
page 1
THE QUESTION THIS UNIT FOLLOWS
Which measure is the question asking for?
ABOUT THIS UNIT
A student may know how to calculate both perimeter and area and still return the wrong one, because the side lengths alone do not say which measure is wanted. This unit begins with one rectangle, yarn around its edge and squares across its face. It then builds perimeter as a sum of side lengths and area as a count organized by multiplication. The final lessons put close-looking phrases side by side so students must read the relation before choosing an operation.
THE MATHEMATICAL ARC
Each lesson does one job the lesson before it made possible.
- 1
- One rectangle, two measures, and which question each answers
- 2
- Perimeter from the sides: walk it, then write the sum
- 3
- Tile it, count by rows, and write the multiplication
- 4
- Area from a formula, checked against a count
- 5
- Four times the area: build four copies and find the extra
- 6
- The phrase sets the operation
- 7
- Say a comparison both ways and track the reversed relation
SOURCE BOOKS
Zachary Zormer, Shape Transformer: A Math Adventure Kitchen Math Ball Game Math
3 lessons
2 lessons 2 lessons
HOW TO USE THIS GUIDE
OPEN THE SOURCE LESSON BEFORE YOU TEACH Each day names a lesson already published under Math lessons. This guide explains its place in the sequence and what to collect; the source lesson carries the full procedure, printables and answers.
THIRTY MINUTES A DAY
Use five minutes to connect, the twenty-minute source lesson for the core, and five minutes to close on visible evidence. If time runs short, protect the core.
TEACH A LESSON ON ITS OWN IF YOU NEED TO Every lesson includes a one-sentence opening for use outside the unit.
STOP AFTER A CHECKPOINT
The unit can pause after either checkpoint without breaking the instructional arc.
WHERE THIS FITS IN YOUR YEAR
WHEN TO TEACH IT
After multiplication facts are secure. Lessons 5 to 7 also require comfortable multiplication of a two-digit or three-digit quantity by a one-digit factor.
WHAT STUDENTS NEED FIRST
Students can multiply within 100, measure whole inches with a ruler, subtract within 10,000, and find half of an even multiple of 100.
page 2
WHAT THIS UNIT DEVELOPS
Perimeter and area as distinct measures; correct linear and square units; perimeter as a sum; area by tiling and multiplication; additive and multiplicative comparisons.
WHAT IT PREPARES THEM FOR
Composite area, scale drawings, and later problems in which wording determines whether a comparison is additive or multiplicative.
The verified connection for your region, with the lessons it covers and its stated limitation, is on the regional placement page at the front of this guide. Individual source lessons carry their own classifications on their own pages, checked lesson by lesson.
UNIT AT A GLANCE
# MATHEMATICAL MOVE
1 Produce perimeter and area from the same 4-by-6 rectangle.
2 Walk all four sides and write perimeter as a four-term sum.
3 Tile by rows and connect the count to multiplication.
4 Draw two pans, compute two areas, and check each by counting.
5 Represent an area four times as large with four copies, not by multiplying both side lengths by four.
6 Contrast four times the area with four more square yards of area.
7 State area and baking-time comparisons in both directions.
SOURCE LESSON
Zachary Zormer, lesson 1
Zachary Zormer, lesson 3
Zachary Zormer, lesson 2
Kitchen Math, lesson 4
Ball Game Math, lesson 4
Ball Game Math, lesson 6
Kitchen Math, lesson 9
COLLECT
20 inches and 24 square inches, correctly labelled.
All sides labelled and one perimeter sum.
Tiled rectangle, edge labels and equation.
Two labelled rectangles with two matching methods.
A labelled scale model and computed areas.
2400 and 604, each tied to its phrase.
Four true sentences about the same two pans.
- UNIT VOCABULARY
- perimeter
- The distance around a figure, measured in linear units such as inches or yards.
- area
- The amount of surface covered, measured in square units.
- square unit
- A square with side length 1 unit, used to measure area.
- four times the area
- An area made from four equal copies of the original area.
- four more square
- An additive increase of 4 square units, not four copies and not four added to a side length.
- units
page 3
MATERIALS
Use each source lesson's own materials list. Add these unit-only items:
- Checkpoint 1 and Checkpoint 2 pages, one per child
- Squared paper, rulers, colored pencils and scissors
- Cut-apart performance-task cards, one per pair
- Culminating-task recording page, one per child
ASSESSMENT PLAN
Daily evidence
Keep the two measures with units from lesson 1, the tiled rectangle and equation from lesson 3, and the two labeled field representations from lesson 6.
Checkpoint 1, after lesson 3: Two measures, two units For a 7-inch by 3-inch rectangle, find perimeter and area and state which question each answers. Look for: 20 inches around and 21 square inches covering the rectangle. A child who writes both in inches has not separated the measures.
Checkpoint 2, after lesson 6: Four times, or four more?
A field is 10 yards by 20 yards, so its area is 200 square yards. Find an area four times as large and an area four square yards greater. Look for: 800 square yards and 204 square yards, each matched to the correct phrase.
Culminating task: Two rectangles, four comparison sentences
Each pair draws the rectangle on its task card, finds area by rows and perimeter by summing all four sides, then builds a larger rectangle from the stated number of equal copies. Students shade the added copies and write multiplicative and additive comparisons in both directions.
- LESSON 1
- One rectangle, two measures, and which question each answers
- SKILL LESSON
- Zachary Zormer, Shape Transformer: A Math Adventure lesson 1, The Same Card, Two Different Numbers - Grade 4 - 20 minutes
- FOCUS
- Distinguishing perimeter from area on the same rectangle
I CAN
I can produce and label two different measures from one rectangle.
BIG IDEA
The same side lengths can produce perimeter and area; the question and the unit tell which measure is wanted.
SUCCESS
The child sorts four questions to the correct measure and identifies the words and units that decide.
CONNECT |
5 MIN
Hold up a 4-inch by 6-inch card and ask, 'How big is it?' Record all defensible answers without choosing one yet.
TAUGHT ON ITS OWN
The book gives the hall pass a perimeter, while its area remains available to be produced from the same dimensions.
SOURCE CORE |
20 MIN
page 4
Pairs run yarn around a 4-by-6-inch card, cut the yarn where it meets, and measure its length. They cover an identical card with 1-inch squares and count the covering.
COLLECT
20 inches and 24 square inches, each written with the measure it represents.
CLOSE |
5 MIN
Pairs sort four questions to perimeter or area, underline the deciding words, and explain why one answer uses inches and the other square inches.
FROM THE SOURCE LESSON
Two 4-by-6-inch cards per pair; yarn; inch rulers; 1-inch paper squares; scissors; pencils; question and word cards.
Watch for
A child may label both answers with the same unit. Ask whether the number came from the length of the yarn or the count of covering squares.
- LESSON 2
- Perimeter from the sides: walk it, then write all four sides as one sum
- SKILL LESSON
- Zachary Zormer, Shape Transformer: A Math Adventure - lesson 3, Twenty Inches Around a Hall Pass - Grade 4 - 20 minutes
- FOCUS
- Finding a rectangle's perimeter from length and width
I CAN
I can find perimeter by moving around every side.
BIG IDEA
A complete trip around a rectangle meets both lengths and both widths.
SUCCESS
All four sides are labeled and the perimeter is written as a four-term sum before any shortcut is used.
CONNECT |
5 MIN
Yesterday one measure came from yarn around the edge. Today students find the same measure from side lengths alone.
TAUGHT ON ITS OWN
The story names a 4-inch by 6-inch card and its perimeter but does not display the calculation.
SOURCE CORE |
20 MIN
Students label all four sides of a 4-by-6 card. They trace around the boundary one side at a time, keeping a running total until returning to the start.
COLLECT
A card labeled 4, 6, 4, 6 and the sum 4 + 6 + 4 + 6 = 20 inches.
CLOSE |
5 MIN
Students write the four-term sum and a shorter equivalent expression. They choose which representation better shows why each side length appears twice.
FROM THE SOURCE LESSON
4-by-6-inch cards; inch rulers; pencils; lined paper; word cards: length, width, perimeter.
page 5
Watch for
Students may label only two adjacent sides. The boundary includes four sides; label each before adding.
- LESSON 3
- Tile the rectangle, count by rows, and write the multiplication
- SKILL LESSON
- Zachary Zormer, Shape Transformer: A Math Adventure - lesson 2, Five Rows of Eight Square Inches - Grade 4 - 20 minutes
- FOCUS
- Finding rectangle area by tiling and multiplying
I CAN
I can find area by tiling and by multiplying.
BIG IDEA
The area equation describes rows of equal square units already visible in the model.
SUCCESS
The child counts by rows and identifies which factor counts rows and which counts squares in each row.
CONNECT |
5 MIN
Yesterday students traveled around the edge. Today they cover the face and produce a different kind of measure.
TAUGHT ON ITS OWN
The book gives a 5-inch by 8-inch example and the area rule; this lesson makes the 40 square units visible first.
SOURCE CORE |
20 MIN
Pairs tile a 5-by-8-inch rectangle with 1-inch squares, label both edges, count by complete rows, and write 5 x 8 = 40 square inches.
COLLECT
The tiled rectangle, edge labels and matching multiplication equation.
CLOSE |
5 MIN
Students find the area of a 3-by-7 rectangle without full tiling, then place one row of 7 tiles to verify what the factors count.
FROM THE SOURCE LESSON
1-inch paper squares; 5-by-8-inch paper rectangles; pencils; lined paper; word cards: area, square inch.
Watch for
Students may count one square at a time. Have them touch a complete row on each count to connect repeated addition with multiplication.
Checkpoint after this lesson
Checkpoint 1 follows: Two measures, two units.
- LESSON 4
- Area from a formula, checked against a count of squares, and two pans compared
- SKILL LESSON
- Kitchen Math - lesson 4, Which Pan Spreads the Batter Thinner? - Grade 4 - 20 minutes
page 6
- FOCUS
- Computing and comparing the areas of two rectangles
I CAN
I can compute two areas, verify them and compare them.
BIG IDEA
A pan's dimensions, its grid model and its product are three representations of the same area.
SUCCESS
Each area is produced by counting and multiplying, and the results agree.
CONNECT |
5 MIN
Students can tile and multiply. Today two rectangles arrive only as dimensions in a sentence and must be drawn.
TAUGHT ON ITS OWN
The book supplies two loaf-pan dimensions and links surface area to baking time.
SOURCE CORE |
20 MIN
Pairs draw both pans on inch grid paper, count each by rows, label the side lengths, and multiply to verify each area.
COLLECT
Two labeled rectangles, each with a counted area and a matching product.
CLOSE |
5 MIN
Pairs identify the larger pan, use the story's sentence to predict which bakes faster, overlay the models, and count the 13-square-inch difference.
FROM THE SOURCE LESSON
Inch grid paper; pan-dimension card; pencils; scissors; word cards: length, width, surface area, square inches.
Watch for
Students may multiply and skip the count. Require agreement between model and product before comparing the pans.
- LESSON 5
- Four times the area: build four copies, find the extra, and halve it
- SKILL LESSON
- Ball Game Math - lesson 4, Four Times as Large, and Only Half to Cover - Grade 4 - 20 minutes
- FOCUS
- Multiplicative comparison of area without multiplying both side lengths
I CAN
I can represent an area four times as large.
BIG IDEA
Four times the area means four equal copies of the original area. It does not mean multiplying both side lengths by four.
SUCCESS
The scale model shows four congruent copies, and the written areas are 600 and 2400 square yards.
page 7
CONNECT |
5 MIN
Students can compute area from side lengths. Today one area is described in relation to another.
TAUGHT ON ITS OWN
The book gives last year's field as 20 yards by 30 yards and says the new field has four times the area.
SOURCE CORE |
20 MIN
Compute 20 x 30 = 600 square yards. On grid paper, draw a 4-by-6 scale model and label its real dimensions 20 yards by 30 yards; each grid step represents 5 yards. Make four identical copies and arrange them edge to edge.
Label the combined area 2400 square yards. Do not count model squares as square yards.
COLLECT
One labeled scale model, four congruent copies, and both computed areas.
CLOSE |
5 MIN
Remove one copy from the four-copy model to reveal the extra 1800 square yards. Split that extra region into two equal parts and identify 900 square yards as half the extra ground.
FROM THE SOURCE LESSON
Grid paper; rulers; scissors; pencils and colored pencils; field-dimension card; word cards: area, four times, extra, half.
Watch for
A child may multiply both side lengths by 4 and create 16 times the area. The four physical copies establish the intended area factor. Also keep scale-model squares distinct from square yards.
- LESSON 6
- Four times the area, or four more square yards of area? The phrase sets the operation
MATH THROUGH THE READING
FOCUS
Ball Game Math - lesson 6, The Word That Sets the Operation - Grade 4 - 20 minutes Separating multiplicative and additive area comparisons
I CAN
I can tell a multiplicative area phrase from an additive one.
BIG IDEA
The number 4 does not choose the operation; the words around it do.
SUCCESS
The student produces 2400 square yards for four times the area and 604 square yards for four more square yards of area.
CONNECT |
5 MIN
Yesterday four copies produced the larger field. Today two words change, and the same starting area produces a very different answer.
TAUGHT ON ITS OWN
The story carries its operation in a phrase rather than an equation.
SOURCE CORE |
20 MIN
page 8
Start with the computed area of 600 square yards. For four times the area, arrange four labeled copies and calculate 4 x 600 = 2400. For four more square yards of area, use an area bar labeled 600, add four unit-square tiles, and calculate 600 + 4 = 604. Do not add 4 to either side length.
COLLECT
Two representations headed by their exact phrases and labeled 2400 square yards and 604 square yards.
CLOSE |
5 MIN
Students write one true sentence about each representation. Partners check the sentence against the model and underline the phrase that selects the operation.
FROM THE SOURCE LESSON
Four scale-model field copies; an area bar labeled 600 square yards; four unit-square tiles; sentence strips; pencils and colored pencils.
Watch for
Students may read four more as four more copies or add 4 to a side length. Keep the 4-square-unit addition on an area bar, not on the field's dimensions.
Checkpoint after this lesson
Checkpoint 2 follows: Four times the area, or four more square yards of area?
- LESSON 7
- Thirteen square inches said both ways, and a time relation that runs opposite
- MATH THROUGH THE READING
- Kitchen Math - lesson 9, Thirteen Squares, Said Both Ways - Grade 4 - 20 minutes
- FOCUS
- Writing area and baking-time comparisons in both directions
I CAN
I can state a comparison both ways and notice when a related comparison reverses direction.
BIG IDEA
Two sentences can describe one area difference, while a second relation on the same pans can point in the opposite direction.
SUCCESS
Four sentences are true of the same models: two about area and two about baking time.
CONNECT |
5 MIN
Students have built and compared areas. Today they state the same 13-square-inch difference from both starting points and compare the pans' baking times.
TAUGHT ON ITS OWN
The book gives two pan dimensions and states that greater surface area usually means less baking time, but it does not write the comparisons.
SOURCE CORE |
20 MIN
Pairs rebuild both pan rectangles, verify each area, overlay them, and count the 13-square-inch difference. They write one area sentence beginning with each pan.
COLLECT
Two overlaid rectangles and four comparison sentences: two about area and two about baking time.
page 9
CLOSE |
5 MIN
Students write the two time comparisons and mark how the comparison direction changes: the pan with more surface area is described as taking less time.
FROM THE SOURCE LESSON
Inch grid paper; scissors; pencils; pan-dimension cards; sentence frames: more area than, less area than, more time than, less time than.
Watch for
Students may copy the direction of the area comparison into the time comparison. Ask which pan the story says bakes faster before the time sentences are written.
CULMINATING PERFORMANCE TASK
Two rectangles, four comparison sentences Draw the original rectangle from the task card at one square per unit. Find its area by rows and its perimeter by adding all four sides. Build the larger rectangle by placing the stated number of identical copies edge to edge.
Shade the added copies and write the multiplicative and additive comparisons in both directions.
COLLECT
Two labeled rectangles, the original perimeter sum, both areas, the shaded difference and four comparison sentences.
WHAT IT ASSESSES
Selecting perimeter or area, using correct units, representing an area multiplier with copies, and stating multiplicative and additive comparisons accurately.
TEACHER KEY AND RUBRIC
Key
- Checkpoint 1: perimeter 20 inches; area 21 square inches.
- Checkpoint 2: starting area 200 square yards; four times the area is 800 square yards; four more
square yards of area is 204 square yards.
- Task A: 3 x 4, area 12, perimeter 14, two copies give 24, difference 12. Task B: 2 x 5, area 10,
perimeter 14, three copies give 30, difference 20. Task C: 4 x 5, area 20, perimeter 18, two copies give 40, difference 20.
STRAND
SECURE LOOKS LIKE
DEVELOPING
Representation Builds the larger area from the stated number of Builds the copy model after a congruent copies and shades only the added prompt or leaves one label copies. incomplete.
Area, perimeter and difference all match the One arithmetic or unit error is Calculation models and carry correct units. corrected from the model.
Meaning Uses linear units for perimeter and square units for Distinguishes the measures but area, and distinguishes times from more. needs a prompt for one comparison phrase.
NOT YET
Multiplies both side lengths by the area factor or draws an unrelated shape.
Area and perimeter are confused or calculations do not match the drawings.
Treats units or comparison phrases as interchangeable.
page 10
Explanation All four comparison sentences are true and can be justified by pointing to the copies and shaded difference.
Three sentences are true or one Sentences conflict with the model. direction is reversed.
TEACHER PLANNING AND HANDOFF
- If a child labels both Checkpoint 1 answers in inches, return to lesson 1; the distinction between
a boundary length and a surface covering is foundational.
- Lessons 5 and 6 now use scale models and area bars. Students calculate the real areas; they do
not draw or count 2,400 one-square-yard cells.
- The performance task says 'built from copies' because multiplying every side length by a factor
would change area by the square of that factor.
- Ball Game Math's perimeter-to-side lesson remains available as an extension for students ready
to add a division step.
Revision status
Second-pass production fixes applied and visually audited. No unit-level standards code has been added.
CHECKPOINT 1 | GRADE 4 Two measures, two units Name
Date
A rectangle is 7 inches by 3 inches. Find the distance around the outside and the area that covers it.
Write each answer with its unit. Which question does each answer?
CHECKPOINT 2 | GRADE 4 Four times, or four more?
Name
Date
A field is 10 yards by 20 yards. Find its area. Then find an area four times as large and an area four square yards greater. Match each answer to the phrase that produced it.
CULMINATING TASK | GRADE 4
Rectangle task cards
Cut apart. Give one card to each pair.
CARD A
Original rectangle: 3 units by 4 units. Build a larger rectangle from 2 identical copies.
CARD B
Original rectangle: 2 units by 5 units. Build a larger rectangle from 3 identical copies.
CARD C
Original rectangle: 4 units by 5 units. Build a larger rectangle from 2 identical copies.
CULMINATING TASK | GRADE 4
Two rectangles, four comparison sentences
Name Date
page 11
Draw the original rectangle from your card. Find its area and perimeter. Build the larger rectangle from the stated number of copies and shade the added copies. Complete the four comparison sentences below.
The larger rectangle has ______ times the area of the original rectangle.
The original rectangle has 1/______ the area of the larger rectangle.
The larger rectangle has ______ more square units than the original rectangle.
The original rectangle has ______ fewer square units than the larger rectangle.
page 12