4th grade math activities

The zoo rebuilt so 4th graders fence a real budget with area and perimeter, five more activities by standard, a free printable, and the standards each one teaches.

  • By Skyler Carr, co-founder and CEO, Mission.io
  • Last updated

Who we are. Mission.io makes Missions: teacher-led, whole-class simulations where students use what they’re learning to work through a real scenario together.

Everything on this page works without us. The standards this page teaches are at the end, with a Mission where one exists, free. (There are four, and A Fraction of the Problem is the one with a possible saboteur on a frozen planet. The evidence comes in fractions.)

On this page

What 4th grade math looks like

Fourth grade math activities are problems where the class has to use the math to decide something, argue about whether the numbers are right, and leave each student answerable for a piece. This page teaches 15 of the 28 4th grade Common Core math standards, with an activity for seven of them and a Mission for eight.

The year has three big jobs. Multi-digit multiplication, and division with multi-digit dividends (4.NBT.B). Fractions: equivalence, adding and subtracting with like denominators, and multiplying a fraction by a whole number (4.NF). And analyzing shapes by their properties: lines, angles, and symmetry (4.G, with angle measure in 4.MD.C). Around them sit multiplicative comparison, factors, and patterns (4.OA), place value and rounding (4.NBT.A), and the measurement cluster where area and perimeter move from counting squares to the formulas (4.MD.A).

You know the activity that usually stands in for area and perimeter: grid paper, a list of animals, a rectangle for each one, and a fence total at the bottom. Who checks that total? Usually nobody, and nothing happens if it’s off. Here, the fence bill decides whether the last animal moves in.

Six things that turn an exercise into math

Math isn’t short on time: grades 3 to 5 average about 63 minutes a day on it (2018 NSSME+). It’s short on talk. Observers in more than 2,500 first, third, and fifth grade classrooms found about 90% of instructional time was whole-group lecture or seatwork, and under 10% was small groups (Pianta and colleagues, 2007). And in 2024, 39% of fourth graders scored at or above Proficient in math (NAEP). Talk is the gap worth closing, because cooperative learning beat whole-class instruction on achievement, and the effect was stronger in science and math than in social sciences and languages (Kyndt and colleagues, 2013).

  1. 1. A real problem with stakes the class can feel.

    “Find the perimeter” is an exercise. “The fence budget is 600 dollars, and over it, one animal doesn’t move in” is a problem.

  2. 2. Apply, don't recall.

    A second round that only works with the numbers from the first. If the zoo can be finished without the formulas, it isn’t a math activity.

  3. 3. Group goals with individual accountability.

    The one most math projects miss: one kid draws, three kids color. When the group shared a goal and each student answered for a part, 84% of studies found a positive effect; without both, 17% (Slavin, 1991).

  4. 4. The teacher leads the thinking.

    Three questions at the grid (which pen has the biggest perimeter for its area, what does the fence total say about the next one, what changes when two pens share a fence) beat a worksheet of twenty at the desk.

  5. 5. A debrief where the class argues it out.

    The layout is the setup. The argument afterward, about whose zoo spent the least fence and why, is the practice the standards name: construct viable arguments and critique the reasoning of others (MP3).

  6. 6. A way to see who did what.

    If you can’t tell which student used the formula and which one counted squares, you can’t teach the formula. You can only grade the fence total.

Fence costs five dollars a meter. Draw like you’re paying.

The sheet at the end of the next section carries the zoo’s animal cards, grid, and cost ledger, with an answer key for you. Get the sheet →

The zoo, rebuilt for 4th grade (4.MD.A.3)

Lay out a zoo on grid paper: animal enclosures with required areas and perimeters, fencing costs, and paths, then total the fence. It’s the area and perimeter project on nearly every 4th grade list, because 4th grade is where area and perimeter move from counting squares to the formulas, and a zoo gives every enclosure a reason to have a size. The way it usually runs is solo or as homework, with one kid drawing and nothing going wrong if the math is wrong. Here’s the version that hits all six.

Time
55 minutes. The 45-minute cut: three animals instead of four, and one budget cut.
Groups
Fours. With 28 students, seven groups of four exactly.
Supplies
7 large grid sheets (or four letter-size grids taped together), pencils, the animal cards on the sheet, and a calculator per group for the Fence Accountant (optional; the multiplication is within reach by hand). About $0.
Standards
4.MD.A.3 (apply the area and perimeter formulas for rectangles to real problems), with 4.OA.A.3 (multistep word problems) once the fence budget is in, and the practices MP4 (model with mathematics: the grid is the land) and MP1 (persevere through the constraints).

  1. Teach first, 10 minutesApply

    Draw a 6 by 4 rectangle on the grid and ask for the area and the perimeter two ways: count, then the formula. Then draw a 12 by 2 and ask which one the animal would rather live in, and which one costs more fence. Name the idea that runs the lesson: same area, different perimeter, different cost.

  2. The problemStakes

    The zoo has 400 square meters of land and $600 for fencing at $5 a meter, and it has to house four animals with minimum areas (60, 50, 40, and 30 square meters, on the sheet’s cards) plus a path. Every enclosure meets its minimum, the fence bill stays at or under $600, and everything fits on the 20 by 20 grid. Rectangles only, and two enclosures can share a fence only if the team shows why that saves money. Say the stakes out loud: if the bill comes in over $600, the zoo opens without one animal, and the team picks which.

  3. Four roles, one job eachAccountability

    On the sheet, and everyone signs their role’s box.

    • Planner

      The only pencil on the master grid.

    • Area Checker

      Computes each enclosure's area with the formula, and signs it off or sends it back.

    • Fence Accountant

      Computes each perimeter, multiplies by $5, keeps the running total, and announces when the budget hits 80%.

    • Advocate

      Argues for the shapes that are better for the animals, and has to use area and perimeter to do it.

  4. You lead the thinkingTeacher leads

    Three questions, asked at the grid: Which enclosure has the biggest perimeter for its area, and why? What does the running fence total say about the next enclosure? If two enclosures share a fence, what changes in the perimeter math? The hardest part is not counting the squares for them. Let them find out the formula is faster.

  5. Two rounds, so the first answer has to be rightApply

    Round one is a first layout and a full cost. Round two: the budget drops to $500 (the second budget line on the sheet), and the team revises one or two enclosures. The revision is where the formula gets used instead of counted.

  6. The debrief, 10 minutesDebrief

    Two team grids under the camera. Which team spent the least fence for the same area, and what did its rectangles look like? When the budget dropped, what did you change: the area, the shape, or a shared fence? Who in your group argued for something the Planner didn’t draw, and would it have saved money? The first question is the lesson: for the same area, the closer a pen is to a square, the cheaper its fence.

  7. See who did whatSee who did what

    The observation sheet, four behaviors per student: used the formula (not counting) for an area or perimeter, argued with a number, disagreed with a reason, changed their mind with a reason. Tally while you walk the seven tables; you’ll catch about half the room. This one is quiet work, so a full loop is possible.

(The same 60 square meters costs $230 of fence as a 3 by 20 strip and $160 as a 6 by 10. Seventy dollars is a lot of zoo.)

Leave round one’s grid on the table when round two starts. What changed between the two is half the debrief.

The zoo fence budget, free

Emailed now, ready to copy: the teacher page, the Planner, Area Checker, Fence Accountant, and Advocate role cards, the four animal cards, the 20 by 20 grid, the cost ledger with both budget lines, an answer key, and the four-behavior tally.

It’s on its way.

Check your inbox for the zoo fence budget.

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Five more 4th grade math activities, by standard

Five more on every 4th grade list: what each one is, how it usually runs, and what it needs to be a math activity, in the order the standards run.

Factors, budgets, line plots, angles, symmetry

2. Factor rainbows and arrays (4.OA.B.4)

Needs paper and colored pencils, grid paper for the arrays. Individual, usually.

Students list every factor pair of a number, write the factors in order, and connect each pair with an arc so the pairs make a rainbow, or they build each pair as an array on grid paper. It’s tidy practice, and the rainbow shows at a glance when a pair is missing. As usually run, though, it’s a solo drill with no problem behind it and no talk afterward, and you can’t see who reasoned it out. That misses four of the six, so treat it as practice and give the problems to something else.

The fix

  1. Keep it to ten minutes of practice, and let a problem like the zoo above do the rest.
  2. Pick numbers with lots of pairs, like 24 or 36, so a missing pair is worth hunting for.

No page for this one; the four misses are the fix.

3. Plan a party on a budget (4.NBT.B.5, 4.OA.A.3)

Needs a menu with prices, a guest list of 25. Individual, usually.

Each student gets a menu with prices and a guest list of 25, prices pizza, juice, and plates for the whole party, and totals the bill. It already has a real problem and real multi-step multiplication, which puts it ahead of most worksheets. As usually run, though, each student works alone, and a final total can’t tell you who multiplied and who added up a neighbor’s numbers.

The fix

  1. Plan it in groups of four with one job each, the way the zoo does: one picks the menu, one multiplies each item for 25 guests, one checks every line, and one keeps the running total.
  2. Halfway through, cut the budget, so the group has to decide what to change and show the math for it.
  3. Have each student sign the lines they worked.

No page for this one; the zoo above is the same fix, built out.

4. The fraction line plot of measured objects (4.MD.B.4)

Needs rulers marked to the eighth inch, pencils or other objects to measure, a line plot.

Students measure pencils, crayons, or other small objects to the nearest eighth inch, mark every length as an X on a line plot, and read the differences off the plot, like how much longer the longest pencil is than the shortest. It’s the standard’s own task, and subtracting fractions from the plot gives the measuring a use. As usually run, though, one student does the plotting for the table, and the plot gets made because the worksheet asks for it.

The fix

  1. Give the plot a question to answer, like how long the class pencil box needs to be, the way the 3rd grade airplanes answer how long the gym lane should be.
  2. Pair a Measurer, who reads each length to the eighth inch aloud, with a Checker, who rereads it before it goes on the plot.
  3. Have each student place and initial their own Xs.

See the airplane line plot rebuilt for 3rd grade →

5. The angle scavenger hunt with a protractor (4.MD.C.6)

Needs a protractor and a recording sheet. A walk around the room.

Students walk the room with a protractor, find angles in the corner of a window, the hands of the clock, an open door, and measure each one to the nearest degree. The protractor gets real use on angles that aren’t printed on a page. As usually run, though, students wander alone or in loose groups, and a sheet of numbers can’t tell you who lined up the protractor and who copied.

The fix

  1. Pair students, and have the Measurer place the protractor and read the angle aloud.
  2. The Recorder checks the reading, sketches the angle, and writes it down, and the pair swaps every three angles.

No page for this one; row 10 below, Sunken Starship, is the Mission on angles.

6. Symmetry with mirrors (4.G.A.3)

Needs small mirrors and shape cards. A station.

At a station, students stand a small mirror on a shape card to see whether the reflection rebuilds the whole shape, then draw every line of symmetry they find. The mirror does honest work, since a wrong line shows up right away. As usually run, though, it’s a quiet solo station, and a page of lines can’t tell you who tested each one and who guessed.

The fix

  1. Pair students: one holds the mirror and tests each line, and the other draws it only after both agree it works.
  2. Have the pair write how many lines each shape has, with both names on the card, and swap jobs on every shape.

No page for this one; the two misses are the fix.

  • Our part · We make Missions

    Then the unit has somewhere to go

    Plenty of teachers rebuild these by hand every unit, and it works. A Mission is a teacher-led, whole-class simulation built from a unit you teach. The zoo is area and perimeter (4.MD.A.3), and no Mission carries that code. Riptide sits in the same cluster, with conversions and money word problems. After the zoo, run Riptide.

    You're at the helm, not on the hook.

    A Fraction of the Problem: fractions, as a Mission

    A Fraction of the Problem · 4th grade · About 30 minutes · One device per student, plus your projector · Free with a teacher account

    An elementary classroom on its feet around Chromebooks, one boy's hand stretched straight up, and a Mission screen on the far wall.
    A room on its feet around the Chromebooks, and one hand all the way up.

    Unexpected ice storms are wrecking a research camp on the frozen planet Korè. The crew has to use what it knows about fractions to investigate the ice and shut down its source, and to work out whether the storms are natural or whether somebody is behind them. The story plays on the projector. The work happens at seven stations (Command, Engineering, Medical, Security, Science, I.T., Operations) and in the arguments between them.

    Every student is assigned to a team, and each team’s work is themed to it, from its own information and challenge to the same problem the rest of the crew is solving. The team gives a student a role in the story and people to lean on while you move between teams. You’re at the helm, asking which fraction is bigger, and how they know.

    It’s built to two fraction standards (4.NF.A.2 and 4.NF.B.3), and the vocabulary is the unit’s: numerator, denominator, equivalent, greater than, less than. Save it for the end of the fraction unit, and tell the class it’s coming: the camp only gets saved by a crew that can say which of two fractions is bigger, and prove it. The lesson prepares them. The Mission is what they’re preparing for.

    “Unlike other tech programs in the district that often have students working in isolation or in pairs, Mission.io emphasizes true collaboration.”

    Lorilee Johnson, District specialist, Alpine School District, UT

    Will it work in my room?

    Students join with a class code: no student accounts, no student email, no passwords. Chromebooks, laptops, or tablets, plus your projector. Free for teachers, no credit card. Student data is covered by COPPA and FERPA, and we signed the Student Privacy Pledge. At about 30 minutes, A Fraction of the Problem fits inside the average 3 to 5 math block of about 63 minutes, with time left for the debrief.

    START FREE →

    Communication first, then two of the year's four

    What the report shows

    A Mission.io class report: the class score in each of six skills, from knowledge and application to collaboration, critical thinking, and resilience, with the class chart across the year below.
    A class report from a real Mission: the class score in each of six skills, then each skill across the year.

    Every Mission produces a report for every student, built from what that student did across the whole Mission, on the skills the Mission captured. The six it can capture are Knowledge, Application, Initiative, Collaboration, Critical Thinking, and Resilience. The first two are what a test already sees. The other four are the human skills every school promises. The test shows what they know. The report shows the rest. SEE THE EVIDENCE →

    You taught it. Now find out who can use it.

    Who's behind it

    Mission.io is a research and design organization with one job: make collaborative, active learning something a teacher can run every unit instead of once a semester, and put a report in your hands when it’s over. Over a million students have run a Mission. The research behind them is funded by the National Science Foundation and the U.S. Department of Education’s Institute of Education Sciences, and Mission.io meets ESSA Level II standards, as validated by Instructure.

    4th grade math standards and the Missions on them

    Fifteen of the 28 4th grade Common Core math standards, each with the Mission or the activity on this page that covers it. Eight have one of the year’s four Missions, numbered 7 to 10, and A Fraction of the Problem is one of them. Each code links to its standard on thecorestandards.org.

    Operations and algebraic thinking (4.OA)

    Multistep word problems, and factors. The zoo’s fence budget and the party both run on the multistep standard, and factor rainbows teach factor pairs.

    4th grade operations and algebraic thinking standards, with the activities on this page for the ones they teach.
    NumberThe standardMissionMinutes
    4.OA.A.3 Multistep word problems with the four operations, remainders includedOn this page: 1. The zoo and 3. The party budget
    4.OA.B.4 Factor pairs and multiples, and prime or composite, for 1 to 100On this page: 2. Factor rainbows

    Number and operations in base ten (4.NBT)

    Rounding, and the operations. Power Struggle rounds and adds its way through a fuel problem, and the party budget multiplies.

    4th grade base ten standards, with the Mission for rounding and adding.
    NumberThe standardMissionMinutes
    74.NBT.A.3, 4.NBT.B.4 Round multi-digit numbers to any place; add and subtract fluently with the standard algorithmPower Struggle28
    4.NBT.B.5 Multiply up to four digits by one digit, and two two-digit numbersOn this page: 3. The party budget

    Number and operations in fractions (4.NF)

    Comparing fractions, and building them from unit fractions. A Fraction of the Problem is built on both.

    4th grade fraction standards, with the Mission for comparing and building fractions.
    NumberThe standardMissionMinutes
    84.NF.A.2, 4.NF.B.3 Compare fractions with unlike denominators; build fractions from unit fractions, and add and subtract like denominatorsA Fraction of the Problem30

    Measurement and data (4.MD)

    Conversions, area and perimeter, line plots, and angles. Riptide is the conversions Mission, and the zoo teaches area and perimeter. Angle measure (4.MD.C.5) sits with Sunken Starship, under geometry.

    4th grade measurement and data standards, with the Mission for conversions and the activities on this page.
    NumberThe standardMissionMinutes
    94.MD.A.1, 4.MD.A.2 Convert within one system of units; word problems with distance, time, liquid volume, mass, and moneyRiptide40
    4.MD.A.3 The area and perimeter formulas for rectangles, in real problemsOn this page: 1. The zoo
    4.MD.B.4 Line plots of measurements in fractions of a unit (1/2, 1/4, 1/8)On this page: 4. The line plot
    4.MD.C.6 Measure angles in whole degrees with a protractor, and sketch themOn this page: 5. The angle hunt

    Geometry (4.G)

    Lines, angles, and symmetry. Sunken Starship is the angles Mission, and the mirrors teach symmetry.

    4th grade geometry standards, with the Mission for lines and angles.
    NumberThe standardMissionMinutes
    104.G.A.1, 4.MD.C.5 Points, lines, rays, and right, acute, and obtuse angles, and what an angle measuresSunken Starship28
    4.G.A.3 Lines of symmetryOn this page: 6. Symmetry with mirrors
    START FREEMISSION BRIEF →

    Free teacher account, no card. Start with the Communication Mission, marked Start here in your library, then A Fraction of the Problem or Riptide, each after its 5-minute Teacher Preview.

    Also at this grade

    The 5th grade math activities page rebuilds the cereal box for the year after; the 3rd grade math activities page is the year before. The 4th grade problem solving activities page rebuilds the handshake problem, with Power Struggle as its Mission, and the 4th grade STEM activities page rebuilds the parachute drop and lists every 4th grade Mission by subject.

Questions 4th grade math teachers ask

Which of these fits a math block?

Grades 3 to 5 average about 63 minutes of math a day, and all four 4th grade Missions fit inside it: Power Struggle and Sunken Starship at 28 minutes, A Fraction of the Problem at 30, and Riptide at 40. The zoo needs 55, or the 45-minute cut.

Which 4th grade math standards does this page teach?

Fifteen of the 28 4th grade Common Core math standards, across five domains: 4.OA, 4.NBT, 4.NF, 4.MD, and 4.G. Four Missions carry eight of them, starting at 4.NBT.A.3, 4.NF.A.2, 4.MD.A.1, and 4.G.A.1, and seven more are taught by an activity on this page.

Should I let them count squares?

In round one, as a check, yes. The standard (4.MD.A.3) is the formulas, and round two’s budget cut is where the formula gets used instead of counted. It’s also the first behavior on the tally: used the formula, not counting. A student who counts every square in round two is telling you something worth a question at the grid.

How do I grade a math project fairly?

Grade the reasoning and the behaviors, not the prettiest zoo. The cost ledger is one grade: does every enclosure meet its minimum, is the fence total right, and can the Fence Accountant show the work? The four-behavior tally over two or three activities is the other. A team that came in under budget by luck shows up in the ledger, and now you can ask how.

Is this aligned to my state's standards, not just Common Core?

Each Mission page lists its Common Core codes and the state sets it maps to. A Fraction of the Problem also maps to Texas (TEKS), Florida (B.E.S.T.), and North Dakota’s math and ELA standards.

The zoo opens when the fence bill adds up

Day one, a problem by hand with the sheet. Day two, Riptide after the zoo, or A Fraction of the Problem when the unit is fractions. Each comes with a 5-minute Teacher Preview, and both are free.

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