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# Real World Math Problems & Engaging Math Lessons

Below are problem based math lesson, three act math tasks and activities I use with my classes.

If you have never taught a lesson like these I suggest you start with Dan Meyer’s post, then head to read about the Make Math Moments 3-Part Framework and finally you can read through my Peek into My Classroom page

Feel free to use and edit these lessons to suit your grade band and individual students.

## New to Using 3 Act Math Tasks?

Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

### Flavour Frenzy

Data Literacy lesson investigating Fractions, Percentages & Relative Frequency Tables in a curious Problem Based Math Lesson.

### Stack ‘Em Up

Real world 1- and 2-digit multiplication lesson investigating associative, commutative and distributive properties with arrays & area models

### Rising Water

Investigate integer operations through real world math problems involving melting glaciers, rising and falling sea levels and changing temperatures.

### Just Keep Digging

Dive into this 5-Day Problem Based Math Unit focused on solving situations involving the multiplication and division and positive and negative integers.

### Grass Is Greener

Use the row and column structure of the array to determine the area of a rectangle through the context of laying sod in order to generalize a formula.

### Going Up?

Problem Based Math Unit focused on representing, describing, and solving contextual problems involving the addition and subtraction of integers.

### Big Tipper

Calculate Rates or “Unit Rates” using strategies and models with ratio and rate reasoning to determine which store has the better buy.

Calculate Rates or “Unit Rates” using strategies and models with ratio and rate reasoning to determine which store has the better buy.

### Bear Builder

Percent lesson that builds fluency using various strategies in a curious Problem Based Math Lesson.

### Counting Cars

Explore addition through the strategy of counting on and using the part whole model as a tool for thinking and tool to represent thinking.

### How Many Cookies? How Many Crackers

Munch on this unit of 3 Act Math Task lessons focused on solving addition and subtraction problems within 100 using place value strategies.

### Fruit Picking

Dive into this 5-Day Problem Based Math Unit focused on strategies to efficiently subtract numbers within 20 using a 3 act math task style approach.

### Bowling Pins

Explore addition through the strategy of breaking apart numbers to make ten or making combinations of ten by decomposing and recomposing numbers.

### Magic Rectangle

Investigate the relationship between the volume of prisms and pyramids with the same base to emerge the volume formula for prisms and pyramids.

### Candle Burning

Investigate the relationship between the volume of prisms and pyramids with the same base to emerge the volume formula for prisms and pyramids.

### Prisms and Pyramids

Investigate the relationship between the volume of prisms and pyramids with the same base to emerge the volume formula for prisms and pyramids.

### Donut Delight

Students will explore multiplication and division with efficient strategies that can be used with large numbers using the array model.

### Hot Chocolate

Engage in a low-floor, high-ceiling series of tasks where students can utilize counting, addition, multiplication, division and ratios and rates.

### Reeses Peanut Butter Cups

Explore multiplication with partial products and extend to ratio and rate reasoning through a unit of context-rich math task lessons.

### Gummy Worms

Explore addition and subtraction structures conceptually through a unit of context-rich math task lessons and purposeful practice opportunities.

### Pizza Party

Explore quotative division of fractions through the context of servings of pizza at a party. Real world math task dividing fractions.

### Salting The Driveway

Explore dividing fractions conceptually through the context of salting a driveway and scaling to reason through these 3 act math task lessons.

Explore the volume of a rectangular prism by determining the number of boxes of Girl Guide cookies contained within the larger case.

### Voting Booth

Investigate a real world math problem including percentages with extensions to creating and solving direct variation linear equations.

### Shot Put

3 Act Math Lessons involving solving equations using equivalence and algebraic substitution and elimination to solve systems of equations.

### Scavenger Hunt

In this Scavenger Hunt 3 act math style unit of lessons, students will explore data management, mean as the great equalizer and bar graphs

### Wooly Worm Race

3 Act Math style unit of lessons involving represent, order, and compare fractional amounts based on the distances travelled by caterpillars

### Snack Time!

Dividing whole numbers through partitive division resulting in a fractional amount & dividing ratios to reveal a rate 3 Act Math Tasks

### Niagara Falls

Problem Based Math Lessons focused on understanding Division of Whole Numbers and Percent 3 Act Math Task Style.

### Piggy Bank

Number talk and practice problem BLM handout exploring the relationship between fractions and decimals using the money model.

### Whirlpool Aero Car

Context leading students to multiply whole numbers by decimals in a 5 lesson, 3 Act Math Task series of lessons with resources

### Shovelling the Driveway

Explore multiplying fractions through a 3 act math task using the area model.

### The Make Math Moments 3-Part Framework Guidebook

How do you create a culture of engagement and participation in your math class to ensure students are leaning in to learn?

Then, once students are leaning in, how are we going to tackle new mathematical ideas in a way that builds the necessary conceptual understanding and develops procedural fluency over time?

Finally, how can we craft our lessons in such a way that every student can access the mathematical content and don’t throw their arms up in frustration?

### No Bikes Allowed

Students will use their understanding of pattering to bring about topics such as linear relations, rate of change, slope, and solving equations.

### Double Jenga [3 Act Task]

Let’s Build a 3-Act Math Lesson together. What could you do with this?

proportions

### Chocolate Mania [3 Act Task]

A yummy, belly aching activity that stretches proportional thinking across many grades levels.

Least Common Multiple

### Hour Glass Multiples

In this 3-Act Task students will be presented with a puzzling video of 3 “hour glass” sand timers. Students will solve a brain-teaser like problem while ultimately learning about common multiples and the least common multiple (LCM).

Modelling Data

### Pumpkin Time-Bomb Activity

This fall themed activity asks students to predict how many rubber bands will implode a pumpkin. Use data collected from over 120 exploded pumpkins and create scatterplots to make predictions.

Similar Triangles

### Eye To Eye – A Similar Triangle Problem

Have your students experience similar triangles by getting them curious and out of their seats. Your students will prove and disprove why two people can or can’t see eye to eye in a mirror.

lesson planning

### Fuel Sense Making & Black Box Defrost

Things are warming up! Students will solve a proportion problem while you learn how to plan and ignite your moves!

angles

### Polygon Pile Up

A puzzling display of angles, polygons, and parallel lines. Can you determine that one angle?

linear relations

### Turbo Texting

Students break out their devices and text away to discover the relationship between the length of a message and how long it takes to text it.

Optimization

### Perimeter Jumble

This takes the classic maximizing the area of a rectangle problem and adds elements of curiosity and purposeful practice to help reveal the relationship.

proportion

### Really Big Lights – A math problem

How big are those holiday lights? How many lights will we need to string up. Use proportional reasoning to help answer these questions.

Liner Relations

### Flippity Flip, Bottle Flip!

This flipping active activity blends volume of cylinders with rates of change and linear relations.

Solving Linear Equations

### Pentomino Puzzles

A Hands-on activity is blended with interactive technology. Students begin with puzzles but ultimately create algebraic expressions and solve equations.

Volume

### Energy Bites! – 3 Act Math

A yummy lesson where students use volume of cylinders and spheres to determine how many energy bites are made from a recipe.

Linear Systems

### Two Trains…

The classic two trains are approaching each other problem without the trains. Students will solve a system of equations to determine the answer to this 3-Act Math Problem.

linear relations

### Reading Relationships – Literacy & Math

Promote literacy while learning math! Students calculate and track over time their words/min reading rate. Students will also explore the relationship between fast reading and comprehension.

Unit Rates

### Fast Clapper

Let’s get a round of applause for this active lesson that asks students to use unit rates or proportions to see if they can beat the fastest clapper in the world.

Parallel Lines

### Make it Parallel – An Activity with Parallel Lines

Students explore properties of parallel lines & transversals. They will create parallel lines on the floor or outside with chalk, and finally use Explain Everything to answer problems.

Linear Systems

### Trashketball – A Spiralled Lesson!

In this multi-strand lesson students will use estimate and calculate how many paper balls fit in a bucket. They then will race to see who can make more shots into the bucket in a minute.

Rates Ratios and Volume

### Proportion Explosion

When will a water balloon explode? How much water does it hold? Use proportions to help!

algebra

### Dora to the Rescue

Finally teach collecting like terms and the distributive property with context! Find the perimeter and area of a counter top using only Doras!

like terms

### Order Up – Making Algebra Meaningful

Teach the need for collecting like terms through problem solving. How much does this order cost?

Unit Rates

### Is Lego Gender Biased?

Use unit rates to help make decisions in consumer gender issues. Is Lego charging more for Disney Princess kits vs. Star Wars kits?

linear

### Knot Again!

A rope magically shrinks! How many knots will make the rope a specific thickness?

exponential functions

### Super Mario – Super Pear Deck

An all-time favourite 3-act task from Nora Oswald! How are the points distributed along the flag pole in Super Mario?

Area of Rectangles

### Spiralling grade 9 applied math

A rich area of rectangles problem with a sequel that extends into optimization.

linear relations

### Popcorn Pandemonium

Students experience rates of change in a race to see who will eat the most popcorn.

Polynomial Functions

### Many Many Volumes

Crowd source the relationship between the volume of a box and the height of the box. Build boxes and use Desmos to investigate.

Volume of Cylinders

### Filling it up!

Use linear relations to determine how many cups to fill a jug of water with an object inside.

Modelling

### Modelling in Clash of Clans

Does the cost of wait time in the game Clash of Clans follow a linear, quadratic, exponential, or other model?

Volume of Prisms

### Minnie’s Juice Cup [3actMath]

How many juice boxes will it take to fill Minnie’s Cup! Use Volume of prisms and cylinders.

Solving Proportions

### SmartCar Smash!

Use proportions to determine how many bird craps could crush a car.

Pythagorean Theorem

### Corner to Corner – 3 Act Lesson

Students use the Pythagorean Theorem to find the length of rope.

Scatterplots

### Vroom

A inquiry activity with a little competition. Who can get their car to the finish line closest without going over? Use lines of best fit