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Winter Multiplication Arrays Real World Math Project | Digital & Printable

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Winter Wonderland Array Architects is designed to help your third grade students apply their knowledge about equal groups, arrays, multiplication and division fact families, and properties of multiplication as they design arrays and solve word problems throughout this campground-themed simulation project.

A digital and printable version of this resource are included making it easy to use whether you are teaching in person, using digital distance learning, or a combination of both.


During this winter-themed math project your third grade students will work toward becoming an Array Architect for Snowflake Valley. As part of their job application process, they must create a winter wonderland festival map that includes a variety of arrays and equal groups, along with a festival directory that features all the equations and problem solving that corresponds with their unique design. 

Here are the steps your students will take as they work towards being hired as an Array Architect:

★ Sketch a Winter Wonderland Festival map, which includes arrays and equal groups.

★ Label the arrays and equal groups on the festival map.

★ Identify the multiplication sentence, repeated addition sentence, and fact family related to each array on their map.

★ Analyze each array on their map, and its relation to the various multiplication properties (Associative, Commutative, Distributive, and Identity Property).

★ Complete a self-assessment of their project using a three-part rubric.



Teacher Guide - a 7-page guide that includes detailed steps for successfully incorporating this resource in your classroom.

Student Guide - a printable and digital version of the student guide is included. This 16-page guide includes detailed instructions and visuals to help your students complete each step of this simulation successfully. The format of this guide makes differentiation easy. Use it as a supplement to your verbal instructions as you provide scaffolding or let your more advanced students work through each step of the project independently.

Printable & Digital Recording Sheets - Reproducible pages or Google Classroom-ready digital slides that guide students through the process of designing a wonderland map, writing the repeated addition sentence, multiplication sentence, the fact family related to the arrays drawn on their map, and answering word problems that help them analyze their arrays and use each array to demonstrate their knowledge of the properties of multiplication.

Editable Rubric - a 4-point rubric students can use to self-assess their ability to neatly design a map featuring arrays and equal groups, apply multiplication skills while writing their festival directory, and demonstrate the habits of a self-directed learner. The same rubric can be used by the teacher to provide a score for student work. An editable version of this rubric is also included.

Sample Project - a completed sample of the project to help you provide scaffolding to students as needed. You will see the first two pages of the Festival Directory are filled out completely, while pages for arrays C-H only include sentence starters for the word problems.

Completion Certificate - this congratulatory certificate is a little extra something you can share with students when they receive their project feedback if you’re looking to bring the project to a close in a more formal way.



This project based learning unit requires the application of students’ knowledge of equal groups, arrays, multiplication and division fact families, and properties of multiplication. Throughout the process of the Winter Wonderland Array Architects simulation, students will have the opportunity to apply their knowledge through creative design, engage in rigorous problem solving incorporates their math knowledge, and build organization skills as they plan and execute this multi-day project.

Every step of the Winter Wonderland Array Architects experience is outlined in a project guide that includes clear visuals and step-by-step instructions. Rubrics and reflection prompts will encourage your students to reach their learning goals. 

The format of this project gives students the opportunity to exercise the standards for mathematical practice, share their creativity, and display understanding in unique and engaging ways.  

The format of this math simulation guide makes it an ideal resource for:

★ Distance learning

★ At your seat & hands on enrichment during math workshop or guided math

★ Math center work

★ Parent volunteer or teacher’s aide enrichment station

★ A focal point for a multiplication room transformation 



Students who have mastered the ability to interpret and create equal groups and arrays and how they relate to multiplication and division fact families, and the properties of multiplication will have the opportunity to extend their learning and deepen their understanding of multiplication through this math project experience.

This project will help them solidify the multiplication and arrays skills they’ve mastered through real world problem solving rather than being bogged down with worksheets or busy work.

This project also serves as a wonderful alternative assessment that allows you to measure student understanding on a deeper level as a culmination to your multiplication unit.



This simulation guide is designed with student independence in mind. Detailed instructions and checklists are provided for students so they can participate with maximum independence.

You can guide them as needed and pull small groups that help address the more individualized needs of your students. This allows students to work at their own pace and take ownership of their learning.

On the day of the simulation launch, you will take 15-20 minutes to set the scene and teach students how to navigate their materials. After that, your students will be off on an independent math adventure that lasts multiple sessions.



Want to incorporate a project into your multiplication unit, but crunched for instructional time?

This resource makes prepping for project based learning a breeze and makes implementation seamless. The detailed visual instructions on each page of the guide make it possible for students to complete their unique project with maximum independence so you have the time you need to teach or reteach essential place value skills to small groups.

Scoring and providing students with feedback is also when using the included rubric. Each of the three project phases: map design, festival directory creation, and word habits has its own rubric so students can participate in the assessment process as they demonstrate learning, and you can provide them with specific feedback about their work.



♥ “Wow - this project has so much to it and will really show me which of my students have an advanced understanding of multiplication and its properties. They are really enjoying it so far. Thank you!” - Paiges of Learning

♥ “Another quality product from Laura! Such a well rounded summative project to show what students have learned about multiplication and division in such a meaningful way. I've bought many products from you and this one is just like the others....exceptional, rigorous and highly engaging for 3rd graders.” - Whaley

♥ “So well organized and easy to follow! The students can do this independently in third grade and are so proud of their finished products! Great to see a combination between their knowledge and creativity!” - McKenna J.

♥ “Fantastic resource for those long winter days! This was a great review and activity to push students to take their learning a little farther. Thank you!” - Amanda C.



Math Project Based Learning Bundle

★ Bundle of Multiplication Word Problem Solving Task Cards for 3rd Grade

3rd Grade Multiplication & Division Fact Fluency Toolkit

3rd Grade Multiplication & Division Math Games


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Total Pages
62 pages
Answer Key
Rubric only
Teaching Duration
3 Weeks
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to see state-specific standards (only available in the US).
Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (𝑦 – 2)/(𝑥 – 1) = 3. Noticing the regularity in the way terms cancel when expanding (𝑥 – 1)(𝑥 + 1), (𝑥 – 1)(𝑥² + 𝑥 + 1), and (𝑥 – 1)(𝑥³ + 𝑥² + 𝑥 + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression 𝑥² + 9𝑥 + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(𝑥 – 𝑦)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers 𝑥 and 𝑦.
Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.


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