Factors and Prime and Composite Numbers: A Hands On Lesson

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4.8 (241 ratings)

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The Teacher Studio

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Grade Levels

3rd - 5th

Subjects

Arithmetic, Basic Operations, Other (Math)

Resource Type

Lesson

Standards

CCSS5.NBT.B.5

CCSS4.OA.B.4

CCSSMP1

CCSSMP4

CCSSMP7

Formats Included

Pages

28 pages

$3.95

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My students have loved using this resource. The attention to detail is amazing, and I love how easy it was to use. The directions were clear, and my students were very engaged! Thank you!

— Kayla T.

Rated 5 out of 5

I used this as part of my observation and we came back to it over several days! This was an amazing resource for teaching the basics before moving on to other ways of finding factors!

— Heather F.

Rated 5 out of 5

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Description

Prime numbers, composite numbers, factors, and multiples can be confusing concepts for intermediate students--and tricky for teachers to teach! Use this engaging hands-on lesson to really help them see how these terms relate to each other--all by using arrays. Basic multiplication concepts are so essential.

Let this easy-to-use, engaging lesson help!

I have included the actual blog posts and full directions with photos to show you this lesson in action, suggestions for anchor charts or classroom displays, and any forms or sheets you would need to do it yourself! It's like professional development at your fingertips!

This resource is meant to be a two-day lesson to help you introduce the concept of multiplication arrays, factors, and prime numbers through a "simulation" where students imagine they work at a candy factory and need to package chocolates into rectangular arrays.

Through this exploration, they build arrays, find combinations of factors, and learn about what prime and composite numbers are. Although written as a 2 day lesson, this possibly could extend to three days--especially if you take advantage of the enrichment opportunities included!

This exploration is a great way for third and fourth grade students (or 5th graders needing remediation) to explore the relationship between arrays, multiplication number sentences, and the concept of “prime” versus “composite”.

Check out the preview for more details!

What does this resource include?

Low-ink student packet
all directions
photographs of the activity in action
differentiation ideas and resources
2 exit slips to help monitor understanding.

If you need to teach this concept, let this exploration be the center of your instruction!

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Total Pages

28 pages

Answer Key

Included

Teaching Duration

2 days

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Standards

to see state-specific standards (only available in the US).

CCSS5.NBT.B.5

Fluently multiply multi-digit whole numbers using the standard algorithm.

CCSS4.OA.B.4

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

CCSSMP1

Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

CCSSMP4

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.

CCSSMP7

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.

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