5th Grade  Project 4 weeks

Division Detectives: Ratios, Decimals, Fractions

Michele K
Updated
CCSS.Math.Content.5.NF.B.7
CCSS.Math.Content.5.NBT.B.6
CCSS.Math.Content.5.NF.B.3
CCSS.Math.Content.5.NBT.B.7
CCSS.Math.Content.5.NF.B.6
+ 5 more
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Purpose

Students investigate how division, fractions, decimals, and rates can help solve real decisions about sharing food fairly in their community. Over four weeks, they use real pantry inventory and package data to choose efficient strategies such as ratio tables, open arrays, division notation, partial quotients, and place-value reasoning with powers of 10. The work builds strong understanding of multidigit division, decimal operations, and fraction division while students explain their thinking through notebook captions, partner discussions, gallery-walk feedback, and a final math museum display.

Learning goals

Students will solve real community food pantry problems by choosing and explaining efficient strategies for whole-number, decimal, and fraction division, including partial quotients, equivalent ratios, open arrays, ratio tables, and division notation. They will use rates and ratios to compare package sizes, inventory amounts, and family needs, and decide how supplies can be shared fairly and reasonably. Students will recognize patterns when multiplying and dividing by powers of 10, use exponents to name those patterns, and apply place-value understanding to estimate and compute decimal products and quotients. They will communicate their mathematical thinking clearly through notebook captions, partner discussions, feedback routines, and a final museum poster and planning board based on pantry data.

Standards
  • [Common Core] CCSS.Math.Content.5.NF.B.7 - Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
  • [Common Core] CCSS.Math.Content.5.NBT.B.6 - Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • [Common Core] CCSS.Math.Content.5.NF.B.3 - Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
  • [Common Core] CCSS.Math.Content.5.NBT.B.7 - Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
  • [Common Core] CCSS.Math.Content.5.NF.B.6 - Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Competencies
  • Critical Thinking & Problem Solving - Students consider a variety of innovative approaches to address and understand complex questions that are authentic and important to their communities.
  • Effective Communication - Students practice listening to understand, communicating with empathy, and share their learning through exhibiting, presenting and reflecting on their work.
  • Content Expertise - Students develop key competencies, skills, and dispositions with ample opportunities to apply knowledge and engage in work that matters to them.
  • Collaboration - Students co-design projects with peers, exercise shared-decision making, strengthen relational agency, resolve conflict, and assume leadership roles.
  • Academic Mindset - Students establish a sense of place, identity, and belonging to increase self-efficacy while engaging in critical reflection and action.

Products

Students will create ongoing notebook entries with labeled ratio tables, open arrays, division notation, estimates, and short captions explaining why a chosen strategy fits each pantry-sharing problem. Midway through the unit, teams will produce draft planning charts and model cards for a gallery walk, revise them using clear/question/suggestion feedback, and refine their calculations with pantry inventory data. By the end, students will present a community pantry planning board and a collaborative data display showing how whole-number, decimal, and fraction division can be used to compare package sizes, rates, and fair shares for families. Each student will also contribute to a math museum poster and a partner presentation that explains one multistep decision using a visual model and justified solution.

Launch

Kick off with a “Division Detective” experience in which students rotate through short mystery stations using food pantry clues: package labels, inventory cards, family-size needs, decimal quantities, and rate puzzles. At each station, teams estimate first, then choose a tool such as a ratio table, open array, or division notation to decide how supplies could be shared fairly and efficiently. End with a reveal from the local food pantry partner through a note, photo set, or brief video asking students to help answer how division, fractions, decimals, and rates can guide real distribution decisions. Students close by naming patterns they noticed about quotients, rates, and powers of 10 and posting questions they want to investigate during the unit.

Exhibition

Host a “Pantry Math Museum” where student teams present their community pantry planning boards and collaborative data displays to families, school staff, classmates, and a representative from the local food pantry. Each team explains one pantry-sharing decision using a ratio table, open array, or division notation and shows how fraction division, decimal computation, and rates helped them make a fair and reasonable recommendation. Include a short feedback walk in which visitors leave comments or questions about the clarity of the model, the usefulness of the strategy, and the reasonableness of the solution. End with partner presentations of the performance task so students practice clear mathematical communication with an authentic audience.