Arrays and Shapes
Dana Campbell
Margaret Frame
Katrina Heit
Veronica Salsa
4th grade
Standards:
Lesson I:
Representation: Create and use representations to organize, record, and communicate mathematical ideas. Students will use external modes-ones that they can build, change and inspect-as well as use mental imaging.
Science: Science as Inquiry: Abilities necessary to do scientific inquiry
Lesson II:
Algebra: Represent and analyze mathematical situations and structures using algebraic symbols. Model problem situations with representations such as an array to draw conclusions.
Connections: Recognize how mathematical ideas interconnect and build on one
another to produce a coherent whole.
Communication: Communicate the mathematical thinking coherently and clearly. Use the language of mathematics to express mathematical ideas precisely.
Lesson III:
Reasoning and Proof: select and use various types of reasoning and methods of proof.
Communication: Communicate their mathematical thinking coherently and clearly
to peers, teachers and others. Analyze and evaluate the mathematical thinking and
strategies of others. Use the language of mathematics to express mathematical
ideas precisely.
Lesson IV:
Problem solving: Students will apply and adapt a variety of appropriate strategies to solve problems.
Communications: Students will communicate their mathematical thinking clearly and coherently to peers, teachers, and others.
Numbers and Operations: Students will understand various meanings of multiplication and division.
Vocabulary: array, share, multiplication, dimension, division.
Reflection: This unit is a good unit for fourth grade because they will have a lot of concrete and pictorial experiences with multiplication and division using arrays and shares. These lessons meet the communication, multiple representation, connection, algebra, and reasoning and proof, problem solving, numbers and operations standards for fourth grade. We believe that the students will grasp the concept easily of multiplication and division through arrays and shares. With this unit we will have shown students the meaning behind multiplication and division instead of just memorizing a fact. Our first lesson introduces arrays and shares through an example and explains how they will use these to show different representations of multiplication and division. In lesson II students will understand that arranging a number can be done in a number of ways . Lesson III lets students explore arrays and shares by playing a game to see how breaking apart a multiplication problem can be combined by two smaller arrays to make one big array. Then lesson IV brings the unit together having the students show their understanding by problem solving using arrays and different problem solving strategies.
Ideas for Integration: This unit can be integrated with Language Arts by having the students write a poem about arrays and shares and how they show multiplication and division, they could also write in a journal so they can look back to it and refresh their memory. Also they could make a strategies poster to hang in the classroom. The students could use the vocabulary words in Spelling. Social Studies could be integrated with this unit by having students look for arrays that are present around the world to connect it to real life and surroundings. Science can be integrated by explaining and using the scientific method, inquiry to solve word problems, and to reason and prove their statements they make about arrays, shares, multiplication, and division.