Lesson Plan :Elementary/Secondary Math

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I was a little confused by the last part of your attachment. There was a lot of information about budgets and price comparisons that I think may have been included by accident. I added some student worksheets at the end.
Lesson: Math Trees

Grade: 5
(You will need to use the Grade 5 standards for your nation, state, and local district here.)
National Standards:
State Standards:
Local Standards:

Standards Number and Operations: Understand meanings of operations and how they relate to one another - develop an understanding of permutations and combinations as counting techniques (PSSM p. 290); Compute fluently and make reasonable estimates - develop fluency in operations with real numbers (PSSM p. 290)
Problem Solving: Build new mathematical knowledge through problem solving (PSSM p. 334)
Reasoning and Proof: Make and investigate mathematical conjectures (PSSM p. 342)
Communication: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others; Analyze and evaluate the mathematical thinking and strategies of others (PSSM p. 402)
Connections: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole (PSSM p. 354)

Objectives: In this lesson, students will
Learn the addition and multiplication counting principles
Create patterns to make a mathematical conjecture
Learn the definition of n!
Determine the number of permutations of an object

Targeted population: Diverse learners in fifth grade math class

Materials: Colored pieces
Shirt, pants, and shoes cutouts
Paper and Pencil
Permutation Worksheet

Lesson style: Exploration for small groups of students with teacher direction and visual aids, followed by self-directed learning

Setting the stage: How many different phones are there if there are three phone models and six colors?
How many different outfits are there if there are two shirts, three pairs of pants, and two shoes?

Lesson development: Students will have a worksheet to complete in groups, which will serve as a reference guide for their own individual assigned practice. After answering the "setting the stage" questions using the tree, each group of three students will be given two shirts, three pairs of pants and two shoes and asked to solve the problem. Different groups can share the ways they solved the problem. The teacher will then introduce the tree method and the multiplication principle will be defined. The addition principle will be introduced in a similar way, using the examples on the worksheet. Students will complete the front of the worksheet together as a class, with the teacher leading them through the steps.
Permutation will be defined as a combination of objects in which order matters, and a few examples will be provided (the letters a, b, and c; the numbers 1, 3, 5, 7). Students will then be asked to explore the next questions on the worksheet using the dice and coins provided. They will be encouraged to make a conjecture regarding the process of finding permutations. The n-factorial concept will be ...