# Lesson 9: Solving Word Problems with the Design Recipe

## Overview

In this stage students practice using the Design Recipe to write functions which solve for word problems. Towards the end of the lesson students should be ready to begin using the Design Recipe on problems from your own math curriculum.

## Anchor Standard

### Common Core Math Standards

• F.BF.1 - Write a function that describes a relationship between two quantities.

## Objectives

### Students will be able to:

• Design functions to solve word problems.
• Continue to practice writing contracts with more complex scenarios.

## Preparation

Heads Up! Please make a copy of any documents you plan to share with students.

# Teaching Guide

## Getting Started

Teaching Tip

#### Beware:

Students will want to just drag and drop to fill in the blanks, often rushing towards a solution without thinking it through.

Challenge students battle their partners and produce a completed version of each broken recipe on the paper form.

### Introduction

With these incomplete or "bugged" Design Recipes, students will need to become expert analyst to find the errors. It is crucial that students are instructed to deliberately de-bug these levels using the Design Recipe.

It should be noted that the examples must be filled in completely. The error message when the example is incomplete is "You have a block with an unfilled input."

## Activity (45 minutes)

### De-Bugging Online Puzzles

In this stage you'll use the Design Recipe to analyze and de-bug broken functions. Head to CS in Algebra stage 9 in Code Studio to get started programming.

Before you let students dive into this lesson, the teacher needs to frame how students are to use their Design Recipe skills to de-bug. It is helpful to do the first one together on the projector, document camera, or board, then let students tackle Level 2 through Level 5 on their own.

With blank Design Recipe forms:

• Students will open Stage 9 Level 1 and fill as much of their Design Recipe form is provided. (They can fill out one form per pair)
• As students fill in their forms, post the question "What is Missing?" and "What would we need to make this work?"
• Once students think they have fixed what went wrong on paper, they should be encouraged to battle their partner to polish their work.
• After they have battled each other have them upload their work into Code Studio and what their functions work!

Make sure you stop class at Stage 9, Level 5 to regroup. Have students share their process for de-bugging and highlight tricks or tips that students used to help them find all the errors.

Level 6 transitions from broken functions of word-problems to blank, unknown functions. This scaffold is helpful but if glossed over, students will be lost.

At this transition point re-energize students that although the problems look different, their process will work! Have students build their functions using their blank Design Recipe forms, again one per pair is good for this level.

## Textbook Problem Extension

In this activity you would draft problems from your textbook or classroom materials so the Design Recipe could be used. Building functions is a major standard in Algebra 1 but there are limited tools to help students take in a description, table, points, or graph and create the function. Many times the "Create an Equation" is just assumed to be obvious but is painfully not for many students. By using this template and your own problems you will help students transfer their analytical thinking from CS to just Algebra!

On the free-play, Level 10, have students use the Design Recipe to build functions that would solve word problems from your textbook or course. You can create a worksheet with problems you want to create a function for or you can you just have them try one.

The Design Recipe - Word Problem Template - Template has 5 example problems that were modified from either teacher's course materials or a textbook to give students access to building their own functions.

View on Code Studio

### Student Instructions

Here's a Design Recipe for a function called `square-circle` with domain Number String and range Image. Click Edit to write the function definition (you will see two examples provided).

View on Code Studio

### Student Instructions

The Design Recipe for `wide-rect` already has a contract and one example. Can you write a second example and then complete the definition? The `wide-rect` function should produce a rectangle of given color that is twice as wide as it is high.

View on Code Studio

### Student Instructions

Use the Design Recipe to create a function `starburst`. When given a number of points and an outer radius, `starburst` returns a yellow radial star with given points, and an inner radius that is half the outer radius.

View on Code Studio

### Student Instructions

Write a function `striped-flag` that takes two colors and produces a flag that is 250 pixels wide, 150 pixels tall, with three even horizontal stripes of given colors, in the order color2, color1, color2.

View on Code Studio

### Student Instructions

Write a function `large-polygon` that should output a solid polygon of given sides and color that takes up most of the window, regardless of the number of sides. To make sure that the polygon doesn't get too large as you increase the number of sides, side length should be inversely proportional to side number, with a length of (800/sides).

View on Code Studio

### Student Instructions

Let's use the Design Recipe to create a function called `cube` - this function should take in a Number and return that number to the power of 3. Make sure to write two example cases! When you're done, use your new function to calculate `cube(7)`.

View on Code Studio

### Student Instructions

Your school is holding a bake sale, and you need to track the cost of making each cookie, the money paid, and the total profit. Cookies cost \$0.25 each to make, and sell for \$1.50/cookie. Write the function `cost`, which takes in the number of cookies you intend to sell, and returns the cost of making those cookies.

View on Code Studio

### Student Instructions

Write the function `sales` which takes in the number of cookies sold, and produces the amount of money customers spent to buy those cookies (each cookie is sold at \$1.50).

View on Code Studio

### Student Instructions

Using the two functions we just wrote, write the function `profit`, which takes in the number of cookies you sold, and gives you back the total profit you make from selling your cookies, accounting for the cost of baking them.

View on Code Studio

### Student Instructions

Free Play: Use the Design Recipe to create some functions of your own design

## Standards Alignment

#### Common Core Math Standards

BF - Building Functions
• F.BF.1 - Write a function that describes a relationship between two quantities.
• F.BF.2 - Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★
CED - Creating Equations
• A.CED.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
• A.CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
• A.CED.3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. For example, represent inequalities describing nutritional and cost constr
• A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
EE - Expressions And Equations
• 6.EE.9 - Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent va
• 7.EE.4 - Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
IF - Interpreting Functions
• F.IF.1 - Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f c
• F.IF.2 - Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
• F.IF.3 - Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
• F.IF.4 - For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
• F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers w
• F.IF.6 - Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★
• F.IF.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
• F.IF.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which
LE - Linear, Quadratic, And Exponential Models★
• F.LE.1 - Distinguish between situations that can be modeled with linear functions and with exponential functions.
• F.LE.2 - Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
MP - Math Practices
• MP.1 - Make sense of problems and persevere in solving them
• MP.2 - Reason abstractly and quantitatively
• MP.3 - Construct viable arguments and critique the reasoning of others
• MP.4 - Model with mathematics
• MP.5 - Use appropriate tools strategically
• MP.6 - Attend to precision
• MP.7 - Look for and make use of structure
• MP.8 - Look for and express regularity in repeated reasoning
NS - The Number System
• 6.NS.8 - Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
OA - Operations And Algebraic Thinking
• 5.OA.1 - Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
• 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three t
Q - Quantities
• N.Q.1 - Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
• N.Q.2 - Define appropriate quantities for the purpose of descriptive modeling.