FAMILY_G

Link to PD Plan Page __ Our Family Members __**: Bob (The Lakehead Lip) Gumkowski Debbie (The Mad Multiplier) Geall Caitlin (The D.I. Diva) Richardson Hudaser (The Crazed Counter) Nizam
 *  Welcome to Family G's page!!


 * __Summary of Analysis__**//://
 * problems/issues existed across all strands.
 * in terms of strengths, the strand that students in grades 3, 6 and 9 experienced the most success in was number sense & numeration.
 * geometry & measurement was the problem area as identified by the members of our family.

__**Our Question**__:

//How do we increase the adaptive reasoning skills of our level two students, in measurement, to level three through the use of balanced instruction with the aid of graphic organizers and frameworks//? **__Target__:** Students should understand and justify measurable attributes of geometric shapes, units and processes of measurement. **__Resources__:**
 * Talk About Assessment (Strategies and Tools to Improve Learning) by Damian Cooper
 * Early Math Strategy (The Report of the Expert Panel on Early Math on Ontario) by The Ministry of Education
 * Elementary and Middle School Mathematics (4th Edition) by John A. Van De Walle
 * The Ontario Mathematics Curriculum
 * Teaching and Learning Mathematics - The Report of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario by the Ministry of Education
 * Teaching Reading in Mathematics 2nd edition, by Mary Lee Barton and Clare Heidema
 * Literacy Strategies for Improving Mathematics Instruction by Joan M. Kennedy, E. Hancewicz, L. Heuer, D. Metsisto, C. Tuttle
 * Stepping Out, Reading and Viewing - Making Meaning of Text
 * Tribes - A New Way of Learning and Being Together by Jeanne Gibbs
 * Transformational Practices Grades K - 12 //Working Together to Achieve Literacy Success//, Peel District School Board
 * Think Literacy, Cross-Curricular Approaches, Grades 7 - 12, 2003
 * Leading Math Success, Mathematical Literacy, Grades 7 - 12 - The Report of the Expert Panel on Student Success in Ontario, 2004
 * Supporting Student Success in Literacy, Grades 7 - 12, Effective Practices of Ontario School Boards, 2004
 * Elementary and Middle School Mathematics, Teaching Developmentally by John A. Van De Walle and Sandra Folk
 * Education for All, The Report of the Expert Panel on Literacy and Numeracy Instruction for Students With Special Education Needs, Kindergarten to Grade 6, 2005. Ministry of Education Resource.
 * Targeted Implementation and Planning supports: Grades 7, 8 and 9 Applied Mathematics (TIPS), By Consortium of Ontario School Boards, 2003
 * [|Course Profiles] Developed by the Ministry of Education
 * Additing it Up. Helping Children Learn Mathematics
 * A Guide to Effective Instruction in Mathematics K-3
 * How to Differentiate Instruction in Mixed-Ability Classrooms by Carol Ann Tomlinson. 2nd Edition.
 * Keeping learning on track: formative assessment and the regulation of learning by Dylan William, ETS. Article used in class.
 * Link to NCTM Principles and Standards for School Mathematics - [|Measurement] K-12
 * Problem Solving, Reasoning and Communicating (K-8): Helping Children think mathematically, by Arthur J Baroody
 * Classroom Discussions. Chapin, O'Connor, Anderson
 * Literacy Strategies for Improving Mathematics Instruction, Kenny, Joan M et al.

10. Adjust the pacing of instruction and provide extra time to complete tasks. 9. Build in extra practice. 8. Provide auditory cues; for example, transition music. 7. Provide visual cues; for example, anchor charts. 6. Use graphic organizers. 5. Build in movement. 4. Group & regroup for different purposes. 3. Vary materials & match texts to readers. 2. Provide CHOICE. 1. Work as a team to identify the resources necessary to support all student needs.
 * __10 Quick & Easy Differentiation Strategies__**:

1. Instruction that uses procedures-based //and// discovery methods, allowing students to effectively construct their own understanding 2. Three-part lesson design. Teacher poses problem; students investigate in cooperative groups, teacher questions, students share thoughts; teacher facilitates discussion, wrap up 3. Develop mental math skills 4. Incorporate math games and puzzles into lessons 5. Use manipulatives to help deepen student understanding 6. Use good textbooks that have lessons based on a progression of mathematical development, that outline tasks that encourage students to think more deeply, make connections, increase abstraction about a given topic. 7. Effectively use technology 8. Use Assessment for learning, not just for data collection
 * __Additional Strategies for Effective Instruction__:**

1. ASSESS-Pretest for interests, learning styles and academic starting points. 2. ADJUST-Adjust for learning. 3. DIFFERENTIATE INSTRUCTION-Conduct ongoing formative assessments to monitor learning. 4. ASSESSMENT OF LEARNING-Provide opportunities to recover pieces and close any gaps.
 * __Planning For Effective Instruction__**:

To help students improve their adaptive reasoning skills, we must help students build their mathematical literacy. When students understand the symbols, conventions, terminology, the relationships and concepts, to name a few, they can then begin to think logically about relationships. A student that possess strong mathematical literacy skills will be able to justify and explain the reasons for their choices within their work more easily.
 * __Mathematical Literacy__**:

Building mathematical literacy resources are noted above. Many excellent teaching and learning strategies that promote mathematical literacy are included in the above texts.

Sternberg has established the theory that there are three types of intelligence. They are:
 * __Sternberg's Triarchic Theory of Intelligence__**:
 * 1) Analytical (school smart) - analyzing, judging, evaluating, comparing, contrasting & critiquing.
 * 2) Creative Smart (imaginative) - creating, inventing, discovering, imagining & supposing.
 * 3) Practical (street smart) - implementing, using, applying & seeking relevance.

We have all some of each of these kinds of intelligences, but are stronger in one or two areas. As teachers we need to develop as fully as possible each of these intelligences in our students. We must also understand where students' strenghts lie & teach to these strenghts as often as possible. In attempting to raise our level two students to level three performers, we, as teachers, must take into account Sternberg's Triarchic Theory of Intelligence in addition to planning for effective instruction and differentiating instruction.

Strategies from **//“Leading Math Success: Mathematical Literacy Grades 7-12”//** __Strategies from Education for All - Focused on Students with Special Needs, K - 6__
 * Provide remedial Education to level 2 students (Defined on Pg. 17)
 * Use similar strategies for at risk students as are used with special education students. (Listed at the bottom of Pg. 17 – 4 bullets)
 * For grade 9 testing, using mathematics TIPS program. Uses these supports in grade 7 8 and 9 to improve grade 6 skills and prepare for grade 9 testing. Pg. 18
 * Ministry Created course profiles for all secondary courses. Provides presentation order, rich learning tasks and assessment techniques. Available online. Pg. 19
 * Developing Effective Lessons focused on Important Mathematics. Pg. 46
 * Making Available and Using a Rich array of Technologies. Technology can help strengthen the conceptual understanding faster, leaving extra time to develop adaptive reasoning skills. Pg. 47
 * Making available and using a rich array of Manipulatives. Once the concept is developed with the aid of manipulatives, questions can be easily adapted to develop deeper understanding of the concept. They have to be able to reason and rationalize the changes using manipulatives. Pg. 48 – Large list of manipulatives
 * Supporting different ways of learning and demonstrating understanding. Using differentiated instruction can allow students to be challenged at an appropriate level. Pg. 51
 * Professional Learning – A deeper understanding of mathematical content and Teaching methodologies. Student learning improves when teachers have both a deep knowledge of mathematic content and a sound understanding of strategies. Pg. 57
 * Contact superintendent to ensure instructional resources are available. Pg. 73
 * Contact principal to ensure instructional strategies and resources are available. Pg. 77
 * Develop ways parents and the community can help support student learning. Pg. 80
 * Cluster a group of students in grade 7-10 with a group of teachers for at least 2 years. They benefit from having teachers get to know them and their learning styles. Pg. 85
 * some of the information below may be directly quoted from the resource

- differentiated instruction which includes differentiated content, process, and product (p. 9) - use of technological tools to facilitate students' learning (p. 13) - focusing on readiness, interests, and students' learning profiles may contribute to improvement of adaptive reasoning skills (p.15) - some suggested instructional and management strategies: varied questioning strategies group investigations interest centers (p. 15) - problem-based approach - teacher presents students with a realistic, believable problem that they solve only with a new skill. They need to determine the best strategy to solve the problem (p.17) - provide a range of structured to un-structured learning opportunities using explicit instruction (p.17) - teachers should monitor their oral and written instructional language to be sure that new skills and concepts are clearly understood by the students (p. 62) - use of scaffolding so ensure that the student is moved from one place to another in the learning process. The responsibility for learning is transferred from the teacher to the student, encouraging a more independent learner. (p. 62) - use of modelling such as think aloud to verbalize the thought processes, also model learning strageties, where students model how they decode words, make predictions, summarize, and evaluate text. (p. 63) - use K-W-L graphic organizer (What I Know, What I Wonder, What I learned) (p.66) - Focus on "big ideas" - identify prior learning - looking at student's thinking and understanding in relation to the mathematical concepts adressed in the curriculum - collecting observations and making anecdotal records - providing feedback to students - determining next steps (p. 73)

Information here directly quoted from this resource.
 * __How to Differentiate Instruction in Mixed-Ability Classrooms__**

Two important features of a differentiated classroom are students' rights to "begin where they are" and to expect to grow as learners. P. 93 In the real world, any sytem that encourages personal growth in every student should be the goal and may be achieved, at least in part, in a variety of ways. P. 94 And most important, learning to face challenges earlier gives these students more time to develop the planning, self-evaluation, and study skills they need to maximize their potential as learners. P. 94 Although teachers employ many useful strategies to chart student tasks and growth, it is important to recall that the dual purpose of all assessment is (1) to chart student growth in regard to valued skills and knowledge and (2) to use information gathered through that process to help in planning the most appropriate learning experiences possible for given individuals and groups of students. P. 95

Information here directly quoted from the resource
 * __Adding it Up__**

A second kind of item that measures adaptive reasoning is one that asks students to justify and explain their solutions. P. 139 Research suggests that young children are able to display reasoning ability if they have a sufficient knowledge base. P.170 Children's first understanding of length measure involves the direct comparison of objects. P. 282
 * ...**but adaptive reasoning should be used to determine whether the procedure is appropriate. P. 131

Information here directly quoted from handout.
 * __Keeping Learning on Track: formative assessment and the regulation of learning__**

In a variety of settings teachers have found that by teaching for deep understanding has resulted in an increase in student performance on externally-set tests and examinations. P. 1 There is substantial evidence that students' learning is enhanced by getting them to generate their own questions. P.5

**__Problem Solving, Reasoning and Communicating (K-8): Helping children think mathematically: By Arthur J. Baroody__** The following are quotes directly from this source. ESTIMATION
 * Developing reasoning competencies is essential to help children go beyond the level of merely memorizing facts, rules and procedures. A focus on reasoning can help children see that mathematics is logical and suppose to make sense. Pg. 2-59
 * Mathematical inquiry often begins with a conclusion drawn from intuitive or inductive reasoning called a conjecture. … Deductive proofs are a means of checking conjectures. Pg. 2-59
 * The psychologist Jean Piaget believed that … Children younger than about 7 years of age (the “age of reason”) were thought to be in a preoperational stage of thinking and, thus, incapable of thinking logically (deductively). Pg. 2-73
 * Piaget also concluded that young children lacked the logical ability to sort (classify) things into groups (classes) systematically. … Preoperational child might make a “graphic collection”. Pg. 2-73
 * According to Piaget, children in the concrete operational stage (approximately 6 to 12 years of age) are capable of limited or elementary logical reasoning. He presumed they could reason about the concrete (objects or things they had experienced), but not about propositions (abstract verbal statements or ideas) Pg. 2-73
 * …Piaget’s view, preadolescents may be capable of engaging in relatively abstract (propositional or hypothetical) reasoning, such as reasoning from a premise they know to be untrue. Pg. 2-75
 * __Important Points from Van de Walle's Elementary and Middle School Mathematics__:**
 * "It is significant that measurement is one of only five standards (each spanning K – 12) around which the NCTM chose to organize the content in the //Principles and Standards//” (p. 294)
 * Van De Walle explains that between kindergarten and grade 8, students must learn the attributes that they will be measuring (length, capacity, mass, area, perimeter, and so on); students learn the concept of measurement including the concept of units. Students learn how unit size affects measurements and how to select measurement tools, and how formulas can be used in calculating measurements.
 * The big ideas in this section include: To measure anything meaningfully, the attribute to be measured must be understood
 * Meaningful measurement and estimation of measurements depend on a personal familiarity with the unit of measure being used
 * Measurement instruments are devices that replace the need for actual measurement units in making comparisons (p. 294)

COMMON DIFFICULTIES (Misconceptions)
 * Van De Walle states that before actually measuring an attribute, it is important that students first estimate the measure of the attribute. This is because of three reasons
 * 1) Estimation helps students focus on the attribute being measured and the measuring process
 * 2) Estimation offers intrinsic motivation for measuring
 * 3) When standard units are used, estimation helps develop familiarity with the unit (p. 297)
 * Van De Walle explains that putting measurement tasks into problem - solving exercises will provide teachers with increased information
 * Van De Walle writes that "Data from the sixth National Assessment of Educational Progress sugges that grade 4 and grade 8 U.S. students have an incomplete understanding of area.
 * Similar findings are revealed in Canada by TIMSS (Third Int'l Mathematics and Science Study) (p. 302)
 * Van De Walle states that when students compare two areas, there is an added consideration of shape, not present when measuring lengths, which causes difficulty
 * Early comparison activities help students distinguish between size (or area) and shape, length and other features (p. 302)
 * It is important that students understand that finding area is all about filling a region with a particular area unit of measure (p.303)
 * A teacher's objective in the beginning is to develop the idea that area is a measure of finding how many units will cover a particular surface. "Do not introduce formulas" (p. 304)
 * Students become so used to formulas and rules that they no longer have a clear understanding of what the formulas are all about
 * "Children often have difficulty applying area measurement formulas." (p. 314)
 * "...[students] often confuse formulas for area and perimeter. For example, they will illustrate the formula for perimeter as (l x w) x 2, multiplying the length by the width, then multiplying this product by 2. Or they might add when they need to multiply." (p. 314)
 * "The most likely explanation is a premature emphasis on formulas with little effort to develop an understanding of why they work." (p. 314)
 * students make errors because of lack of understanding of height in 2 - D and 3 - D geometric figures
 * Why? Students are introduced to area formula for rectangle early in school career. In rectangle, the height equals the side length

__**D.I. - Help!! Where do I Begin?**__ 1. Develop Student profiles 2. Phyical Environment 3. Building Community 4. Vary Presentation - Hook the students with a grabber 5. Vary Content 6. Vary Process - teaching strategies, journal entries, graphic organizers, exit cards, etc. 7. Vary the product 8. Managing the variables in the classroom


 * __How Do I Successfully Accomplish Differentiated Instruction In My Classroom?__**

Step #1 - **Get to Know Your Students** Before you begin to learn about your students, it is a good idea for you to know yourself and your learning abilities and preferences. A learning environment should be one where you are meeting the learning styles of your students, NOT one where you teach according to your own personnal learning style.

Step #2 - **Gather Resources** When you know who your students are, the next step involves developing materials, finding resources and organizing those resources to meet their needs.

Step #3 - **Determine the Best Differentiation Process to Accomplish Your Goals** There are 3 differentiation processes to choose from depending on the personalities and interests of the students in your classes; whole class, small group or individual student differentiation. Here are some examples:

__Whole Class Differentiation__ 1. Tiered Lessons 2. Using interest groups to differentiate instruction 3. Learning Centers 4. Flexible Grouping

__Small Group Differentiation__ 1. Literature Circles 2. Study Groups 3. Cubed Discussion Groups 4. Ordered Sharing

__Individualized Instruction__ 1. Research Projects 2. Curriculum Compacting 3. Learning Contracts 4. Independent Study

Step #4 - **Plan Strategies for Determining Acceptable Evidence of Learning** Once you feel more comfortable with differntiation, many questions arise as to how to differentiate a product so that assessment will be fair to all students. Teachers should use a variety of techniques that allow for a wide variety of student abilities, interests and demonstrate mastery of skills and understanding of concepts. They also need to develop measurement tools that are not only quantitative, but those that are also holistic, analytical and qualitative.

Assessment can include any of the following major categories:
 * Question-based assessment
 * Problem-based assessment
 * Performance based assessment
 * Affective domain-based assessment
 * Self and/or peer-based assessment

Step #5 - **Put All Your Work Into Units & Daily Lesson Plans** When planning a unit, ask yourself these question: 1. What will students learn? 2. How will you determine acceptable evidence? 3. What differentiated activities will maximize learning for all students? 4. What material will you need to teach the lesson? 5. How will you present the lesson to the students and in what order?


 * __Classroom Discussions__**

p.17 "Whole class discussion allows students to engage in sustained reasoning. The teacher is a facilitator and guide but does not provide answers, it's focused on student answers (thinking)." p. 20 "Partner talk allows students to be ready to participate in whole-group discussion."

__**Problems and Tasks for Learning Mathematics (Van De Walle)(pg 45)**__ A problem is defined here as any task or activity for which the students have no prescribed or memorized rules or methods and no preception that there is a specific "Correct" solution method. Problem learning must
 * begin where the students are - design or selection of the task must take into consideration that current understanding of the student - approptiate ideas to engage and solve the problem
 * The problematic or engaging aspect of the problem must be de tothe mathematics that the students are to learn.
 * It must require justifications and explanations for answers and methods


 * __Teaching Tips and Questions (Van De Walle) (Pg 59)__**
 * Predict! Don't hope - its not sufficient to think about how it will work if everything goes well. Predict their likely responses and be prepared to deal with them.
 * Be clear in your own mind about the purpose of the task or activity - Don't select problems simply because they are interesting. Ask "what mathematics will students develop by working on this task?
 * Recognize that there is much more to a problem than the answer - most learning occurs during the class discussion. social interaction is at least as important as their independent reflection
 * Don't confuse open ended problem solving with encouraging creativity - open ended solutions are not the same as creative stories, artistic drawings or students supplying their own numbers for a problem. the latter approaches detract from the mathematics of the task.

__**Types of Discourse**__ Traditional - Teachers ask questions, questions directed at students, they respond to the teacher Probing - Teacher is the leader, conversations is between teacher and individual students, questions are more open, teachers desire to hear students thinking Discourse Rich - Young people are working towards mathematical understanding by sharing ideas with each other and the teacher.
 * __Literacy Strategies for Improving Math Instruction (Pg 72)__**
 * There is general agreement that discussion and argumentation improve conceptual understanding
 * Defining discourse as the genuine sharing of ideas among participants in a mathematics lesson, including both talking and active listening

**Sources:** Ontario Ministry of Education Exemplars, Candidate-Created Rating Scale, Activity Sheets and Teacher Answer Sheets **Grade:** Four **Curriculum Strand:** Number Sense and Numeration **Purpose:** This is the first term’s formative assessment. The purpose is to guide planning and gauge student understanding and competence. The students will be given a quiz in order to fulfill my need to have a formative assessment take place. The task will not be referred to as a quiz, although it is a quiz, in order to minimize student anxiety. The task will be divided into three components; these components are, firstly, a multiple choice component, secondly, a short answers component and, thirdly, a fill-in-the-blanks component. After the students have completed the activity, the papers will be collected and marked according to a rating scale that is included in this assignment. The rationale for including a multiple choice component in this activity is to fin out if the students can apply the learning that took place, in the classroom, to questions involving the simulated purchases of items. The multiple choice questions are included in order to determine if the student is able to show **knowledge** in various contexts. Question #3 is an example of giving the student the opportunity to show that he can add money amounts and decimal numbers to tenths. Another component of the activity involves short answer questions and the purpose for including short answer questions is to allow the student to illustrate his/her **thinking**. Space is given under each question, in Part C, in order for the student to show the thinking process they employed in working out a question and then arriving at a solution. Students need to justify their answers. The reason that students are asked to justify their answers is so that the student can demonstrate that he/she can effectively communicate his/her ideas. **Communication** is a skill that needs to be used effectively in justifying an answer. The questions in Part C are rich and open ended and they allow the opportunity to show thinking in multiple ways. The first activity in this assessment asks students to draw money amounts using the least possible number of bills and coins. Knowledge will be demonstrated here in regard to reading and representing money amounts. The questions here are detailed and clear with no room for misinterpretation. The task is accessible to all. The task presented here has many strengths. One strength, in particular, is that the questions in Part C are written in a way so that students can demonstrate what strategies they are using in arriving at an answer. Another strength is how scaffolding exists in terms of the questions. The questions become more difficult as the students progresses through the problems. The questions are rich and in addition to being rich, all students will be able to show understanding, to various degrees in completing the questions. A potential weakness of the activity is that it may be biased against students who are tactile learners as no currency manipulatives are used in solving questions. Students new to Canada may not be familiar, as of yet, with Canadian money and the value of money. Perhaps a class on currency conversion would be useful to aid understanding and demonstrate the principle of inclusion in this regard. The principles this cumulative task stresses are **inclusion** and **equity**. Equity is stressed by the questions taking into account that students have different learning styles. The tasks challenge students to use higher order thinking skills to make connections between math and the real world. Equity is also demonstrated as the tasks promote the active participation of all students. The principles that guide this cumulative task are many. Firstly, a balanced approach was taken to this task in that the tasks are varied in order to improve the learning of all students. Secondly, the assessment has been carefully planned and it is purposeful. The purpose of this assessment is to assist in planning and measure student understanding. In addition to **balance** and **purpose**, another principle of this task is sensitivity. There is no room for criticism here; the students will learn what they have done well and what they need to improve upon. ** Show Me How You Can Work With Money! ** Name: Part A: Draw each amount using the fewest number of  bills and coins. 1. 23 cents
 * __An Example of a Rich Assessment Task For Grade 4 Based on The Number Sense & Numeration Strand:__**
 * Specific Curriculum Expectations: **
 * **read** and **represent money amounts** to $100 (e.g., five dollars, two quarters, one nickel, and four cents is $5.59);
 * **add** and **subtract money amounts** by making simulated purchases and providing change for amounts up to $100, using a variety of tools (e.g., currency manipulatives, drawings);
 * represent, compare, and order decimal numbers to tenths, using a variety of tools (e.g., concrete materials such as paper strips divided into tenths and base ten materials, number lines, drawings);
 * **add** and **subtract decimal numbers** to tenths, using concrete materials (e.g., paper strips divided into tenths, base ten materials) and student-generated algorithms.
 * Task: **
 * Rationale: **
 * Strengths and Weaknesses: **
 * Principles: **
 * Assessment Principles: **

2. 2 dollars and 50 cents

3. 50 dollars and 34 cents

4. 89 dollars and 49 cents

__ Part B: __ 1. Arrange from least to greatest. $17.99 / $100 / $0.05 / $79.85 / $19.95 / $69.32 / $95.01 / $0.26    Circle the correct answer.

1. Lucia bought a book for $4.16. She gave the clerk $4.25. How much change should she have received? a. $0.09 b. $0.11 c. $0.34 d. $0.90 2. $55.20 + $16.43 = ? a. $60.62 b. $60.63 c. $61.63 d. $71.63 3. Alicia bought a 64-ounce bottle of laundry detergent on sale for $3.20. If the regular price was $5.03, how much did she save? a. $1.53 b. $1.63 c. $1.73 d. $1.83 4. Sara bought a pack of gum for $0.99 and a hair brush for $3.50. How much money did she spend? If she began shopping with a five dollar bill, how much would she have left after her purchases? a. $0.49 b. $0.50 c. $0.51 d. $0.52 5. Dion had 2 twenties, 3 tens, 2 fives, 3 quarters, 1 dime, and 4 pennies. How much money did he have? a. $40.63 b. $50.63 c. $70.89 d. $80.89 Part C: Read the questions and then solve in the space provided. Be sure to write a concluding statement and show all work and calculations. Explain the strategy you used and justify the strategy you used. 1. Aaron bought a tiny turtle for $1.25 and turtle food for $0.31. He gave the clerk $2. How much change did he get? Explain how you got an answer.

2. **Large Pizza-$13.99** each additional topping is $1.25 (max. of 3 toppings) **Medium Pizza-$9.99** each additional topping is $1.00 **Small Pizza-$6.99** each additional topping is $0.75 Would it cost Frank less money to buy a large pizza with one topping or a medium pizza with 3 toppings? Show and explain your work.

3. How much would it cost Frank to buy each size of pizza if each pizza had 2 toppings on it? Would Frank have enough money to buy all 3 sizes if he has $30.00?

4. Show all the possible prices Frank can pay for large and small pizzas.

__ Part D: __ Teddy has 5 ten dollar bills, 3 twenty dollar bills, 6 loonies and 7 quarters. Edward has 6 ten dollar bills, 9 five dollar bills, 3 dimes and 2 nickels. Who has more money? Justify your answer and use words, pictures and numbers to explain your solution.

** Teacher Answer Sheet  ** 1. 2 dimes and 3 pennies should be drawn/pictured 2. 1 toonie and 2 quarters should be drawn/pictured 3. 2 twenty dollar bills, 1 quarter, 1 nickel and 4 pennies should be drawn/pictured 4. 4 twenty dollar bills, 1 five dollar bill, 2 toonies, 1 quarter, 2 dimes and 4 pennies should be drawn pictured Part B: ** 1. $0.05/$0.26/$17.99/$19.95/$69.32/$79.85/$95.01/$100 1. (a) 2. (d) 3. (d) 4. (c) 5. (d) Part C: ** 1. 44 cents 2. It would cost Frank less money to buy a medium pizza with 3 toppings. A medium pizza with 3 toppings costs $12.99 and a large pizza with one topping costs $15.24. 3. It would cost Frank $36.97 to buy all 3 pizzas if each had 2 toppings. He would not have enough money to buy all three. The large would be $16.49, the medium would be $11.99 and the small would be $8.49. 4.· large pizza with 1 topping - $15.24 · large pizza with 2 toppings - $16.49 · large pizza with 3 toppings - $17.74 · small pizza with 1 topping - $7.74 · small pizza with 2 toppings - $8.49 · small pizza with 3 toppings - $9.24
 * Part A: **
 * Part D:** Teddy has $117.75. Edward has $105.40. Ted has more money.