Grade 1 Math

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Grade 3 Math

GRADE: 2

TOPIC: ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS

STAGE 1: IDENTIFY DESIRED RESULTS
Content Standard(s) Generalizations about what students should know and be able to do
Established Goals: State Standards: Model and describe patterns and functional relationships. Model and analyze quantitative data. Using algebraic symbols to represent and interpret data and physical phenomena. National (NCTM) Standards: Understand patterns, relations, and functions. Represent and analyze mathematical situations and structures using algebraic symbols. Use mathematical models to represent and understand quantitative relationships. Analyze change in various contexts.
Enduring Understandings Insights learned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
1. Patterns and functions help us describe data and physical phenomena and solve a variety of problems. 2. Patterns help us predict. 3. Patterns are repeating or growing sequences that can be created or occur naturally in our world. 4. Objects can be organized based on various explainable elements and rules. 5. An equation is a number sentence that shows two quantities that are equal. 6. Graphic organizers such as Venn diagrams can help us see relationships (patterns, changes, opposites, similarities).	1. What is a pattern? 2. How does a pattern extend? 3. Why and how are patterns useful to us? 4. How do you find the value of unknown numbers? 5. Why are equations important? 6. What does balance have to do with an equation? 7. How are graphic organizers helpful to us? 8. When should you use a graph instead of a paragraph to share information? 9. When is sorting helpful?
Knowledge and Skills What students are expected to know and be able to do
Students will know… Patterns have rules and the rules may be described using attributes and numbers. Graphic organizers such as tables or Venn diagrams can be used to solve problems involving logic, classification and patterns Patterns can be used to analyze change in terms of quantity and quality. Number sentences may be used to represent real-life situations.	Students will be able to… Describe and classify data and objects based on more than one attribute. Organize data with tables, charts, and Venn diagrams, and use the display to solve problems such as identifying a missing object, objects with common or different attributes and the complement of a set of objects. Use tables and graphs to display patterns in data and explore a variety of ways to describe and write rules for patterns using pictures, letters and numbers. Explore and describe number patterns on hundreds charts and number lines, including odd and even numbers, counting by 2s, 5s, 10s, 100 and counting on by 10 (i.e., 4, 14, 24, 34…). Make comparisons of data and analyze observable changes using qualitative and quantitative descriptions. 3. Model situations that involve addition and subtraction of whole numbers using objects, pictures and symbols, including open sentences (3+ _ =10).
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task(s) Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards)	Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results
Task 1 Goal: Describe and extend repeating or growing patterns. Use flips and turns to create patterns. Write a short paragraph describing how your pattern meets the stated criteria. Role: You are an interior designer who works for Home Depot in the wallpaper department. Audience: The boss of the Home Depot wallpaper department. Situation: Home Depot would like you to design a new wallpaper border using one object (Ex. footprints). Product Performance and Purpose: You must design a border that uses three colors. Your border must have a repeating or growing pattern. Your border pattern should have flips or turns. Your border should be made up of the same object repeated, flipped and turned. You need to write a short paragraph describing how your pattern meets the stated criteria. Standards and Criteria for Success: Your work will be judged by the accuracy of your design. A successful result will be a design that uses three colors, is repeating or growing, shows flips or turns, and uses the same object throughout. Scoring Rubric: The student: Score of 3: Meets or exceeds the objectives of the task. Demonstrates a high level of understanding. The student created a design that has three different colors. The design uses one object, such as footprints, in a repeating or growing pattern. The design shows flips or turns. The paragraph describes how the pattern meets the stated criteria. Score of 2: Partially meets the objectives of the task. Demonstrates some understanding. The student created a design that may or may not be completed according to the directions in every way. The paragraph somewhat describes how the pattern meets the stated criteria. Score of 1: Does not meet the objectives of the task. Demonstrates poor or incorrect understanding. The student did not create a design that has three different colors. The design did not use the same object. The design does not show flips or turns and it is not repeating or growing. This student does not demonstrate an understanding of repeating or growing patterns, flips or turns. The paragraph does not describes how the pattern meets the stated criteria Score of 0: Does not demonstrate any understanding of the task. The student shows no understanding of the problem or how to arrive at a solution.	Teacher Observations Center Activities Group Work Class Work Homework Topic Assessment District Assessment

GRADE: 2

TOPIC: GEOMETRY AND MEASUREMENT

STAGE 1: IDENTIFY DESIRED RESULTS
Content Standard(s) Generalizations about what students should know and be able to do
Established Goals: State Standards: Develop and apply units, systems, formulas, and appropriate tools to estimate and measure. Use spatial reasoning, location and geometric relationships to solve problems. Use attributes of two-and three-dimensional shapes and geometric theorems to describe relationships and communicate ideas and solve problems. National (NCTM) Standards: Understand measurable attributes of objects and the units, systems, and processes of measurement. Apply appropriate techniques, tools, and formulas to determine measurements. Analyze characteristics and properties of two-and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. Specify locations and describe spatial relationships using coordinate geometry and other representational systems. Apply transformations and use symmetry to analyze mathematical situations. Use visualization, spatial reasoning, and geometric modeling to solve problems.
Enduring Understandings Insights learned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
1. Geometric relationships and measurements help us to solve problems and make sense of our world. 2. Measurement is something we use every day. 3. We can use standard benchmarks to help us understand amounts. 4. The measurement tool must be carefully examined prior to use. (All rulers are not the same.). 5. Estimation is helpful in all daily activities. 6. The appropriate tool needs to be used when measuring attributes such as length, area, weight, volume and time. 7. Symmetry is seen when you imagine an object folded into two parts that are congruent. 8. Shapes that are the same can be identified even when there are changes in the position.	1. Why do we measure? 2. Is it necessary for measurement to always be exact? 3. Why do we use customary units of measurement? 4. Can everything be measured? 5. How do we use measurement every day? 6. How far is far? 7. Is the measurement tool (i.e. ruler, clock) always right? 8. How is estimating helpful? 9. Where is symmetry in your world? 10. What makes a shape? 11. What’s in a name? (shape name)
Knowledge and Skills What students are expected to know and be able to do
Students will know that… Shapes which are the same can be identified even when there are changes in the position such as translations (slides), reflections (flips) and rotations (turns). A line of symmetry is formed when you flip a polygon across a line or divide a polygon into two parts that are congruent (the same shape and size). Calendars and clocks help to estimate and measure how long activities and tasks take to complete. Measurement can be made through direct comparison and iteration (repetition) of units.	Students will be able to… Explore slides, flips, and turns of simple polygons using manipulative materials. Identify and explain how shapes are the same even when they are flipped or turned. Build, draw, classify and identify two-and three- dimensional shapes in the environment and describe similarities and differences using physical features such as number of sides, number of angles, lengths of sides and straight and curved parts. Explore combining and subdividing polygons and solids with manipulative materials and reconstruct them from visual memory. 1. Build and identify shapes that have one or more lines of symmetry. Use the calendar to write, discuss and solve problems involving time. Tell time to the half-hour, and explore time to the quarter-hour (analog and digital). Introduce a.m. and p.m. as labels for times of day. Use nonstandard referents and standard benchmarks to make estimates of length, capacity and area. Describe the estimation strategy and identify reasonable estimates. Estimate and measure length, area, weight and volume using nonstandard units. Explore using the standard units centimeter, inch, foot, square, centimeter, square inch, square foot, gram, pound, cubic centimeter and cubic inch. Explore using measurement tools such as thermometer, basic ruler and balance scale to measure temperature, length, and weight. Explore covering a shape with various manipulative materials. Explore finding the area and perimeter of squares and rectangles using nonstandard and standard units (without using formulas).
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task(s) Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards)	Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results
Task 1 Goal: Design a robot using pattern blocks and copy it onto grid paper. Role: You are a robot inventor for Toys R Us. Audience: Your boss at Toys R Us. Situation: You need to draw a design for a new robot toy for Toys R Us. Product Performance and Purpose: The design for your robot should be made up of shapes. It must also have symmetry. Some parts of the shapes robot will slide, flip or turn. You must identify where one part of the design slides. Label the part that slid with the word “slide.” Your design must have a part that is flipped. Label the flipped part with the word “flipped.” Your design must have a part that is turned. Label the part that turned with the word “turned.” Use a ruler to draw the line of symmetry in your design. Bonus: Determine the area of your robot’s head. Use one of the pattern blocks as your unit. Example: The area of my robot’s head is 10 green triangles. Scoring Rubric: The student: Score of 3: Meets or exceeds the objectives of the task. Demonstrates a high level of understanding. Student’s design expertly represents a robot that has a slide, a flip, and a turn. Each transformation is identified. The design is symmetrical. The student has drawn a line of symmetry. Score of 2: Partially meets the objectives of the task. Demonstrates some understanding. Student’s design represents a robot that has a slide, a flip, or a turn. Each transformation is identified. The design is symmetrical. Score of 1: Does not meet the objectives of the task. Demonstrates poor or incorrect understanding. Student’s design represents a robot which is symmetrical. The design has a line of symmetry. Score of 0: Does not demonstrate any understanding of the task. Student shows no understanding of the problem or how to arrive at a solution.	Teacher observations Blackline master Monster Molly Center Activities Group Work Class Work Homework Topic Assessments District Assessments

GRADE: 2

TOPIC: NUMERICAL AND PROPORTIONAL REASONING

STAGE 1: IDENTIFY DESIRED RESULTS
Content Standard(s) Generalizations about what students should know and be able to do
Established Goals: State Standards: Use a variety of numerical representations in the base ten system to describe quantitative relationships. Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. National (NCTM) Standards: Understand numbers, ways, of representing numbers, relationships among numbers, and number systems. Understand meanings of operations and how they relate to one another. Compute fluently and make reasonable estimates.
Enduring Understandings Insights learned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
1. The base ten number system and fractions, decimals, percents and ratios are related. 2. Adding is a combining of things and can be drawn as pictures and symbols. 3. Addition strategies assist in the memorization/ understanding of addition and subtraction facts. 4. Numerical standing is derived from place value. 5. Estimation is a helpful skill in daily activities. 6. Many things in the world around us are divided into parts of a whole. Fractions represent a relationship between the part and the whole. 7. Fractions come in many different forms in our everyday life. 8. Fractions can be compared and added. 9. Multiplication and addition,	1. Why is it important to know different strategies to solve addition facts? 2. How do you know which symbol to use in a number sentence? 3. Why do you think it is important to know addition facts?