AK-DLM ESSENTIAL ELEMENTS AND COMPLEXITY EXAMPLES FOR SEVENTH GRADE Seventh Grade Mathematics Standards: Ratios and Proportional Relationships AK Grade-Level Clusters AK-DLM Essential Elements Instructional Examples Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. 7.RP.2. Recognize and represent proportional relationships between quantities. ƒ Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or EE7.RP.1-3. Use a ratio to model or describe a relationship. Students will: EE7.RP.1-3. Complete the ratio using numbers to show relationships. Ex. Given one component of a ratio in standard form (1:_) complete the ratio. Ex. Given a family picture, what is the ratio of people wearing hats compared to the total number of people in the picture? Ex. Describe the relationship between miles driven and the time taken by creating a ratio (e.g., Katie knows she can drive one mile in two minutes is 1:2). Students will: EE7.RP.1-3. Use a ratio to model or describe a relationship. Ex. Given a bag of green and red chips, identify the ratio of green chips compared to red chips. Ex. Use a pictorial representation to show part-whole relationship (e.g., What part of the picture is shaded? Three parts are shaded and one part is not). Students will: EE7.RP.1-3. Demonstrate a simple ratio relationship. Ex. Using a dry ease board demonstrate a ratio relationship of squares to circles. Ex. When playing a board game, move one space for every dot on the die. Ex. Complete a pattern given a simple ratio. Students will: EE7.RP.1-3. Identify one item as it relates to another. Ex. When given two baskets with markers, count the number in each basket and compare.
Seventh Grade Mathematics Standards: Expressions and Equations AK Grade-Level Clusters AK-DLM Essential Elements Instructional Examples Use properties of operations to generate equivalent expressions. 7.EE.1. Apply properties of operations as strategies to EE7.EE.1. Use the properties of operations as strategies to demonstrate that expressions are equivalent. EE.7.EE.2 Identify an arithmetic sequence of whole numbers with a whole number common difference. Students will: EE7.EE.1-2. Apply the commutative property to complete an equation. Ex. Given 12 objects and an equation with three groups on one side of the equals sign and two groups on other side, create a balanced equation by recognizing that the side with three groups will have two objects in each group, and the side with two groups will have three objects in each group. add, subtract, factor, and Ex. 5 x 7 = x (7 x 5) expand linear expressions with rational coefficients. Ex. + = 4 + 8 (8 + 4) 7.EE.2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” will: EE7.EE.1-2. Use the relationship within addition and/or multiplication to illustrate that two expressions are equivalent. Ex. 4 + 7 = 7 + Ex. 2 x 4 = x 2 Ex. 3 + = 5 + 3 Students will: EE7.EE.1-2. Use the relationship within addition to illustrate that two expressions are equivalent. Ex. Given a model showing five objects plus two objects on one side of an equals sign and two objects on the other side, recognize that five objects are needed to get the same amount. Ex. Is 2 + 3 = to 3 + 2? Answer yes/no. Ex. Is 2 + 3 = to 4 + 2? Answer yes/no. Students will: EE7.EE.1-2. Understand that different displays of the same quantity are equal. Ex. Recognize that three discs and three squares are the same quantity. Ex. Recognize that different arrangements of the same amount are equal
AK Grade-Level Clusters AK-DLM Essential Elements Instructional Examples Ex. When given a shape, find another shape like the one just given. Ex. Compare shapes when given manipulatives – to say two shapes are the same (congruent) after matching the sides on each. Ex. Use various media for students to form a simple geometric shape (e.g., sand, shaving cream). Ex. Given a sample shape, trace the shape (touch board, raised paper, wiki sticks, etc.). 7.G.3. Describe the figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. EE7.G.3. Match a two- dimensional shape with a three-dimensional shape that shares an attribute. Students will: EE7.G.3. Pair two- and three-dimensional shapes to complete a real-world task. Ex. Given a shape and several different two- dimensional shapes (e.g., cube, cylinders), select the two-dimensional shape that represents one face of the shape (e.g., square, circle). Ex. Given a diagram to show the placement of different shaped objects in a storeroom, use the two-dimensional shape in the diagram to place three- dimensional objects appropriately on the shelf (e.g., square boxes on squares, rectangular boxes on rectangles, and bottles on circles). Students will: EE7.G.3. Match a shape with a shape that shares an attribute. Ex. Given a circle, find objects that are counterparts (e.g., ball, globe, sphere). Ex. Given a square, find objects that are counterparts (e.g., box, locker). Ex. Given a square, find three-dimensional objects that share one attribute (e.g., square with cube, circle with cylinder). Students will: EE7.G.3. Identify the attributes of a three-dimensional shape (color, number of sides, faces, size, textures, shape, etc.). Ex. Given a red ball and communication device, identify words that three- dimensional
AK Grade-Level Clusters AK-DLM Essential Elements Instructional Examples describe the attributes of the ball. Ex. Given a group of shapes, describe common attributes. Ex. Given a class of objects, identify common attributes and choose one to sort by. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7.G.4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown EE7.G.4. Determine the perimeter of a rectangle by adding the measures of the sides. EE7.G.5. Recognize angles that are acute, obtuse, and right. Students will: EE7.G.3. Replicate the two-dimensional of a shape (cube, sphere, cylinder) when given a complete shape. Ex. Given a cube, outline the base to form a square. Ex. Given a soda can, outline the base to form a circle. Students will: EE7.G.5. Solve simple perimeter problems with rectangles. Ex. Given a rectangle with identified dimensions, determine the perimeter. Ex. A bulletin board is 5’ by 5’. How much border paper is needed for the perimeter? Ex. When given a picture of a garden with only the length and width identified, solve for perimeter.
Seventh Grade Mathematics Standards: Statistics and Probability AK Grade-Level Clusters AK-DLM Essential Elements Instructional Examples Use random sampling to draw inferences about a population. 7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a EE7.SP.1-2. Answer a question related to the collected data from an experiment, given a model of data, or from data collected by the student. Students will: EE7.SP.1-2. Answer a question about data collected from an experiment and explain or demonstrate the results. Ex. Poll classmates to determine where to go on a field trip and explain results. Ex. Given data on height of students in two classes, identify which class has the tallest students. Students will: EE7.SP.1-2. Answer a question related to the collected data from an experiment, given a model of data, or from data collected by the student. Ex. Given data (e.g., a frequency table) of favorite pizza toppings, which type of pizza would be ordered most often. Ex. Asked what their favorite season is, place themselves in one of the four groups and answer a question about the results. (What is the group’s favorite season? What is the group’s least favorite season?) Students will: EE7.SP.1-2. Collect data to answer a given question. Ex. Ask fellow classmates what their favorite activity subject is and keep tally marks of the responses. Ex. Use a grid to record the number of tennis shoes in the classroom. Students will: EE7.SP.1-2. Answer a question for data collection. Ex. Answer a question about what they ate for breakfast. Ex. Answer a question about their favorite candy bar.