Mathematics Support Guide

Transcription

1 Mathematics Support Guide

2 Table of Contents 3rd Grade...1 Key Concept: Number Sense and Base Ten... 2 Key Concept: Number Sense Fractions... 4 Key Concept: Algebraic Thinking and Operations... 5 Key Concept: Measurement and Data Analysis th Grade Key Concept: Number Sense and Base Ten Key Concept: Number Sense and Operations Fractions Key Concept: Algebraic Thinking and Operations Key Concept: Geometry Key Concept: Measurement and Data Analysis th Grade Key Concept: Number Sense and Base Ten Key Concept: Number Sense and Operations Fractions Key Concept: Algebraic Thinking and Operations Key Concept: Geometry Key Concept: Measurement and Data Analysis th Grade Key Concept: The Number System Key Concept: Ratios and Proportional Relationships Key Concept: Expressions, Equations, and Inequalities Key Concept: Geometry and Measurement Key Concept: Data Analysis and Statistics Key Concept: The Number System Key Concept: Ratios and Proportional Relationships Key Concept: Expressions, Equations, and Inequalities Key Concept: Geometry and Measurement Key Concept: Data Analysis and Statistics i-

3 8th Grade Key Concept: The Number System Key Concept: Functions Key Concept: Expressions, Equations, and Inequalities Key Concept: Geometry and Measurement Key Concept: Data Analysis, Statistics, and Probability th Grade Key Concept: Arithmetic with Polynomials and Rational Expressions Key Concept: Creating Equations Key Concept: Reasoning with Equations and Inequalities Key Concept: Structure and Expressions Key Concept: Interpreting Functions Key Concept: Quantities Key Concept: Real Number System Key Concept: Interpreting Data ii-

4 3rd Grade -1-

5 3rd Grade Key Concept: Number Sense and Base Ten Prioritized Standards: Round whole numbers up to 100 to the nearest 10 (3.NSBT.1). Add and subtract single-digit numbers (3.NSBT.2). Multiply one-digit whole numbers by 10 (3.NSBT.3). Read numbers up to 999 (3.NSBT.4). Compare and order numbers up to 999 using the symbols >, =, or < (3.NSBT.5). It is essential for students to know: Students need to recognize place value up to hundreds place and recognize mathematical symbols in order to round whole numbers, compare numbers, add and subtract numbers, and multiply one-digit whole numbers by NSBT.1: Recognize a unit in the place value system (limited to ones and tens place values). 3. NSBT.2: Recognize the addition, subtraction, and equal signs. 3. NSBT.3: Recognize the numbers 1 10 as a set for the tens place. 3. NSBT.4: Identify numbers in word form (limit to numbers 1 50). 3. NSBT.5: Recognize the <, >, and = signs. 3. NSBT.1: Understand the point when a number should be rounded up (limited to numbers from 1 10). 3. NSBT.2: Identify the functions of addition, subtraction, and equal signs (limited to numbers 1 5). 3. NSBT.3: Identify sets of numbers in tens using numbers NSBT.4: Identify numbers in word form (numbers ranging from 1 50). 3. NSBT.5: Arrange a set of numbers from least to greatest. 3. NSBT.1: Round whole numbers from 0 30 to the nearest NSBT.2: Demonstrate the concept of addition and subtraction (limited to single-digit numbers from 1 10). 3. NSBT.3: Demonstrate the concept of counting by 10 by counting the sets of 10 and adding a zero to the end of the number of sets (limited to the numbers 1 50). 3. NSBT.4: Identify numbers in word form (numbers ranging from 1 100). 3. NSBT.5: Compare 2 numbers up to 50 using symbols (=, <, >). 3. NSBT.1: Round whole numbers from to the nearest NSBT.2: Determine the unknown in an addition/subtraction equation. 3. NSBT.3: Count by tens starting at a multiple of 10 (using a set of 10 objects, numbers, etc., e.g., count with dimes). 3. NSBT.4: Read numbers up to NSBT.5: Compare 2 numbers up to 100 using symbols (=, <, >). -2-

6 Applying the Standards to Functional Skills Using a hundred chart or ones place value chart, show how a collection of 10 pennies (is the same as and) makes one dime to show students place value concepts. Demonstrate addition and subtraction of single digit numbers using student preferred items such as crackers, stickers, coins, counting bears, etc. This can be done as a group of activity or individually with students Using items two students have in their desks or pencil boxes, demonstrate comparing numbers by counting the number of items each student has and comparing who has the most or least amount. -3-

7 3rd Grade Key Concept: Number Sense Fractions Prioritized Standards: Develop an understanding of fractions (i.e., denominators 2, 3, 4, 6, 8, 10) as numbers (3. NSF.1). Explain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that two fractions are equal if they are the same size, based on the same whole, or at the same point on a number line. (3. NSF.2). It is essential for students to know: Students need to identify parts of a fraction and recognize when a fraction model is divided into equal parts 3. NSF. 1: Identify a fraction from a list of numbers (i.e., 3 choices, 2 whole numbers, and 1 fraction). 3. NSF.2: Identify shapes divided into equal parts. 3. NSF.1: Identify parts of a fraction (denominator/numerator). 3. NSF.2: Identify fraction models that are divided into the same number of parts. 3. NSF.1: Identify a part of a whole using fraction models. 3. NSF.2: Recognize that two fractions are equal if they are the same using different numbers in the denominators (using pictures limiting the denominators to 2, 3, and 4). 3. NSF.1: Match fractions to their models (i.e., denominators limited to 2, 3, 4, 6, 8, 10). 3. NSF.2: Identify equal fractions that are the same size, but have different fraction sizes, using models and numbers to show fractions using the denominators 2, 3, 4, 6, 8, 10. Applying the Standards to Functional Skills Students can share a bar of chocolate equally between two people to practice being able to recognize equal parts. The teacher can do an activity with pizza or square shaped crackers to practice fractions. Demonstrate breaking or cutting the item into equal parts such as halves or fourths. Demonstrate where the denominator and numerator come from -- the total number of parts of the cracker or slices of pizza (denominator) and the number of parts remaining, eaten, or shared (numerator). -4-

8 3rd Grade Key Concept: Algebraic Thinking and Operations Prioritized Standards: Use concrete objects, drawings, and symbols to represent multiplication facts of two single-digit whole numbers (i.e., 0 5) (3.ATO.1). Solve real-world problems involving equal groups, area/array, and number line models using basic multiplication (i.e., 0 5) (3.ATO.3). Determine the unknown whole number in a multiplication equation relating three whole numbers when the unknown is a missing factor or product (3.ATO.4). Apply the Commutative Property of Multiplication (3.ATO.5). Demonstrate basic multiplication facts of products through 25 (3.ATO.7). Solve one-step, real-world problems using addition and subtraction of whole numbers and having whole number answers (3.ATO.8). Identify a rule for an arithmetic pattern limited to multiples of 1, 2, 5, 10, and 25 up to 100 (3.ATO.9). It is essential for students to know: Students need to be able to count by multiples and recognize number patterns. Students need to also recognize visual models of expressions (2 rows of 3 apples is the same as 2 x 3). 3. ATO.1: Identify the multiplication symbol. 3. ATO.3: Recognize a group, an array, and a number line using models or pictures. 3. ATO.4: Identify the key terms, factor/product, in a multiplication equation. 3. ATO.1: Demonstrate the concept of multiplication by using the repeated addition strategy (limiting the numbers to 0 2). 3. ATO.3: Match a basic multiplication expression with its model. 3. ATO.4: Determine the unknown whole number in a multiplication equation by selecting the missing product from a set of whole numbers (limiting the numbers 0 5). 3. ATO.1: Demonstrate the concept of multiplication using the multiplication sign using numbers (limiting numbers 0 3). 3. ATO.3: Apply the concept of multiplying using equal groups by solving a simple word problem limiting the numbers from ATO.4: Determine the unknown whole number in a multiplication equation by selecting the missing factor from a set of whole numbers (one missing factor between the numbers 0 5). 3. ATO.1: Multiply two single-digit whole numbers using ATO.3: Solve a real-world problem using basic multiplication with equal groups, arrays, and/or the number line. 3. ATO.4: Determine the unknown whole number in a multiplication equation by selecting the missing factor and product from a set of whole numbers (limiting the numbers 0 5). -5-

9 3. ATO.5: Identify multiplication problems. 3. ATO.7: Recognize basic multiplication sets (limited to the multiples of 0, 1 and 2). 3. ATO.8: Recognize onestep equations. 3. ATO.9: Count by 1, 2, and ATO.5: Match a basic multiplication expression with its model. 3. ATO.7: Demonstrate the concept of multiplication by using pictures of group members being distributed a set number of items. 3. ATO.8: Demonstrate addition/subtraction problems using manipulatives. 3. ATO.5: Match equivalent multiplication expressions using models. 3. ATO.7: Demonstrate the concept of multiplication by matching pictures of multiplication to the correct multiplication equation (limit the factors to between 0 and 5). 3. ATO.8: Determine the unknown in an addition/subtraction equation. 3. ATO.9: Count by 10s. 3. ATO.9: Identify a rule for an arithmetic pattern limited to multiples of 1, 2, 5, and ATO.5: Demonstrate the understanding of the concept by filling in the missing factors in a commutative property equation (filling in one missing factor from both sides). 3. ATO.7: Demonstrate basic multiplication facts of products through ATO.8: Solve addition/subtraction word problems (limit the products to up to 10). 3. ATO.9: Identify a rule for an arithmetic pattern limited to multiples of 1, 2, 5, 10, and 25, up to 100. Applying the Standards to Functional Skills The teacher can use real objects to show 3 groups of 2, which demonstrates the multiplication expression 3 x 2. The students can match or name the multiplication expression that is being demonstrated and find the solution. (For example, there are 3 baskets and there are 2 apples in each basket. This shows 3 x 2, how many apples are there in all?) Using a hundred chart and preferred objects, the teacher can demonstrate counting multiples of 2, 5, and

10 3rd Grade Key Concept: Geometry Prioritized Standards: Recognize rhombuses, rectangles, and squares as quadrilaterals (3.G.1). Partition two-dimensional shapes into two parts with equal areas (3.G.2). It is essential for students to know: Students need to be able to recognize quadrilaterals and their attributes such as having 4 sides and 4 angles. 3. G.1: Identify sides or angles of a quadrilateral. 3. G.2: Identify twodimensional shapes 3. G.1: Identify quadrilaterals. 3. G.2: Recognize the equal parts of a two-dimensional shape. 3. G.1: Recognize rhombuses, rectangles, and squares as quadrilaterals. 3. G.2: Recognize one-half on an area model. 3. G.1: Identify all attributes of quadrilaterals (i.e., 4 sides, 4 angles). 3. G.2: Recognize when a shape is not equal to one-half. Applying the Standards to Functional Skills Identify quadrilaterals in everyday objects, for example open a box of cereal to see that it is made up of three different sized rectangles. -7-

11 3rd Grade Key Concept: Measurement and Data Analysis Prioritized Standards: Use analog and digital clocks to record time to the nearest hour and half hour, using a.m. and p.m. (3.MDA.1). Measure liquid volumes (capacity) in customary units (i.e., c., pt., qt., gal.) and metric units (i.e., ml, L) to the nearest whole unit (3.MDA.2). Interpret data from a picture graph and a bar graph (3.MDA.3). Measure length to the nearest inch (3.MDA.4). It is essential for students to know: Students need to be able to identify tools of measurement. Students need to be able to read time (e.g., 2:30), length with a ruler, and bar graphs. Students need to also identify objects that have volume (e.g., a cup can contain water). 3. MDA.1: Identify a clock as a tool to measure time. 3. MDA.2: Identify threedimensional shapes. 3. MDA.3: Identify a bar graph. 3. MDA.1: Match the time to an activity from a list. 3. MDA.2: Identify shapes that can have volume. 3. MDA.3: Identify information from a bar graph. 3. MDA.4: Identify a ruler. 3. MDA.4: Identify an inch on a ruler. 3. MDA.1: Use analog and digital clocks to record time to the nearest hour and half hour using a.m. and p.m. 3. MDA.2: Demonstrate the concept by choosing the appropriate volume unit for a given substance to be measured (i.e., what is the best unit to measure for a box of cereal?) 3. MDA.3: Identify information from a picture graph. 3. MDA.4: Recognize inches as a measure of length. 3. MDA.1: Demonstrate the concept of telling time to the half hour on both types of clocks. 3. MDA.2: Demonstrate the concept by choosing the appropriate volume unit for various given substances to be measured. 3. MDA.3: Interpret data from a picture graph and a bar graph. 3. MDA.4: Measuring length to the nearest inch. -8-

12 Applying the Standards to Functional Skills The students can practice reading a digital and/or analog clock or watch by incorporating activities throughout the day that require the students to read the clock and compare the time to a class schedule that shows what is happening at different times in the day. Measure liquids using measuring cups or weigh objects using a scale to help with understanding of volume and units of measure. Use bar graphs in newspapers and magazine articles to demonstrate how to interpret the graph data. Measure objects using an inch ruler, for example, the students can measure the length and width of a picture to see if it can fit in a certain frame size. -9-

13 4th Grade -10-

14 4th Grade Key Concept: Number Sense and Base Ten Prioritized Standards: Recognize mathematical periods through 999,999 (4.NSBT.2). Round whole numbers up to 1,000 to the nearest 10 or 100 (4.NSBT.3). Add and subtract two-digit whole numbers (4.NSBT.4). Demonstrate basic multiplication facts of products through 100 (4.NSBT.5). Divide up to a two-digit dividend by a one-digit divisor without remainders using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division (exclude long division) (4.NSBT.6). It is essential for students to know: Students need to recognize place value up to the thousands place and recognize the written form of numbers. Students need to be able to add and subtract two digit whole numbers, and recognize multiplication facts. 4. NSBT.2: Recognize the word form for numbers through NSBT.3: Recognize a place value unit. 4. NSBT.4: Recognize the addition or subtraction symbols. 4. NSBT.5: Recognize multiplication factors and products. 4. NSBT.6: Recognize the division sign. 4. NSBT.2: Recognize the word form for numbers through NSBT.3: Identify when a number can be rounded up to the nearest unit. 4. NSBT.4: Add/subtract two-digit whole numbers within NSBT.5: Demonstrate the concept of multiplication. 4. NSBT.6: Identify the components of a division problem (i.e., What is the dividend? What is the divisor? What is the quotient?). 4. NSBT.2: Recognize the word form for numbers through NSBT.3: Round whole numbers from 0 30 to the nearest NSBT.4: Add/subtract within 100 with a two-digit number and a multiple of NSBT.5: Multiply two single-digit whole numbers using NSBT.6: Demonstrate the concept of division using manipulatives to divide into equal groups. 4. NSBT.2: Recognize the word form for numbers through 999, NSBT.3: Round whole numbers to the nearest 10 or nearest NSBT.4: Solve addition/subtraction word problems within NSBT.5: Multiply two whole numbers using NSBT.6: Solve a division word problem using a twodigit dividend by a one-digit divisor. Applying the Standards to Functional Skills -11-

15 Read and recognize the word form of numbers through bingo game activities. Demonstrate solving addition, subtraction, multiplication, and division problems using preferred objects. Demonstrate multiplication and division facts with preferred objects displayed in arrays. -12-

16 4th Grade Key Concept: Number Sense and Operations Fractions Prioritized Standards: Using visual fraction models, recognize equivalent fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) (4.NSF.1). Compare two given fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) with common denominators using the symbols >, =, or < (4.NSF.2). Develop an understanding of addition and subtraction of fractions with common denominators (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) based on unit fractions. a. Develop an understanding of mixed numbers (4.NSF.3). Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100, and use this technique to add two fractions with respective denominators of 10 and 100 (4.NSF.5). Write a fraction with a denominator of 10 or 100 using decimal notation (4.NSF.6). Compare decimal numbers to hundredths using visual models (4.NSF.7). It is essential for students to know: Students need to identify a fraction of a whole and compare fractions using models. Students also need to recognize decimals, the place value of decimals using models, and compare decimals using symbols. 4. NSF.1: Identify a fraction from a whole number. 4. NSF.2: Recognize greater than and less than signs. 4. NSF.1: Identify models that have been divided in half or equal parts (i.e., denominators limited to 2 10). 4. NSF.2: Demonstrate the concept of greater than and less than using models/groups of manipulatives to choose which ones have more, less or equal (<, >, =). 4. NSF.1: Use same-size models that have been divided differently to solve equivalent fraction problems (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25). 4. NSF.2: Compare two fractions with like denominators using a pictorial model (=, <, >). 4. NSF.1: Use same-size models that have been divided differently to solve equivalent fraction problems (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100). 4. NSF.2: Compare two fractions with like denominators (=, <, >). -13-

17 4. NSF.3: Identify common denominators in fractions. 4. NSF.5: Recognize part of a whole using models. 4. NSF.6: Identify where a decimal point is on the place value chart. Identify the tenths and hundredths place on the value chart. 4. NSF.7: Recognize greater than, less than, and equal signs. 4. NSF.3: Identify numerators and denominators in fractions. 4. NSF.5: Given a model, recognize tenths/hundredths using a model. 4. NSF.6: Demonstrate the function of a decimal point as it represents a fraction using a place value chart. 4. NSF.7: Demonstrate the function of a decimal point as it represents a fraction using a place value chart. 4. NSF.3: Use simple fractions with common denominators (limited between the numbers 2 9); add or subtract the numerators in the fraction. 4. NSF.5: Identify when two fractions are equivalent with the denominators of 10 and NSF.6: Write a fraction from a decimal notation with the denominator of NSF.7: Using visual models, compare decimals to hundredths place. 4. NSF.3: Add/subtract fractions with common denominators (i.e., denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, 25, 100). a. Develop an understanding of mixed numbers. 4. NSF.5: Identify fractions with the denominators of 10 and 100 when comparing two fractions. 4. NSF.6: Write a fraction with a denominator of 10 or 100 as a decimal. 4. NSF.7: Compare decimal numbers to hundredths place. Applying the Standards to Functional Skills Demonstrate adding and subtracting fractions by sharing objects that can be divided such as a piece of paper or large crackers. Demonstrate decimals using a hundred chart with pennies and dimes. Connect the decimals shown with the coins to the written decimal number. Compare decimals using a hundred chart and two sets of pennies and dimes (e.g., 2 dimes and 1 penny is greater than 4 pennies). -14-

18 4th Grade Key Concept: Algebraic Thinking and Operations Prioritized Standards: Solve one-step, real-world problems using basic multiplication (0 10) or division (with no remainders) (4.ATO.2). Find all factor pairs for whole numbers 1 24 (4.ATO.4). Given the rule for a pattern, determine the next term in the sequence/pattern (4.ATO.5). It is essential for students to know: Students need to be able to recognize symbol and picture patterns. Students need to also recognize multiplication facts 1 10 to solve multiplication and division problems. 4. ATO.2: Identify the components of a multiplication problem. 4. ATO.4: Recognize what a factor pair is for a whole number. 4. ATO.5: Recognize patterns. 4. ATO.2: Demonstrate the concept of multiplication/division. 4. ATO.4: Identify factors for whole numbers ATO.5: Identify symbolic, repeating, and pictorial patterns. 4. ATO.2: Determine the unknown in multiplication/division equation. 4. ATO.4: Identify factors for whole numbers ATO.5: Given the rule, determine the next term in a picture pattern/sequence. 4. ATO.2: Solve one-step multiplication or division word problems. 4. ATO.4: Identify factors for whole numbers ATO.5: Given the rule, determine the next term in a number pattern/sequence. Applying the Standards to Functional Skills Use a rug with a pattern or another familiar object with a pattern, and have the student identify the pattern shown on the object Use student preferred objects and create real-life word problems demonstrating multiplication facts 1 through 10. Show the student a multiplication fact they know using objects and the written fact (e.g., 2 x 3 = 6). Connect how the multiplication fact helps solve the related division problem (6 / 2 = 3 or 6 / 3 = 2). -15-

19 4th Grade Key Concept: Geometry Prioritized Standards: Identify points, line segments, and angles in two-dimensional figures (4.G.1). Identify parallel and perpendicular lines (4.G.2). It is essential for students to know: Students need to be able to recognize points, lines, and line segments. Students need to be able to recognize parallel and perpendicular lines. 4. G.1: Recognize a point. 4. G.1: Identify a line or line segment. 4. G.2: Identify lines. 4. G.2: Identify shapes with parallel lines. 4. G.1: Recognize different types of angles (acute, right, obtuse, and straight). 4. G.2: Identify parallel and perpendicular lines. 4. G.1: Recognize angle, point, or line segment in a two-dimensional figure. 4. G.2: Identify parallel and perpendicular lines in shapes. Applying the Standards to Functional Skills Place marking spots on the classroom floor and engage students to act or show points, lines, and line segments by moving to the different marking spots in the classroom. Use objects in the classroom to demonstrate parallel and perpendicular lines. Use objects in the classroom or pictures of familiar places to demonstrate parallel and perpendicular lines. -16-

20 4th Grade Key Concept: Measurement and Data Analysis Prioritized Standards: Distinguish measurements within a single system of measurement customary (i.e., in., ft., yd., min., hr.) or metric (i.e., cm, m, km, g, kg, ml, L) as larger or smaller (4.MDA.1). Find the area and perimeter for rectangles when given the side lengths (4.MDA.3). Determine the value of a collection of coins and bills greater than $1 (4.MDA.8). It is essential for students to know: Students need to be able to identify length and width of a shape. Students need to be able to distinguish between and compare types of measurement (e.g., inches, minutes, feet). Students also need to be able to recognize coins. 4. MDA.1: Compare two pieces of data with the same unit of measurement. 4. MDA.3: Recognize side lengths. 4. MDA.8: Recognize money. 4. MDA.1: Distinguish between systems of measurement. 4. MDA.3: Recognize a rectangle. 4. MDA.8: Identify a penny, a nickel, a dime, and a quarter. 4. MDA.1: Determine if measurements within one system are larger or smaller (i.e., in., ft., min., hr., ml, L). 4. MDA.3: Find area and perimeter by counting squares. 4. MDA.8: Identify the value of a penny, a nickel, a dime, and a quarter. 4. MDA.1: Compare the size of measurements within one system measure (i.e., in., ft., yd., min., hr.) or metric (i.e., cm, m, km, g, kg, ml, L). 4. MDA.3: Find area and perimeter for rectangles when given the side lengths. 4. MDA.8: Determine the value of a collection of coins and bills greater than $1. Applying the Standards to Functional Skills Show advertisements and sales flyers and have students select the appropriate coins needed to purchase certain items Use classroom objects to measure side lengths. Use classroom objects and using counting squares to determine perimeter and area. -17-

21 5th Grade -18-

22 5th Grade Key Concept: Number Sense and Base Ten Prioritized Standards: Use whole-number exponents to explain patterns in the number of zeroes of the product when multiplying a number by powers of 10 (5.NSBT.2). Read and write decimals in standard form. Compare two decimal numbers to the hundredths place using the symbols >, =, or < (5.NSBT.3). Round decimals to the nearest whole number (5.NSBT.4). Multiply a multi-digit whole number by a one-digit whole number using strategies to include a standard algorithm (5.NSBT.5). Divide up to a four-digit dividend by a one-digit divisor using strategies based on place value, the properties of operations, and the relationship between multiplication and division (5.NSBT.6). Add and subtract decimal numbers to hundredths using concrete area models and drawings (5.NSBT.7). It is essential for students to know: Students need to be able to continue a pattern and identify equal groups. Students need to be able to recognize multiplication facts up to 100. Students also need to be able to define decimals, compare decimals up to hundredths place, and recognize decimals when written as money. 5. NSBT.2: Identify or continue a pattern. 5. NSBT.3: Recognize larger, smaller, and equal. 5. NSBT.2: Multiply a product of 10 by NSBT.3: Identify and define a decimal. 5. NSBT.4: Identify a unit. 5. NSBT.4: Identify a decimal. 5. NSBT.5: Identify and represent repeated addition with an equation. 5. NSBT.6: Identify equal groups. 5. NSBT.5: Solve repeated addition problems. 5. NSBT.6: Understand that equal groups can be represented by division. 5. NSBT.2: Identify the product, given the number 10, with an exponent. 5. NSBT.3: Compare two decimals to the hundredths (=, <, >). 5. NSBT.4: Round a decimal to the nearest whole number (limit to decimals over 0.50). 5. NSBT.5: Demonstrate the concept of multiplication related to repeated addition. 5. NSBT.6: Apply the relationship between multiplication and division. 5. NSBT.2: Identify the power of 10, given the product. 5. NSBT.3: Compare two decimals to the hundredths (=, <, >). Read and write monetary values. 5. NSBT.4: Round a decimal to the nearest whole number. 5. NSBT.5: Multiply by 1, 2, 3, 4, and/or NSBT.6: Divide by 1, 2, 3, 4, and/or

23 5. NSBT.7: Identify whole and part. 5. NSBT.7: Identify a whole number when presented in monetary form. Identify a decimal when presented in monetary form. 5. NSBT.7: Add and subtract monetary amounts, including in whole numbers (with the $.00 included). Students may use a model or drawing. 5. NSBT.7: Add and subtract multi-digit decimal numbers without regrouping. Add and subtract monetary amounts, including dollars and cents. Students may use a model or drawing. Applying the Standards to Functional Skills Use advertisements, printed website pages, or sales flyers to demonstrate adding, subtracting, and comparing decimals. Use student preferred objects to demonstrate repeated addition is the same as a multiplication array and multiplication expression. Use student preferred objects to demonstrate similarities between multiplication facts and division. -20-

24 5th Grade Key Concept: Number Sense and Operations Fractions Prioritized Standards: Add and subtract fractions with unlike denominators using a variety of models, including an area model and number line (5.NSF.1). Multiply a whole number by a fraction (5.NSF.4). It is essential for students to know: Students need to be able to divide a whole into equal parts. Students need to be able to add, subtract, and multiply fractions using models. 5. NSF.1: Partition any shape into equal parts. 5. NSF.4: Add two of the same fractions (limit to halves, thirds, and fourths). Applying the Standards to Functional Skills 5. NSF.1: Create a model of a fraction (partition and shade). 5. NSF.4: Understand the relationship between adding and multiplying the fraction. 5. NSF.1: Add or subtract fractions with like denominators using models (limit to halves, thirds, fourths, sixths, and eighths). 5. NSF.4: Multiply a whole number by a fraction (limit to compatible numbers that result in a whole-number product). 5. NSF.1: Add or subtract fractions with unlike denominators (limit to halves, thirds, fourths, sixths, and use visual models). 5. NSF.4: Multiply a whole number by a fraction. Have students add and subtract fractions with like denominators by using a large measuring cup and an individual measuring spoon. -21-

25 5th Grade Key Concept: Algebraic Thinking and Operations Prioritized Standards: Evaluate two-step numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces) (5.ATO.1). Translate verbal phrases into simple numerical expressions (5.ATO.2). It is essential for students to know: Students need to be able to recognize computation terms (e.g., how many are left, altogether). Students need to be able to create and solve one step addition and subtraction equations. 5. ATO.1: Identify grouping symbols in an expression (parentheses, brackets, braces). 5. ATO.2: Identify the symbol that correlates with sum, product, take away, and divide. 5. ATO.1: Evaluate a onestep expression that contains grouping symbols. 5. ATO.2: Given a verbal phrase, identify the operation. 5. ATO.1: Evaluate a twostep numerical expression involving grouping symbols (limit to addition and subtraction). 5. ATO.2: Translate verbal phrases into simple numerical expressions (limit one-step addition or subtraction). 5. ATO.1: Evaluate two-step numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces; limit to addition and subtraction). 5. ATO.2: Translate verbal phrases into simple numerical expressions. Applying the Standards to Functional Skills Demonstrate solving one-step addition and subtraction problems using preferred objects. For example, have students count how many items they have in their pencil box. Then have students give away or add more items to the box. Create addition or subtraction expressions demonstrating how the amount of supplies changed. -22-

26 5th Grade Key Concept: Geometry Prioritized Standards: Define a coordinate system (5.G.1). a. The x- and y-axes are perpendicular number lines that intersect at 0 (the origin) (5.G.1a). b. Any point on the coordinate plane can be represented by its coordinates (5.G.1b). c. The first number in an ordered pair is the x-coordinate and represents the horizontal distance from the origin (5.G.1c). d. The second number in an ordered pair is the y-coordinate and represents the vertical distance from the origin (5.G.1d). Plot points in the first quadrant (5.G.2). It is essential for students to know: Students need to be able to identify various points on a number line. Students need to be able to recognize line segments and intersecting lines. 5. G.1: Recognize a point on a number line (limit to numbers greater than 0). 5. G.1a: Recognize a point on a number line (limit to numbers greater than 0). 5. G.1b: Recognize a point on a number line (limit to numbers greater than 0). 5. G.1c: Recognize a point on a number line (limit to numbers greater than 0). 5. G.1d: Recognize a point on a number line (limit to numbers greater than 0). 5. G.1: Identify a number on a vertical or horizontal number line. 5. G.1a: Identify a number on a vertical or horizontal number line. 5. G.1b: Identify a number on a vertical or horizontal number line. 5. G.1c: Identify a number on a vertical or horizontal number line. 5. G.1d: Identify a number on a vertical or horizontal number line. 5. G.2: Recognize a point. 5. G.2: Recognize intersecting lines/line segments. 5. G.1: Plot a number on a vertical or horizontal number line. 5. G.1a: Plot a number on a vertical or horizontal number line. 5. G.1b: Plot a number on a vertical or horizontal number line. 5. G.1c: Plot a number on a vertical or horizontal number line. 5. G.1d: Plot a number on a vertical or horizontal number line. 5. G.2: Recognize perpendicular lines/line segments. 5. G.1: Identify an ordered pair on a coordinate plane. 5. G.1a: Identify an ordered pair on a coordinate plane. 5. G.1b: Identify an ordered pair on a coordinate plane. 5. G.1c: Identify an ordered pair on a coordinate plane. 5. G.1d: Identify an ordered pair on a coordinate plane. 5. G.2: Plot a point on a map given the x and y variables. -23-

27 Applying the Standards to Functional Skills Have students roll a die and place a marker on a number line corresponding to the number rolled on the die. Using pictures of real life locations and objects, demonstrate the difference between line segments and intersecting lines. -24-

28 5th Grade Key Concept: Measurement and Data Analysis Prioritized Standards: Convert measurements within a single system of measurement customary (i.e., in., ft., yd., min., hr.) or metric (i.e., cm, m, km, ml, L) from a larger to a smaller unit (5.MDA.1). Differentiate among perimeter, area, and volume, and identify which application is appropriate for a given situation (5.MDA.4). It is essential for students to know: Students need to be able to determine and compare the length of two objects or the mass of two objects. Students need to be able to determine the perimeter and area of a shape. 5. MDA.1: Recognize measurable attributes. 5. MDA.4: Recognize measurable attributes. 5. MDA.1: Make a direct comparison of two lengths. Make a direct comparison of two masses. 5. MDA.4: Calculate perimeter by adding all the side lengths. Calculate the area by counting the square units. 5. MDA.1: Use an appropriate tool for measuring length using inches; use an appropriate tool for measuring length using feet; use an appropriate tool for measuring mass in pounds; use an appropriate tool for measuring mass in ounces. 5. MDA.4: Solve word problems involving perimeter of polygons. 5. MDA.1: Convert measurements within a single system of measurement. 5. MDA.4: Solve word problems by using perimeter, area, or volume. Applying the Standards to Functional Skills The students can practice the difference among perimeter, area, and volume by identifying which is needed for certain real-life activity. For example: -25-

29 The amount of water in the beaker requires calculating volume. Determining where the rug can fit requires calculating area. Determining the amount of fencing needed for the vegetable garden requires calculating perimeter. NOTE: The images are just examples, final images may be slightly different. -26-

30 6th Grade -27-

31 6th Grade Key Concept: The Number System Prioritized Standards: Fluently divide multi-digit whole numbers limited to four-digit dividends and two-digit divisors using a standard algorithmic approach (6.NS.2). Fluently add and subtract multi-digit decimal numbers to the hundredths place using a standard algorithmic approach (6.NS.3). Find common factors and multiples using two whole numbers up to 50 for factors and less than or equal to 10 for multiples (6.NS.4). Understand that the positive and negative representations of a number are opposites in direction and value. Use integers to represent quantities in real-world situations (6.NS.5). Plot integers on number lines and ordered pairs on the coordinate plane (6.NS.6). a. Interpret statements using equal to (=) and not equal to ( ) (6.NS.7a). b. Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations on the number line (6.NS.7b). c. Use concepts of equality and inequality to write and to explain real-world and mathematical situations (6.NS.7c). d. Understand that absolute value represents a number s distance from zero on the number line, and use the absolute value of an integer number to represent real-world situations (6.NS.7d). Explore and translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100 (6.NS.9). It is essential for students to know: Students need to be able to add and subtract decimals to the hundredths place. Students need to know multiplication and division fact families. Students need to be able to recognize and compare points on a number line. Students also need to recognize points on the first quadrant of a coordinate plane. 6. NS.2: Demonstrate the concept of division. 6. NS.3: Identify whole and part. 6. NS.2: Apply the relationship between multiplication and division. 6. NS.3: Identify a whole number when presented in monetary form. Identify a decimal when presented in monetary form. 6. NS.2: Divide by 1, 2, 3, 4, and/or NS.3: Add and subtract monetary amounts including in whole numbers (with the $.00 included); students may use a model or drawing. 6. NS.2: Divide by numbers up to and including NS.3: Add and subtract multi-digit decimal numbers without regrouping. Add and subtract monetary amounts including the dollar and cents; student may use a model or drawing. -28-

32 6. NS.4: Identify fact families of a number using multiplication. 6. NS.5: Given a real-world context, identify the value of the situation (limit to positive numbers under 15). 6. NS.6: Identify a number on a vertical or horizontal number line. 6. NS.7a: Identify if two statements are equal (=) and not equal ( ). 6. NS.7b: Identify if two statements are equal (=) and not equal ( ). 6. NS.7c: Identify if two statements are equal (=) and not equal ( ). 6. NS.4: Find the factors of a number (limit to fact families under 50). 6. NS.5: Given a real-world context, identify the value of the situation (limit to positive numbers under 100). 6. NS.6: Plot a number on a vertical or horizontal number line. 6. NS.7a: Given two points on a number line, identify a statement using less than (<), greater than (>), and equal to (=) to describe their locations on the number line. 6. NS.7b: Given two points on a number line, identify a statement using less than (<), greater than (>), and equal to (=) to describe their locations on the number line. 6. NS.7c: Given two points on a number line, identify a statement using less than (<), greater than (>), and equal to (=) to describe their locations on the number line. 6. NS.4: Given the factors of two numbers, identify the common factors (for two whole numbers up to 50 and multiples of 5 or 10). 6. NS.5: Given a real-world context, identify whether the value in the situation is positive, negative, or zero. 6. NS.6: Identify an ordered pair on a coordinate plane. 6. NS.7a: Given a real-world or mathematical situation, identify a statement of equality or inequality that describes it. 6. NS.7b: Given a real-world or mathematical situation, identify a statement of equality or inequality that describes it. 6. NS.7c: Given a real-world or mathematical situation, identify a statement of equality or inequality that describes it. 6. NS.4: Find common factors for whole numbers up to 50 and less than or equal to 10 for multiples. 6. NS.5: Given a real-world context, identify the value of the situation which may include negative numbers. 6. NS.6: Plot an ordered pair on a coordinate plane. 6. NS.7a: Identify the absolute value of a number as the distance from zero on a number line. 6. NS.7b: Identify the absolute value of a number as the distance from zero on a number line. 6. NS.7c: Identify the absolute value of a number as the distance from zero on a number line. -29-

33 6. NS.7d: Identify if two statements are equal (=) and not equal ( ). 6. NS.9: Identify a whole number. Applying the Standards to Functional Skills 6. NS.7d: Given two points on a number line, identify a statement using less than (<), greater than (>), and equal to (=) to describe their locations on the number line. 6. NS.9: Identify the definition of a rational number. 6. NS.7d: Given a real-world or mathematical situation, identify a statement of equality or inequality that describes it. 6. NS.9: Identify multiple representations of a rational number. 6. NS.7d: Identify the absolute value of a number as the distance from zero on a number line. 6. NS.9: Translate multiple representations of rational numbers (fractions, decimal numbers, and percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100. Identify equality statements when given a real-world situation, for example, Mary is 12 years old, Chris is 11 years old. Which statement correctly compares Mary and Chris s ages? Create a number line using electric tape on the ground and measure steps from zero in both directions to demonstrate the concept of absolute value. Add and subtract monetary amounts including the dollar and cents. For example, Craig has $ He spends $2.65 to buy a notebook and $1.50 on an eraser from the school store. How much money does Craig have left? Calculate the final price when things are on sale. For example, calculate 25% off a pair of jeans that are $

34 6th Grade Key Concept: Ratios and Proportional Relationships Prioritized Standards: Understand the concept of a ratio as the relationship between two quantities, including part to part and part to whole (6.RP.1). It is essential for students to know: Students need to be able to recognize ratios. 6. RP.1: Identify a ratio. 6. RP.1: Identify a ratio that matches a context. 6. RP.1: Understand the concept of a ratio as the relationship between two quantities (limit to part to whole). 6. RP.1: Understand the concept of a ratio as the relationship between two quantities, including part to part and part to whole. Applying the Standards to Functional Skills Determine solutions to real-world problems like the recipe for 12 muffins uses 2 eggs. How many eggs are needed to make 36 muffins? -31-

35 6th Grade Key Concept: Expressions, Equations, and Inequalities Prioritized Standards: Write numerical expressions involving whole numbers using the Order of Operations (6.EE.1). Identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and variables (6.EE.2). Identify linear equations for real-world situations (6.EE.7). It is essential for students to know: Students need to be able to differentiate between a variable, a number, and recognize expressions and equations. Students also need to know the order of operations. 6. EE.1: Given an equation, identify the symbols for the four functions (+, -, x, ). 6. EE.1: Given an equation, identify the first step for Order of Operations. 6. EE.1: Given an equation, identify the Order of Operations. 6. EE.1: Write numerical expressions involving whole numbers using the Order of Operations. 6. EE.2: Distinguish between a number and a letter. 6. EE.2: Identify an algebraic expression. 6. EE.2: Identify the parts of an expression using mathematical terminology (limit to term and variable). 6. EE.2: Identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and variable. 6. EE.7: Recognize that an unknown value can be represented by a variable. 6. EE.7: Identify the relationship between two variables. 6. EE.7: Identify a situation where the variables create an increasing linear equation (e.g., The more hours you work, the higher your paycheck; the further away your destination, the longer the bus ride). 6. EE.7: Identify linear equations related to wages, finances, time, and distance. -32-

36 Applying the Standards to Functional Skills Read articles with graphs and interpret the graphs. Identify linear equations that represent real-life situations, for example, Peter is paid $5 for walking 1 dog, $10 for walking 2 dogs, and $15 for walking 3 dogs. Which line shows how much Peter gets paid for walking dogs? -33-

37 6th Grade Key Concept: Geometry and Measurement Prioritized Standards: Find the area of right triangles and rectangles (6.GM.1). It is essential for students to know: Students need to be able to identify triangles and right angles. 6. GM.1: Identify a triangle. 6. GM.1: Identify a triangle that has a right angle. 6. GM.1: Find the area of a rectangle given the side lengths and tiles. 6. GM.1: Find the area of right triangles and rectangles when given side lengths. Applying the Standards to Functional Skills The students can practice finding the area by measuring the length and width of a window to determine what size curtains are needed, or they can measure the length and width of the classroom and their desks to determine approximately how many desks would fit in the classroom. Have students identify triangles inside everyday objects such as picture on flags, road signs, or entrance of a tent. -34-

38 6th Grade Key Concept: Data Analysis and Statistics Prioritized Standards: Find the mean, median, mode, and range (6.DS.1). It is essential for students to know: Students need to be able to order numbers from least to greatest. Students need to be able to identify the smallest and largest number within a data set. 6. DS.1: Find the largest/smallest number in a data set. 6. DS.1: Put a data set in order from least to greatest. 6. DS.1: Determine the middle point of a collection of objects. 6. DS.1: Identify the median and/or range of a data set. Applying the Standards to Functional Skills The students can collect data within the classroom such as shoes sizes. For example, the students can collect information on each person s shoe size and plot the information on a large number line on the board or interactive whiteboard. Discuss with students what the range, median, and mode of the shoe sizes are in the classroom. This can be expanded to collecting data across people or classrooms in the school building. -35-

39 7th Grade -36-

40 7th Grade Key Concept: The Number System Prioritized Standards: Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line (7.NS.1). Extend prior knowledge of operations with positive rational numbers to multiply and divide all rational numbers (7.NS.2). Apply the concepts of all four operations with positive rational numbers to solve one-step, real-world and mathematical problems (7.NS.3). Understand and apply the concepts of comparing and ordering rational numbers on a number line. Interpret statements using less than (<), greater than (>), less than or equal to ( ), greater than or equal to ( ), and equal to (=) as relative locations on the number line (7.NS.4). Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers). Exclude the conversion of repeating decimal numbers to fractions (7.NS.5). It is essential for students to know: Students need to be able to differentiate between a whole number, a fraction, and a decimal. Students need to be able to order whole numbers, fractions, and decimals on a number line. Students need to be able to convert a fraction (with single digit numerators and a denominator of 10) to the equivalent decimal. Students also need to be able to apply all four operations to solve problems with decimals in the tenths place. 7. NS.1: Identify a whole number or a fraction. 7. NS.2: Identify a whole number or a fraction. 7. NS.1: Convert a whole number into a fraction. 7. NS.2: Convert a whole number into a fraction. 7. NS.1: Extend prior knowledge of operations with positive rational numbers to add and subtract all rational numbers. 7. NS.2: Extend prior knowledge of operations with positive rational numbers to multiply and divide all rational numbers. 7. NS.1: Extend prior knowledge of operations with positive rational numbers to add and subtract all rational numbers and represent the sum or difference on a number line. 7. NS.2: Extend prior knowledge of operations with positive rational numbers to multiply and divide all rational numbers and represent the result on a number line. -37-

41 7. NS.3: Apply the concepts of the operations of addition and subtraction with positive rational numbers to solve one-step, real-world and mathematical problems. 7. NS.4: Understand and apply the concepts of comparing and ordering whole numbers on a number line. 7. NS.5: Identify same and different fractions or decimal numbers from pictorial representations. 7. NS.3: Apply the concepts of the operations of multiplication and division with positive rational numbers to solve one-step, real-world and mathematical problems. 7. NS.4: Understand and apply the concepts of comparing and ordering whole numbers on a number line. Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations on the number line. 7. NS.5: Identify equivalent fractions and decimal numbers up to 100. Exclude the conversion of repeating decimal numbers to fractions. 7. NS.3: Apply the concepts of all four operations with positive rational numbers to solve one-step, real-world and mathematical problems. 7. NS.4: Understand and apply the concepts of comparing and ordering rational numbers on a number line. Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations on the number line. 7. NS.5: Extend prior knowledge to translate among fractions and decimal numbers up to 100. Exclude the conversion of repeating decimal numbers to fractions. 7. NS.3: Apply the concepts of all four operations with positive rational numbers to solve two-step, real-world and mathematical problems. 7. NS.4: Understand and apply the concepts of comparing and ordering rational numbers on a number line. Interpret statements using less than (<), greater than (>), less than or equal to ( ), greater than or equal to ( ), and equal to (=) as relative locations on the number line. 7. NS.5: Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers). Exclude the conversion of repeating decimal numbers to fractions. Applying the Standards to Functional Skills Using a scale and some fruits and vegetables, you can create a store scenario and have the students calculate the total cost of the fruits and vegetables per pound by weighing the fruits and vegetables and then multiplying by the price per pound. Calculating the price of an item that is discounted is a real-life example of a skill that helps the students practice solving real-world problems involving all rational numbers. -38-

42 7th Grade Key Concept: Ratios and Proportional Relationships Prioritized Standards: Identify proportional relationships given multiple representations, including tables, graphs, and real-world situations (7.RP.2). a. Determine when two quantities are in a proportional relationship (7.RP.2a). e. Identify the graph of a proportional relationship in a real-world situation (7.RP.2e). Solve real-world and mathematical problems involving ratios and percentages (7.RP.3). It is essential for students to know: Students need to be able to recognize part to whole relationships. Students need to be able to recognize ratios in real-world settings (such as what proportion of the class is made up of boys). 7. RP.2: Identify equivalent relationships in real-world situations. 7. RP.3: Understand part and whole relationships. 7. RP.2: Identify proportional relationships in real-world situations. 7. RP.3: Solve real-world problems involving percentages. 7. RP.2: Identify proportional relationships given multiple representations, including tables, graphs, and realworld situations. a. Determine when two quantities are in a proportional relationship. 7. RP.3: Solve real-world problems involving ratios and percentages. 7. RP.2: Identify proportional relationships given multiple representations, including tables, graphs, and real-world situations. a. Determine when two quantities are in a proportional relationship. e. Identify the graph of a proportional relationship in a real-world situation. 7. RP.3: Solve real-world and mathematical problems involving ratios and percentages. Applying the Standards to Functional Skills The students can collect data on how many boys and girls are in the classroom, and discuss the proportion of boys to the whole class and the girls to the whole class. This can be extended to collecting data and identifying proportions with other objects and resources in the classroom. -39-

43 7th Grade Key Concept: Expressions, Equations, and Inequalities Prioritized Standards: Apply mathematical properties (e.g., commutative, associative) to simplify linear algebraic expressions with wholenumber coefficients (7.EE.1). Extend previous understanding of Order of Operations to solve multi-step, real-world and mathematical problems involving whole numbers. Exclude exponents and fraction bars as a grouping symbol (7.EE.3). It is essential for students to know: Students need to be able apply the order of operations and commutative property of addition and multiplication. 7. EE.1: Apply mathematical commutative property of addition. 7. EE.3: Identify a mathematical operation by its symbol. 7. EE.1: Apply mathematical commutative property of addition and multiplication. 7. EE.3: Know the Order of Operations in a mathematical expression. 7. EE.1: Apply mathematical commutative property to simplify linear algebraic expressions with whole-number coefficients. 7. EE.3: Extend previous understanding of Order of Operations to solve two-step, real-world problems involving whole numbers. Exclude exponents and fraction bars as a grouping symbol. 7. EE.1: Apply mathematical properties (e.g., commutative, associative) to simplify linear algebraic expressions with whole-number coefficients. 7. EE.3: Extend previous understanding of Order of Operations to solve multistep, real-world and mathematical problems involving whole numbers. Exclude exponents and fraction bars as a grouping symbol. Applying the Standards to Functional Skills Use simple directions to show the real-world use of the commutative property. For example, here are directions to the principal s office: take a right out of the classroom door, walk 10 feet, then take a left, walk 5 feet, and the office is in front of you. When going back to class, you will walk 5 feet from the principal s office and then take a right, walk 10 feet, and the class will be on your left. -40-

44 7th Grade Key Concept: Geometry and Measurement Prioritized Standards: Understand that the concept of area applies to two-dimensional figures. Understand that the concept of volume applies to three-dimensional figures (7.GM.6). It is essential for students to know: Students need to be able to differentiate between two- and three-dimensional objects. Students also need to be able to determine when to find the area or volume of an object (such as you find the area of a window but you find the volume of a cereal box) 7. GM.6: Understand the difference between two dimensional and threedimensional figures. 7. GM.6: Understand the concept of area. Understand the concept of volume. 7. GM.6: Understand that the concept of area applies to two-dimensional figures. Understand that the concept of volume applies to threedimensional figures. 7. GM.6: Understand that the concept of area applies to two-dimensional figures. Understand that the concept of volume applies to threedimensional figures. Understand which formula to use to calculate either area or volume. Applying the Standards to Functional Skills Discover the concept of area by measuring the length and width of papers, then use unit squares to prove if your calculation methods were correct. Discover the concept of volume by estimating the number of dried beans that can fill a three-dimensional object. First, count the number of beans that cover the bottom of the shape. Then count the number of beans needed to make the height of the object and multiply the numbers. Verify your findings by counting the number of beans in the container. -41-

45 7th Grade Key Concept: Data Analysis and Statistics Prioritized Standards: Understand that a sample is a subset of a population. Distinguish between populations and samples. Distinguish between random and nonrandom samples (7.DS.1). Draw inferences about a population by collecting random samples (7.DS.2). Use the numerical measures of center (mean, median, mode, and range) (7.DS.4). Understand that probability measures likelihood of a chance event occurring (7.DS.5). It is essential for students to know: Students need to be able to determine if an event is possible or likely. Students need to be able to differentiate between a population and a sample. Students need to be able to make statements about a data set (i.e., lunch choices). Students also need to be able to determine the median of a data set. 7. DS.1: Distinguish between a whole and a part. 7. DS.2: Determine if it is a random sample. 7. DS.4: Determine the middle point of a collection of objects. 7. DS.5: Recognize the outcome of an event. Applying the Standards to Functional Skills 7. DS.1: Determine if it is a population or a sample. 7. DS.2: Identify a statement about a given random sample. 7. DS.4: Identify the median of a data set. 7. DS.5: Identify if an event is possible or impossible. 7. DS.1: Understand that a sample is a subset of a population. Identify populations and samples. Identify random and nonrandom samples. 7. DS.2: Draw inferences about a population when given random samples. 7. DS.4: Use the numerical measures of center (mean and median). 7. DS.5: Understand that probability measures likelihood of a chance event occurring. 7. DS.1: Understand that a sample is a subset of a population. Distinguish between populations and samples. Distinguish between random and nonrandom samples. 7. DS.2: Draw inferences about a population by collecting random samples. 7. DS.4: Use the numerical measures of center (mean, median, mode, and range). 7. DS.5: Determine the probability of simple events. Collect data in the classroom by asking everyone on the basketball team their shoe size, then find the mode of the data to help the coach determine how many different sized shoes should be ordered for the team. -42-

46 8th Grade -43-

47 8th Grade Key Concept: The Number System Prioritized Standards: Recognize the differences between rational and irrational numbers. Understand that all real numbers have a decimal expansion (8.NS.1). Estimate the value of irrational and rational numbers by plotting them on a number line (8.NS.2). Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Exclude the conversion of repeating decimal numbers to fractions (8.NS.3). It is essential for students to know: Students need to be able to identify rational numbers and plot fractions on a number line. Students need to be able to convert fractions with denominators 2, 4, 6, and 8 to equivalent decimals. 8. NS.1: Identify whole numbers and fractions. 8. NS.2: Plot whole numbers and fractions on a number line. 8. NS.1: Identify rational numbers. 8. NS.2: Plot rational numbers on a number line. 8. NS.3: Identify fractions. 8. NS.3: Translate fractions with the denominators 2, 4, 6, 8, and 10 into decimals. 8. NS.1: Recognize the differences between rational and irrational numbers. 8. NS.2: Plot irrational and rational numbers on a number line. 8. NS.3: Translate among multiple representations of rational numbers (fractions and decimal numbers). Exclude the conversion of repeating decimal numbers to fractions. 8. NS.1: Recognize the differences between rational and irrational numbers. Understand that all real numbers have a decimal expansion. 8. NS.2: Estimate the value of irrational and rational numbers by plotting them on a number line. 8. NS.3: Translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Exclude the conversion of repeating decimal numbers to fractions. -44-

48 Applying the Standards to Functional Skills The students can practice translating among multiple representations of rational numbers by doing everyday things like making a monthly lunch budget and calculating a percentage of their monthly allowance that they want to save. -45-

49 8th Grade Key Concept: Functions Prioritized Standards: Understand that a function assigns to each input exactly one output. Determine if a relation is a function using multiple representations, including tables, graphs, and equations. Graph a function from a table of x and y values. Extend the knowledge of the coordinate plane to use the set of ordered pairs of that function (8.F.1). Compare two functions, including tables, graphs, and equations in order to draw conclusions (8.F.2). Understand that the slope is the constant rate of change, and the y-intercept is the point where x = 0. Interpret the meaning of the slope and the y-intercept of a linear function in the context of the situation (8.F.4). It is essential for students to know: Students need to be able to graph ordered pairs on a coordinate plane. Students need to be able to identify the rise and run of line on a graph. Students also need to be able to identify if a line has a positive or negative slope. 8. F.1: Identify a point. 8. F.1: Graph a point when given an ordered pair of numbers. 8. F.2: Identify the slope or intercepts of a function in graph form. 8. F.4: Identify a line on a graph. 8. F.2: Identify the slope and intercepts of a function given in equation form. 8. F.4: Understand that slope is related to the direction of the line. 8. F.1: Graph a function from a table of x and y values. 8. F.2: Compare the slopes of two functions given in equation form (slope intercept form). 8. F.4: Understand that the slope is the constant rate of change, and the y-intercept is the point where x = F.1: Generate ordered pairs from two distinct numerical patterns. Extend a symbolic pattern by applying the rule. 8. F.2: Compare two functions, including tables, graphs, and equations to draw conclusions. 8. F.4: Understand that the slope is the constant rate of change, and the y-intercept is the point where x = 0. Interpret the meaning of the slope and the y-intercept of a linear function in the context of the situation. Applying the Standards to Functional Skills Using a wooden plank and a toy car, explore the concept of steepness. -46-

50 Graph real-life situations and explore the meaning of slope and y-intercept within a real-world context. For example, the students can analyze the following graph that shows the number of hours Rudolph works and the amount of cash he has. The y-intercept of the graph shows that before he started working he had already saved $10, and the slope shows that as he works more his cash is increasing, which is why the slope of the line is positive. NOTE: images are just examples and the final images may be slightly different -47-

51 8th Grade Key Concept: Expressions, Equations, and Inequalities Prioritized Standards: Understand exponents to simplify numerical expressions that include integer exponents (8.EE.1). Investigate concepts of square roots (8.EE.2). Compare two different proportional relationships using tables and graphs (8.EE.5). It is essential for students to know: Students need to be able to recognize the relationship between repeated addition and multiplication. Students need to be able to convert repeated addition into exponents (i.e., 2x2x2 = 2 3 ). Students also need to be able recognize a proportional relationship when displayed in a table or graph. 8. EE.1: Identify repeated multiplication (4x4x4) as the exponent notation (4 3 ). 8. EE.2: Understand multiplication as repeated addition. 8. EE.5: Identify a table or graph. 8. EE.1: Expand exponents into repeated multiplication. 8. EE.2: Understand multiplication facts of whole numbers with products up to EE.5: Compare two relationships using tables and graphs. 8. EE.1: Understand exponents to simplify numerical expressions. 8. EE.2: Understand how to square a number. 8. EE.5: Compare two different proportional relationships using tables and graphs. 8. EE.1: Understand exponents to simplify numerical expressions that include integer exponents. 8. EE.2: Understand that the square root is the inverse of squaring a number. 8. EE.5: Compare two different proportional relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions. -48-

52 Applying the Standards to Functional Skills Show repeated multiplication using objects. -49-

53 8th Grade Key Concept: Geometry and Measurement Prioritized Standards: Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools to recognize congruence (8.GM.1). It is essential for students to know: Students need to be able to recognize two shapes are congruent when displayed in different orientations. 8. GM.1: Recognize when two-dimensional shapes are the same. 8. GM.1: Recognize congruent figures. 8. GM.1: Investigate the properties of rigid transformations (rotations, reflections, translations). 8. GM.1: Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools to recognize congruence. Applying the Standards to Functional Skills Explore properties of rigid transformations by moving a small rug around the room or a desk. Describe how the orientation of the rug or desk changes based on the transformation. -50-

54 8th Grade Key Concept: Data Analysis, Statistics, and Probability Prioritized Standards: Recognize patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, or no correlation) (8.DS.1). It is essential for students to know: Students need to be able to identify a point on a scatterplot. 8. DS.1: Identify a point. 8. DS.1: Graph points when given an ordered pair of numbers. 8. DS.1: Recognize patterns observed on a scatter plot, including clustering and outliers. 8. DS.1: Recognize patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, or no correlation). Applying the Standards to Functional Skills Analyze patterns on scatter plots from articles and magazines. This article is looking at which states have the happiest people in the United States. -51-

55 11th Grade -52-

56 11th Grade Key Concept: Arithmetic with Polynomials and Rational Expressions Prioritized Standards: Add and subtract polynomials (limit to linear) (A1.AAPR.1). It is essential for students to know: Students need to be able to add and subtract like terms. A1. AAPR.1: Add two like terms (limited to constants). A1. AAPR.1: Add and subtract like terms (limited to constants). A1. AAPR.1: Add and subtract like terms that may include a variable. A1. AAPR.1: Add and subtract like terms with simple expressions. Applying the Standards to Functional Skills The students can practice adding and subtracting polynomials by determining which objects should be grouped together. Comedy movies should be grouped with other comedy movies, action movies with other action movies, and drama movies with other drama movies. -53-

57 11th Grade Key Concept: Creating Equations Prioritized Standards: Solve linear equations with one variable (A1.ACE.1). It is essential for students to know: Students need to be able to identify a variable, coefficient, and constant in a linear equation. Students need to be able to solve one step equations with the variable isolated to one side (i.e., x = 2*4; x= 8 + 9). A1. ACE.1: Given a linear equation, identify parts of the equation (variable, constant, and coefficient). A1. ACE.1: Solve an equation written with the variable isolated on the left side. A1. ACE.1: Solve a linear equation with one variable with one step (addition, subtraction). A1. ACE.1: Solve linear equation with one variable. Applying the Standards to Functional Skills Solve simple linear equations with one variable, for example, If John earns $10 per hour, how many hours does he need to work to earn $100? -54-

58 11th Grade Key Concept: Reasoning with Equations and Inequalities Prioritized Standards: Understand that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original (A1.AREI.1). Solve systems of linear equations, graphically focusing on pairs of linear equations in two variables (A1.AREI.6). Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane (A1.AREI.10). Graph the solutions to a simple inequality with one variable on a number line (A1.AREI.12). It is essential for students to know: Students need to be able to differentiate between an equation and an inequality. Students need to be able to identify an inequality on a number line (i.e., x > 4). Students also need to be able to recognize the first step to solve an equation. A1. AREI.1: Determine if two expressions are equal (2x3, 3x2, commutative property, associative property). A1. AREI.6: Identify a set of lines that intersect. A1. AREI.10: Identify a point in the first quadrant. A1. AREI.1: Identify the possible first step in solving an equation. A1. AREI.6: Identify the point at which a given set of lines intersect. A1. AREI.10: Identify an equation in the first quadrant. A1. AREI.1: Identify the possible next step in solving an equation. A1. AREI.6: Given the graph of one equation and a simple equation, identify the graph that models the solution. A1. AREI.10: Identify the graph of an equation in two variables that models the set of all its solutions plotted on the coordinate plane (limit to the first quadrant). A1. AREI.1: Understand that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original. A1. AREI.6: Solve systems of linear equations, graphically focusing on pairs of linear equations in two variables. A1. AREI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted on the coordinate plane. -55-

59 A1. AREI.12: Identify a point on the number line. A1. AREI.12: Identify an inequality on the number line (limit to greater than and less than, limit to positive number line starting at zero). A1. AREI.12: Identify an inequality on the number line (where the solution is a positive number, but the number line may include negative numbers). A1. AREI.12: Identify a simple inequality with one variable on a number line (include greater than or equal to). Applying the Standards to Functional Skills To solve real-world inequality problems, the students must determine if they have enough money to make a certain purchase. Jim gets $5 per week for his allowance. He already has $20 saved. How many more weeks will Jim need to save his allowance to have $60? 60 = 5x + 20, solve for x, which is the number of weeks, x = 8. Jim needs to save up for 8 more weeks to reach his goal. -56-

60 11th Grade Key Concept: Structure and Expressions Prioritized Standards: Determine the meanings of coefficients, variables, terms, and expressions based on their real-world contexts (A1.ASE.1). It is essential for students to know: Students need to be able to differentiate between an equation and an expression. Students need to be able to identify the unknown. A1.ASE.1: Given an expression, identify a part (variable, term). A1.ASE.1: Identify the meaning of the unknown in a real-world context. A1.ASE.1: Given a realworld context and a variable, determine what the variable represents. A1.ASE.1: Determine the meanings of coefficients, variables, terms, and expressions based on their real-world contexts. Applying the Standards to Functional Skills Create a real-world context and expression, and determine the meaning of each part of the expression. For example, Jim is using the expression 5x + 20 to calculate his savings based on his weekly allowance. What does each part of the expression represent? The slope, which represents Jim s weekly allowance, is $5. The variable represents the number of weeks, and the y-intercept represents the amount of money Jim has already saved. -57-

61 11th Grade Key Concept: Interpreting Functions Prioritized Standards: 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 (A1.FIF.1). Recognize features of a linear function in graphical form (e.g., slope, intercepts; if the function is increasing, decreasing, constant, positive, or negative) (A1.FIF.4). Graph linear functions using their key features (A1.FIF.7). It is essential for students to know: Students need to be able to identify if a graph is increasing, decreasing, or constant. Students need to be able to identify the domain and the range of a function. A1. FIF.1: Given a set of table values, identify the set of x-values. A1. FIF.4: Given a key feature (increasing, decreasing, or constant), identify the graph. A1. FIF.7: Identify whether a given graph is increasing, decreasing, or constant. A1. FIF.1: Given a table of values, identify a possible missing x-value (so that an x- value does not repeat). A1. FIF.4: Given an intercept of the graph, identify the graph. A1. FIF.7: Given a graph of a linear function, identify the x-intercept. A1. FIF.1: Identify if a relation given in table form is a function. A1. FIF.4: Given a description of a function, identify the graph (positive slope, negative slope, constant, given y-intercept, limit to first quadrant). A1. FIF.7: Given a graph of a linear function in the first quadrant, identify features of the graph (positive slope, negative slope, constant, intercepts). A1. FIF.1: Identify the domain and range of a given function. A1. FIF.4: Given the slope and intercept of a function, identify its graph. A1. FIF.7: Given a graph of a linear function, identify the slope and intercepts. -58-

62 Applying the Standards to Functional Skills Identify the domain and range of a function in a real-world context. For example, the following function is used to find the temperature, F, in degrees Fahrenheit for any given temperature C, given in Celsius. The domain of the function is the temperature given in Celsius and the range is the temperature given in Fahrenheit. Another example would be the function y = 10x + 40, where y represents the total money Erika needs for a school trip. She is saving $10 per week and has already saved $40. She has 5 weeks to save the money. What are possible domains for the function? In this case, because she has only 5 weeks to save the money, the only domains for this function would be {1, 2, 3, 4, 5}. -59-

63 11th Grade Key Concept: Quantities Prioritized Standards: Choose the appropriate labels, units, and scales when constructing graphs (A1.NQ.1). It is essential for students to know: Students need to be able to identify the different parts of the graph (such as the title and axis labels). A1. NQ.1: Given data and context, identify an appropriate title for a graph of the data. A1. NQ.1: Given context, identify a graph with correct labels. A1. NQ.1: Given a data set, identify the appropriate units for a graph of the data. A1. NQ.1: Given a data set, identify an appropriate scale for a graph of the data. Applying the Standards to Functional Skills Explore scale of graphs using Excel, where you can create graphs using data. Play around with the scale to show how you can manipulate data to prove a point. For example, the graph below shows the average house prices for 1998 and 1999 in a certain city. See how the scale of the vertical axes can make it look like the average price of the houses increased dramatically or barely. NOTE: The images are just examples, final images may be slightly different. -60-

64 11th Grade Key Concept: Real Number System Prioritized Standards: Evaluate square roots of perfect squares (A1.NRNS.1). It is essential for students to know: Students need to be able to recognize perfect squares. A1. NRNS.1: Understand multiplication facts of whole numbers with products up to 100. A1. NRNS.1: Understand how to square a number. A1. NRNS.1: Understand that the square root is the inverse of squaring a number. A1. NRNS.1: Evaluate square roots of perfect squares. Applying the Standards to Functional Skills Evaluating square roots is used when using the Pythagorean theorem. For example, Simon has a 10 ft ladder against the wall. The distance from the bottom of the ladder to the wall is 8 ft. How far up on the wall is the ladder placed? -61-

65 11th Grade Key Concept: Interpreting Data Prioritized Standards: Identify the general form of a given data set as linear or non-linear (A1.SPID.6). It is essential for students to know: Students need to be able to recognize a pattern in scatterplots (such as positive association, negative association, and no association). A1. SPID.6: Identify a graph that is a straight line. Applying the Standards to Functional Skills A1. SPID.6: Identify a data set that can be modeled as a straight line. A1. SPID.6: Identify a data set that is linear. Analyze data from articles, and determine if the data is linear or non-linear. A1. SPID.6: Identify the general form of a given data set as linear or non-linear. -62-

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