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In 7th grade, students learn to construct, solve and interpret proportions and two step equations using rational numbers in order to apply and represent these skills in real world situations including statistics, percent, geometry and probability.
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Learning Progression 1
Add, Subtract, Multiply & Divide Integers
Learning Intention 1: I am learning to understand the concept of a "zero pair" using manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). 1.2 Activities 1-3, 1.3 Activity 2
Learning Intention 1: I am learning to understand the concept of a "zero pair" using manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). 1.2 Activities 1-3, 1.3 Activity 2
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
1a. I can interpret zero pairs from a field of manipulatives like colored chips or algebra tiles. (Conceptual - Level 1)
1b. I can draw the field and annotate the zero pairs. (Conceptual - Level 1)
1b. I can write a numerical expression and/or equation from the same field of manipulatives like colored chips or algebra tiles. (Conceptual - Level 1)
1c. I can create zero pairs from a given numerical, addition expression using manipulatives like colored chips or algebra tiles. (Conceptual - Level 1)
1d. I can draw a field and annotate the zero pairs from a given numerical, addition expression using the manipulatives like colored chips or algebra tiles as a reference. (Conceptual - Level 1)
1e. I can write equivalent expressions and/or equations using zero pairs from a field of manipulatives like colored chips or algebra tiles. (Conceptual - Level 1)
Learning Intention 2: I am learning to add integers using zero pairs manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). Lesson 1.2
Learning Intention 2: I am learning to add integers using zero pairs manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). Lesson 1.2
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
2a. I can add two positive integers. (Conceptual, level 1)
2b. I can add two negative integers. (Conceptual, level 1)
2c. I can add a positive integer and a negative integer or a negative and a positive integer. (Conceptual, level 1)
2d. I can explain 2a-2c using the hot rocks & cold rocks context. (Conceptual, level 1)
2e. I can explain 2a-2c using the + means "and" and - means opposite definitions. (Conceptual, level 1)
2f. I can apply number bonds/fact families from earlier grades to solve integer addition problems using the associative property and mental math. For example, use the number bonds of 6 in the problem 6+(-2) to create zero pairs for (-2); [6]+(-2) = [4+2] + (-2) = 4+[2 + (-2)] OR use the number bonds of -6 in the problem -6+2 to create zero pairs for 2; [-6]+2 = [-4+(-2)] + 2 = -4+[(-2) + 2] . (Conceptual, level 1)
Learning Intention 3: I am learning to subtract integers using zero pairs (hot rocks & cold rocks - manipulatives like colored chips, base-ten blocks, and/or algebra tiles). Lesson 1.3
Learning Intention 3: I am learning to subtract integers using zero pairs (hot rocks & cold rocks - manipulatives like colored chips, base-ten blocks, and/or algebra tiles). Lesson 1.3
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
3a. I can subtract two positive integers. (Conceptual, level 1)
3b. I can subtract two negative integers. (Conceptual, level 1)
3c. I can subtract a positive integer and a negative integer or a negative and a positive integer. (Conceptual, level 1)
3d. I can explain 3a-3c using the hot rocks & cold rocks context. (Conceptual, level 1)
3e. I can explain 3a-3c using the + means "and" and - means opposite definitions. (Conceptual, level 1)
3f. I understand the relationship between subtraction and the additive inverse. For example, adding a cold rock is the same as subtracting a hot rock. (Application, level 3)
Learning Intention 4: I am learning to add & subtract integers on numberlines, horizontal and vertical. 1.2 Activity 4, 1.3 Activity 3-4
Learning Intention 4: I am learning to add & subtract integers on numberlines, horizontal and vertical. 1.2 Activity 4, 1.3 Activity 3-4
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
4a. I can annotate positive integers on a number line. (Conceptual, level 1)
4b. I can annotate negative numbers on a number line. (Conceptual, level 1)
4c. I can model an addition expression with integers on a number line. (Conceptual, level 1)
4d. I can model a subtraction expression with integers on a number line. (Conceptual, level 1)
4e. I can add integers on a number line. (Conceptual, level 1)
4f. I can subtract integers on a number line. (Conceptual, level 1)
4g. I can relate zero pairs (hot rocks/cold rocks) to number lines. (Conceptual, level 1)
Learning Intention 5: I am learning to add and subtract integers in real-world and mathematical problems about temperature, money, sandbags & hot air balloons, deposits & withdrawls, above sea level & below sea level, army men, friends & not friends, etc. 1.2 & 1.3 Exercises
Learning Intention 5: I am learning to add and subtract integers in real-world and mathematical problems about temperature, money, sandbags & hot air balloons, deposits & withdrawls, above sea level & below sea level, army men, friends & not friends, etc. 1.2 & 1.3 Exercises
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
5a. I can solve real-world problems with two terms and one operation. (Procedural, level 1)
5a. I can solve real-world problems with multiple terms and different operations. (Procedural, level 1)
5a. I can solve mathematical problems with multiple terms and different operations. (Procedural, level 2)
5a. I can solve mathematical problems with multiple terms and different operations. (Procedural, level 2)
Learning Intention 6: I am learning to multiply integers using manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). 1.4 Activity 3 & 4 (do 4 with hot rock/cold rock context and manipulatives)
Learning Intention 6: I am learning to multiply integers using manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). 1.4 Activity 3 & 4 (do 4 with hot rock/cold rock context and manipulatives)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
6a. I can multiply nonnegative integers. (Conceptual, level 1)
6b. I can multiply integers, positive & negative. (Conceptual, level 1)
6c. I can multiply two negative integers. (Conceptual, level 1)
6d. I can explain 6a-6c using groups of hot rocks/cold rocks context. (Conceptual, level 1)
6e. I can explain 6a-6c using the + means "and" and - means opposite definitions. (Conceptual, level 1)
6f. I can relate factors and their products to number bonds/fact families from earlier grades. (Conceptual, level 1)
Learning Intention 7: I am learning to divide integers using manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). 1.5 Activity 1 & 4 (do 4 with hot rock/cold rock context and manipulatives)
Learning Intention 7: I am learning to divide integers using manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). 1.5 Activity 1 & 4 (do 4 with hot rock/cold rock context and manipulatives)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
7a. I can divide nonnegative integers. (Conceptual, level 1)
7b. I can divide integers, positive & negative. (Conceptual, level 1)
7c. I can divide two negative integers. (Conceptual, level 1)
7d. I can explain 7a-7c using groups of hot rocks/cold rocks context. (Conceptual, level 1)
7e. I can explain 7a-7c using the + means "and" and - means opposite definitions. (Conceptual, level 1)
7f. I can relate dividends, divisors, and their quotients to number bonds/fact families from earlier grades. (Conceptual, level 1)
Learning Intention 8: I am learning to multiply & divide integers on number lines, horizontal and vertical. 1.4 Activity 1-2
Learning Intention 8: I am learning to multiply & divide integers on number lines, horizontal and vertical. 1.4 Activity 1-2
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
8a. I can divide nonnegative integers on a number line. (Conceptual, level 1)
8b. I can divide integers, positive & negative, on a number line. (Conceptual, level 1)
8c. I can divide two negative integers on a number line. (Conceptual, level 1)
8d. I can model a multiplication expressions with integers on a number line. (Conceptual, level 1)
8e. I can model a division expression with integers on a number line. (Conceptual, level 1)
Learning Intention 9: I am learning to multiply and divide integers in real-world and mathematical problems about temperature, money, sandbags & hot air balloons, deposits & withdrawals, above sea level & below sea level, army men, friends & not friends, etc. Lesson 1.4 & Lesson 1.5
Learning Intention 9: I am learning to multiply and divide integers in real-world and mathematical problems about temperature, money, sandbags & hot air balloons, deposits & withdrawals, above sea level & below sea level, army men, friends & not friends, etc. Lesson 1.4 & Lesson 1.5
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
9a. I know, understand, and use the rules for multiplying signed numbers. (Application, level 1)
9b. I know, understand, and use the rules for multiplying signed numbers. (Application, level 1)
Learning Progression 2
Converting Between Fractions and Decimals
Learning Intention 10: I am learning to convert between familiar fractions and decimals using multiplication. 6.2 & 6.1, especially Examples 3 & 4
Learning Intention 10: I am learning to convert between familiar fractions and decimals using multiplication. 6.2 & 6.1, especially Examples 3 & 4
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
10a. I can use multiplication & the identify property to create friendly denominators before converting familiar fractions to decimals. (Conceptual, level 2)
10b. I can use place value to create friendly denominators before converting familiar decimals to fractions. (Conceptual, level 2)
Learning Intention 11: I am learning to convert between familiar fractions and decimals using long division. 2.1
Learning Intention 11: I am learning to convert between familiar fractions and decimals using long division. 2.1
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
11a. I can use long division to divide the numerator by the denominator. (Conceptual, level 2)
11b. I can use long division to discover patterns in the decimal conversion of familiar fractions. (Conceptual, level 2)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
12a. I can convert from a fractional form of rational numbers to a decimal from of rational numbers. (Procedural, level 3)
12b. I can convert from a fractional form of rational numbers to a decimal from of rational numbers in order to solve problems. (Procedural, level 3)
Learning Progression 3
Add, Subtract, Multiply & Divide Rational Numbers
Learning Intention 13: I am learning to understand the concept of a rational "zero pair" using drawn manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). [Not in the text; visual problems like +2 1/2 and -1/2 seeing the fractional parts as zero pairs. If able, progress to visual problems like +2 and -1/2 (rewriting it as +1 1/2 and +1/2 and -1/2) as a transition to the next lesson.]
Learning Intention 13: I am learning to understand the concept of a rational "zero pair" using drawn manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). [Not in the text; visual problems like +2 1/2 and -1/2 seeing the fractional parts as zero pairs. If able, progress to visual problems like +2 and -1/2 (rewriting it as +1 1/2 and +1/2 and -1/2) as a transition to the next lesson.]
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
13a. I can interpret rational zero pairs from a drawn field of manipulatives like colored chips, base-ten blocks, or algebra tiles. (Conceptual - Level 1)
13b. I can annotate the rational zero pairs. (Conceptual - Level 1)
13c. I can write a numerical expression and/or equation from the same field of draw rational manipulatives like colored chips, base-ten blocks, or algebra tiles. (Conceptual - Level 1)
13d. I can create zero pairs from a given numerical, rational addition expression using drawings of rational manipulatives like colored chips, base-ten blocks or algebra tiles. (Conceptual - Level 1)
13e. I can write equivalent expressions and/or equations using zero pairs from a field of rational manipulatives like colored chips or algebra tiles. (Conceptual - Level 1)
Learning Intention 14: I am learning to add rationals using zero pairs manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). Lesson 2.2 (Using drawn pictures of manipulatives)
Learning Intention 14: I am learning to add rationals using zero pairs manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). Lesson 2.2 (Using drawn pictures of manipulatives)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
14a. I can create common denominators visually and symbolically. (Conceptual, level 1)
14b. I can add two positive rationals - integer, fractional or decimal or any combination thereof. (Conceptual, level 1)
14b. I can add two negative rationals - integer, fractional or decimal or any combination thereof. (Conceptual, level 1)
14c. I can add a positive integer, fractional or decimal and a negative integer, fractional or decimal OR a negative and a positive integer, fractional or decimal or any combination thereof. (Conceptual, level 1)
14d. I can apply number bonds/fact families from earlier grades to solve integer addition problems using the associative property and mental math. For example, use the number bonds of 6 in the problem 6+(-1/2) to create zero pairs for (-1/2); [6]+(-1/2) = [5 1/2 + 1/2] + (-1/2) = 5+[1/2 + (-12)] OR use the number bonds of -6 in the problem -6+1/2 to create zero pairs for 1/2; [-6]+1/2 = [-5 1/2+(-1/2)] + 1/2 = -5 1/2+[(-1/2) + 1/2] . (Conceptual, level 1)
Learning Intention 15: I am learning to subtract rationals using zero pairs (hot rocks & cold rocks - manipulatives like colored chips, base-ten blocks, and/or algebra tiles). Lesson 2.3 (Using drawn pictures of manipulatives)
Learning Intention 15: I am learning to subtract rationals using zero pairs (hot rocks & cold rocks - manipulatives like colored chips, base-ten blocks, and/or algebra tiles). Lesson 2.3 (Using drawn pictures of manipulatives)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
15a. I can create common denominators visually and symbolically. (Conceptual, level 1)
15b. I can subtract two positive rationals - integer, fractional or decimal or any combination thereof. (Conceptual, level 1)
15b. I can subtract two negative rationals - integer, fractional or decimal or any combination thereof. (Conceptual, level 1)
15c. I can subtract a positive integer, fractional or decimal and a negative integer, fractional or decimal OR a negative and a positive integer, fractional or decimal or any combination thereof. (Conceptual, level 1)
Learning Intention 16: I am learning to add & subtract rationals on number lines, horizontal and vertical. 2.2 Activities, 2.3 Activity 3-4
Learning Intention 16: I am learning to add & subtract rationals on number lines, horizontal and vertical. 2.2 Activities, 2.3 Activity 3-4
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
16a. I can annotate positive rationals on a number line. (Procedural, level 2)
16b. I can annotate negative rationals on a number line. (Procedural, level 2)
16c. I can model an addition expression with rationals on a number line. (Procedural, level 2)
16d. I can model a subtraction expression with rationals on a number line. (Procedural, level 2)
16e. I can add rationals on a number line. (Procedural, level 2)
16f. I can subtract rationals on a number line. (Procedural, level 2)
Learning Intention 17: I am learning to apply properties of operations as strategies to add/subtract rational numbers. 2.2 & 2.3 Exercises
Learning Intention 17: I am learning to apply properties of operations as strategies to add/subtract rational numbers. 2.2 & 2.3 Exercises
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
17a. I can add and subtract rational numbers in real-world problems. (Procedural, level 2)
17b. I can add and subtract rational numbers in mathematical problems. (Procedural, level 2)
Learning Intention 18: I am learning to multiply rationals using manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). Lesson 2.4 Example 2 (Using drawn pictures of manipulatives)
Learning Intention 18: I am learning to multiply rationals using manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). Lesson 2.4 Example 2 (Using drawn pictures of manipulatives)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
18a. I can multiply nonnegative rationals, visually & symbolically. (Conceptual, level 1)
18b. I can multiply rationals, positive & negative, visually & symbolically. (Conceptual, level 1)
18c. I can multiply two negative rationals, visually & symbolically. (Conceptual, level 1)
18d. I understand why multiplying by a rational number can make the product smaller, and I can communicate it orally & in writing. (Conceptual, level 1)
Learning Intention 19: I am learning to divide rationals using manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). Lesson 2.4 Example 1 (Using drawn pictures of manipulatives)
Learning Intention 19: I am learning to divide rationals using manipulatives like colored chips, base-ten blocks, and/or algebra tiles (hot rocks & cold rocks). Lesson 2.4 Example 1 (Using drawn pictures of manipulatives)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
19a. I can divide nonnegative rationals. (Conceptual, level 1)
19b. I can divide rationals, positive & negative. (Conceptual, level 1)
19c. I can divide two negative rationals. (Conceptual, level 1)
19d. I understand why dividing by a rational number can make the product larger, and I can communicate it orally & in writing. (Conceptual, level 1)
Learning Intention 20: I am learning to extend my understanding of order of operations to include negative rational numbers. Lesson 2.4 Examples 3 & 4
Learning Intention 20: I am learning to extend my understanding of order of operations to include negative rational numbers. Lesson 2.4 Examples 3 & 4
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
20a. I can utilize order of operations when using rational numbers to solve real-world problems. (Application, level 2)
20b. I can utilize order of operations when using rational numbers to solve mathematical problems. (Application, level 2)
Learning Intention 21: I am learning to apply properties of operations as strategies to multiply rational numbers. 2.4 Exercises
Learning Intention 21: I am learning to apply properties of operations as strategies to multiply rational numbers. 2.4 Exercises
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
21a. I can multiply rational numbers in real-world problems. (Procedural, level 2)
21b. I can multiply rational numbers in mathematical problems. (Procedural, level 2)
Learning Intention 22: I am learning to apply properties of operations as strategies to divide rational numbers. 2.4 Example 4 & 2.4 Exercises
Learning Intention 22: I am learning to apply properties of operations as strategies to divide rational numbers. 2.4 Example 4 & 2.4 Exercises
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
22a. I can divide rational numbers in real-world problems. (Procedural, level 2)
22b. I can divide rational numbers in mathematical problems. (Procedural, level 2)
Learning Intention 23: I am learning to apply my knowledge of integers to understand absolute value. Lesson 1.1
Learning Intention 23: I am learning to apply my knowledge of integers to understand absolute value. Lesson 1.1
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
23a. I can describe situations when opposites combine to make zero. (Procedural, level 2)
23b. I can interpret rational number values on a number line. (Conceptual, level 2)
23c. I can model addition expressions on a number line. (Conceptual, level 3)
23d. I can model subtraction expressions on a number line. (Conceptual, level 3)
23e. I understand the difference between the value of a number and its absolute value. For example, why does -6 win the fight with +2 in -6 +2 when -6 is worth less than +2? (Conceptual, level 2)
Learning Progression 4
Problem Solving with All 5 Operations
Learning Intention 24: I am learning to solve mathematical problems involving the four operations with rational numbers. 2.4 Exercises 35-40 & FIAB
Learning Intention 24: I am learning to solve mathematical problems involving the four operations with rational numbers. 2.4 Exercises 35-40 & FIAB
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
24a. I can identify equivalency between two rational numbers. (Conceptual, level 3)
24b. I can I can solve multi-step problems with integers. (Conceptual, level 1)
24c. I can I can solve multi-step problems with common fractions with denominators of 2 through 10, 25, 50, or 100. (Conceptual, level 1)
24d. I can solve multi-step problems with decimals to the hundredths place. (Conceptual, level 1)
24e. I can solve multi-step problems with rationals. (Procedural, level 2)
24f. I can solve multi-step problems mathematical problems involving the four operations with rational numbers. (Procedural, level 3)
24g. I can apply properties of operations to evaluate numeric expressions, including converting between different forms of rational numbers. (Procedural, level 3)
Learning Intention 25 (optional depth day): I am learning to solve real-world problems involving the four operations with rational numbers. FIAB
Learning Intention 25 (optional depth day): I am learning to solve real-world problems involving the four operations with rational numbers. FIAB
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
25a. I can solve multi-step, real world problems involving the four operations with rational numbers. (Procedural, level 4)
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