In this unit, students will extend their knowledge of place value and standard algorithms for operations to include decimals and multidigit division of whole numbers. This unit also builds on studentsâ€™ previous knowledge of how to find factors and multiples of a given number to the new knowledge of the unit of finding the greatest common factor of two numbers and the least common multiple of two numbers. Students also use factors and multiples to apply the distributive property to write equivalent expressions. Students are likely to struggle with the abstractness of the distributive property; the unit builds an understanding of the property with the use of area models.
Key Concepts:
 Rules for all operations with whole numbers and decimals are based on the place value system.
 A common multiple of a set of numbers has each number in the set as a factor. Furthermore, the list of factors of the common multiple also includes every factor of the numbers in the original set.
 We can use the distributive property and common factors to write equivalent expressions.
Prior Knowledge Needed:
 Identify factors and multiples of a given number, so they can understand the parts of the distributive property.
 Know the difference between a factor and a multiple, so they can find greatest common factor and least common multiple.
 Use the standard algorithm to multiply, add and subtract multidigit numbers, so they can extend the standard algorithm to decimals.
 Use representations to add, subtract, multiply and divide positive decimal numbers, so they can transfer their understanding to the standard algorithm.
 Use the standard algorithm to divide with a singledigit divisor, so they can extend their knowledge of the standard algorithm to dividing multidigit numbers.
Units on the Horizon:
 Extending rules for operations to include rational numbers. (Grade 7, Unit 5)
 Writing equations, in the form p(x+q) = r, from word problems. (Grade 7, Unit 6)
 Applying distributive property to solve linear equations with rational number coefficients. (Grade 8, Unit 10)
Lessons

1. Use the standard algorithm for operations with decimals (C)
Lesson objective: Extend understanding of the rules for all operations to include decimals and to understand that, like wholenumbers, decimal operations are based on the place value system. Students bring prior knowledge of wholenumber operations usin...

2. Add and subtract decimals using the standard algorithm (FP)
Lesson objective: Fluently add and subtract decimals using the standard algorithm. This lesson helps to build fluency with adding and subtracting decimals. The standard algorithm is used here because it is the most efficient method for operations. This ...

3. Multiply and divide decimals using the standard algorithm (FP)
Lesson objective: Fluently multiply and divide decimals using the standard algorithm. This lesson helps to build fluency with multiplying and dividing decimals. The standard algorithm is used here because it is the most efficient method for operations. ...

4. Divide multidigit numbers using the standard algorithm (FP)
Lesson objective: Fluently divide multidigit numbers using the standard algorithm. This lesson helps to build fluency with dividing multidigit numbers. The standard algorithm is used here because it is the most efficient method for operations. This wo...

5. Understand least common multiple and greatest common factor (C)
Lesson objective: Understand that a common multiple of a set of numbers has each number in the set as a factor. Furthermore, the list of factors of the common multiple also includes every factor of the numbers in the original set. Students bring prior k...

6. Pratice least common multiple and greatest common factor (FP)
Lesson objective: Find the least common multiple and greatest common factor of two given numbers. This lesson helps to build procedural skill with least common multiples and greatest common factors. Lists and prime factorization are used here because th...

7. Apply knowledge of least common multiples and greatest common factors (A)
Lesson objective: Generate a rule for the relationship among the product, GCF and LCM of two given numbers. This lesson provides an opportunity for students to apply their knowledge and understanding of factors and multiples to a mathematical situation....

8. Understand the distributive property (C)
Lesson objective: Understand how we can use the distributive property and common factors to write equivalent expressions. Students bring prior knowledge of properties of multiplication from Grade 3 (3.OA.5). This prior knowledge is extended to formalizi...

9. Use the distributive property (FP)
Lesson objective: Fluently use the distributive property and the greatest common factor to write equivalent expressions. This lesson helps to build fluency with the distributive property. Prime factorization is used here because it supports finding the ...

10. Use distributive property to solve problems (A)
Lesson objective: Write equivalent expressions using the greatest common factor and the distributive property. This lesson provides an opportunity for students to apply their knowledge and understanding of the distributive property to a mathematical sit...
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