**4.1-Unit 4 Operations with Fractions**This week, most students will be finishing Unit 4. Students are at different points in their learning progressions and will continue to work towards demonstrating mastery of all the standards this week. Many students will be taking quizzes on either NF.3 or NF.4 this week with the goal of taking the unit assessment by the end of the week or early next week as we prepare to move on to Unit 5.

__Homework__

Tuesday - iReady for 30 minutes

Thursday - iReady for 30 minutes

__4.1 Standards for the Week:__4.NF.B.3.C

Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

4.NF.B.3.D

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

4.NF.B.4.B

Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

4.NF.B.4.C

Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

__4.2-Fifth Grade: Unit 1: Place Value and Order of Operations__Similar to the work students did with multi-digit multiplication last week, students are learning how to estimate quotients in long division. The focus is not on the standard algorithm, but rather on determining partial quotients in order for students to recognize the values of the digits in the dividends. The strategy of estimating a quotient allows students to decompose numbers in different ways, thus giving them mental visuals to work with while solving problems. In addition to this work, students will be introduced to interpretation of expressions and numerical expressions as they apply to the Order of Operations. They will work through specific expressions to help them discover the rules for solving an expression in a determined order. For those of you familiar with PEMDAS (parenthesis, exponents, multiplication/division, addition/subtraction), this will be an acronym saved for the end of the unit as a resource, but not as a rule. Students need to identify the purpose behind using parenthesis and exponents as they apply to real-world situations so that they aren't always solving problems from left to right as would be natural to do.

Homework:

Tuesday: iReady 30 minutes

Thursday: iReady 30 minutes

__4.2 Standards for the Week:__*5.NBT.1: Recognize that in a multi-digit number, a digit in one place represents ten times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.*

5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of a decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.

5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5.OA.1: Write and interpret numerical expressions.

5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of a decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.

5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5.OA.1: Write and interpret numerical expressions.

5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

**5.1-Unit 4 Part B: Multiplying and Dividing Fractions**This week, students will be focusing on multiplying fractions by whole numbers and other fractions,as well as finding the area of rectangles with fractional side lengths, and learning how multiplication is a way of scaling. Students already have a strong foundation when multiplying fractions by whole numbers, so now we are building on that foundation. Students will be using various visual models to also show their multiplication and practice these skills.

*Please note that Mrs. Alterman's class is now also following the new Math Workshop structure which was explained/communicated by the other Fourth Grade teachers prior to Winter Break. Due to Mrs. A's long term sub this workshop structure was not in place, but now that Mrs. A is back, her class will also be following this workshop model. Below is the blurb that was previous communicated to the other math classes about our new workshop:

"Last week, students were introduced to a "Learning Ladder," also known as a way for the students to individually track their learning. They have been given goal statements (I can statements) that they have to work towards for each standard that will be taught within the unit. As the students work towards their goal statement they have to provide to solid pieces of evidence to the teacher to prove mastery of the goal. Once the teacher has signed off on all of the goal statements for the standard, then the student will be eligible to take a quiz for the standard. Therefore, quizzes will not be posted each Friday anymore. In an effort to help students take more ownership over their learning, we are trying out this system to allow students to work at a pace that is comfortable for them with the teacher facilitating their learning. Don't worry!! Teacher guided lessons are still happening each day, but when they leave the lesson, they have choice in what they want to learn and how they want to learn it. Games, activities, and online tools have been provided for the students to select from. "

**Homework:**

Tuesday – Workbook pages 739-742

Thursday - iReady (30 minutes)

__5.1 Standards for the Week:__*5.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction*

a. Apply and use understanding of multiplication to multiply a fraction or whole number by a fraction.

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.

*5.NF.5:*

*Interpret multiplication as scaling (resizing), by:*

a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Example 4 x 10 is twice as large as 2 x 10.

b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.