**Write and interpret numerical expressions**

Numerical Expressions Clock

**5.OA.A.2 **Write simple expressions that record calculations with
numbers, and interpret numerical expressions without evaluating them.
For example, express the calculation “add 8 and 7, then multiply by 2”
as 2 x (8+7). Recognize that 3 x (18932 + 921) is three times as large
as 18932 + 921, without having to calculate the indicated sum or
product.**Sample Activity:****Equivalent Expressions Match**

**Analyze patterns and relationships****5.OA.B.3 **Generate two
numerical patterns using two given rules. Identify apparent
relationships between corresponding terms. Form ordered pairs consisting
of corresponding terms from the two patterns, and graph the ordered
pairs on a coordinate plane. For example, given the rule “Add 3” and the
starting number 0, generate terms in the resulting sequences, and
observe that the terms in one sequence are twice the corresponding terms
in the other sequence. Explain informally why this is so.**Sample Activity:Patterns on the Coordinate Plane Task Cards**

**Understand the place value system**

**5.NBT.A.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 the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.**Sample Activities:**

Multiplying a Whole Number by a Power of 10

Multiplying a Decimal by a Power of 10**Also included in ****5th Grade Math Centers:****Dividing a Whole Number by a Power of 10****Dividing a Decimal by a Power of 10Exponent Roll**

Representing Decimals

Sample Activity:

Comparing Decimals

Roll and Round (nearest hundredth)

**Perform operations with multi-digit whole numbers and with decimals to hundredths****5.NBT.B.5 **Fluently multiply multi-digit whole numbers using the standard algorithm.**Sample Activity:**

Multiplication Race (2 x 3 digit)**Also included in**** ****5th Grade Math Centers:****Double and Halve (3 x 2 digit)Make the Largest Product (v. 4)**

Division Strategy: Partition the Dividend (v. 2)

Estimate the Quotient (v. 2)

**5.NBT.B.7 **Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, relate the strategy to a written method and explain the reasoning used.**Sample Activities:**Total Ten

Magic Triangle: Decimals

Decimal Subtraction Spin

Double and Halve (decimals)

Race to a Flat: Decimals

Building with Decimals

Decimal Sums

Factor Cover Up

Partial Products: Decimals (v. 1)

Partial Products: Decimals (v. 2)

Partition the Dividend: Decimals

Word Problems: Decimals (Division)

Decimals of the Week

**Use equivalent fractions as a strategy to add ****and subtract fractions**

**5.NF.A.2 **Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + ½ = 3/7 by observing that 3/7 < ½.**Sample Activities:**Word Problems: Adding Mixed Numbers

Create and Solve: Adding Unlike Fractions

Create and Solve: Subtracting Unlike Fractions

The Wishing Club (v. 1)

The Wishing Club (v. 2)

**Apply and extend previous understandings of multiplication and division to multiply and divide fractions****5.NF.B.3** Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g. by using visual fraction models or equations to represent the problem.**Sample Activity:Interpret Fractions as Division**

**5.NF.B.4 **Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (a/b) x q as a parts of a partition of

q into b equal parts; equivalently, as the result of a sequence of operations a x q÷b. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context

for this equation. Do the same with (2/3) x (4/5) = 8/15.

(In general, (a/b) x (c/d) = ac/bd)**Sample Activities:**

Multiply Unit Fractions by Non-Unit Fractions**Find a Fractional Part of a Group (v. 1)**

Cover Up: Fractions

Double and Halve with Fractions

Find Areas of Rectangles

**5.NF.B.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.

b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; 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= nxa)/(nxb) to the effect of multiplying a/b x 1.**Sample Activity:**

**5.NF.B.6** Solve real world problems involving multiplication of fractions and mixed numbers, e.g. by using visual fraction models or equations to represent the problem.**Sample Activities:**

Mixed Number x Fraction Models

Whole Number x Mixed Number Models**Also included in**** ****5th Grade Math Centers:****Word Problems: Fraction x Fraction****Word Problems: Multiplying Mixed Numbers**

a. Interpret division of a unit fraction by a non-zero whole number and compute such quotients. For example, create a story context for (1/3)÷4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3)÷4 = 1/12 because (1/12) x 4 = 1/3.

Divide a Unit Fraction by a Whole Number

b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4÷(1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) =20 because 20 x (1/5 )=4.

Divide a Whole Number by a Unit Fraction (v. 1)

Divide a Whole Number by a Unit Fraction (v. 2)

c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g. by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?