# What is a Growth Mindset?

## In this class, we believe:

Everyone can learn math to the highest levels.

Questions are really important.

Math is about creativity and making sense.

Math is about connections and communicating.

Math is about learning, not performing.

Depth is more important than speed.

Mistakes are valuable.

Mistakes are where the new learning goes!

Math Units Listed in Sequence:

1.  Place Value, Addition, and Subtraction:

Student Goals:

• I can persevere when approaching a new task and try different strategies.
• I can explain my thinking using pictures, numbers, and words.
• I can use base-ten concepts to explain the value of numbers.
• I can read, write and compare multi-digit whole numbers.
• I can round multi-digit whole numbers to any place and explain my reasoning.
• ​I can add and subtract multi-digit numbers using the standard algorithm.

Vocabulary:
• place value
• value
• standard algorithm
• compute
• calculate
• open number line
• estimation
• equation
• whole number
• number name
• expanded form
• standard form
• round
• place value
• standard algorithm
• compute
• calculate
• open number line

Adding on an Open Number Line

Subtracting on an Open Number Line

2.  Patterns, Multiplication and Division

Student Goals:
• I attend to precision when I show my work using pictures, numbers and words.
• I know multiplication facts and related division facts 12 x 12.
• I can demonstrate an understanding of factors, multiples, primes and composites.
• ​I can extend and analyze number and shape patterns to solve problems.
• I can write a number sentence with a variable to represent a problem.

Vocabulary
• estimation
• factor
• factor pairs
• multiples
• prime
• composite
• dividend
• divisor
• quotient
• diagram

• remainder
• sequence
• area model
• equation
• open sentence
• unknown
• variable
• multiplicative comparison
• growing pattern
• table

3.  Estimation and Partial Products Multiplication

Student Goals:
• I can use the distributive property and the base-ten structure of numbers to explain and show multiplication strategies.
• I can model and explain multiplication using an open array and partial products.
• I can use multiplication and division with whole numbers to solve problems.
• I can use a number line to demonstrate my understanding of rounding whole numbers.
• I know multiplication facts and related division facts 12 x 12.
Vocabulary
• estimation
• factor
• factor pairs
• multiples
• partial-products
• number names
• expanded form
• area model
• open array
• equation
• round
• place value
• relationship
• ten thousands
• millions

Area Model

Open Array

Partial Products

4.  Perimeter and Area

Student Goals:

• I can apply the area and perimeter formulas for rectangles in real-life examples.

• I can decompose shapes into rectangular parts to find the area of the shape.

• I can attend to precision when labeling answers with the appropriate unit.

• I can represent the context of an area and perimeter word problem using a variety of models (graph paper, square tiles, open array).

• I can make sense of problems and persevere when a problem has more than one solution.

Vocabulary:

• area, perimeter
• equation
• expression
• unknown
• variable
• formula
• length, width, dimensions
• array
• units, square units
• tiling

5.  Division

Student Goals:

• I can explain partial quotients by reasoning about the relationship between multiplication and division.
• I can divide 4-digit numbers by 1-digit numbers using partial quotients.
• I can show and explain my work for solving multi-step word problems.
• I can explain the meaning of remainders and reason about them in different contexts.
Vocabulary
• estimation
• factor
• factor pairs
• multiples
• divisor
• dividend
• quotient
• remainder
• partial-quotients algorithm
• diagram
• area model
• equation
• expression
• unknown
• variable
What to do with remainders in word problems?
• Ignore (Four friends are sharing 17 pencils. If they each want the same amount how many do they each get? Answer: 4)
• Round Up (I made 17 muffins. I'm putting 4 muffins in a bag. How many bags do I need to bag all the muffins? Answer: 5)
• Split in to fractions or decimal (4 friends had a lemonade stand and made \$17. They are sharing the money equally. How much do they get? Answer \$4.25)

Notice every problem is 17÷4 but there are three different answers. You need to choose what makes sense.

6.  Context Unit: Fractions

Student Goals:
• I can show and explain my thinking about fractions with visual models, numbers, and words.
• I can decompose a fraction into a sum of fractions with the same denominator in more than one way (3/8 = 1/8 + 2/8 = 1/8 + 1/8 + 1/8).
• I can use different strategies to solve the same problem.
• I can listen to and interpret the strategies of others and make connections.
• I can solve real world story problems involving fraction by using a variety of strategies.
Vocabulary
• estimation
• distribution
• division
• diagram
• model
• equation
• equivalent fractions
• mixed number
• improper fraction
• ratio table
• whole
• unit fraction
• fraction model

7.  Operations with Fractions

Student Goals:
• I can show and explain why fractions are equivalent by using a visual fraction models.
• I can attend to precision when I compare and order fractions by using benchmark fractions and common denominators.
• I can add and subtract fractions and mixed numbers with like denominators using different models.
• I can multiply a fraction by a whole number by using a visual fraction model and then record the equation.
• I can create a line plot to display a data set involving fractions of a measurement unit.
• I can use a line plot to solve fraction word problems involving addition and subtraction.

Vocabulary
• estimation
• equation
• equivalent
• equivalent fractions
• mixed number
• improper fraction
• denominator
• numerator
• pattern block model
• bar model
• array model
• number line
• diagram
• represent

8.  Fractions and Decimals

Student Goals:
• I can show and explain why fractions are equivalent by using visual fraction models.
• I can read and write multi-digit whole numbers and decimals.
• I can represent decimals using expanded form, base ten blocks, the number line and other visuals
• I can compare numbers to the hundredths by reasoning about their size (>, <, =)
• I can use decimal notation for fractions with denominators of 10 or 100.
• I can add fractions with denominators of 10 and 100 by reasoning about fraction equivalence.
• ​I can compare fractions and decimals using place value and models (base-ten blocks and grids).

Vocabulary
• multiples
• area model
• fraction model
• visual model
• diagram
• equation
• whole
• equivalent fractions
• mixed number
• improper fractions
• decimal
• tenths
• hundredths
• whole number
• unit fraction
• compare (<, >, =)

9.  Measurement Conversions

10. Naming and Constructing Geometric Figures

11.  Symmetry

National Common Core Standards Link for Mathematics