Number Sense- Whole Numbers and Decimals

#
*(taken from “Big Ideas by Dr. Small”)***:**

1.

2. Students gain a sense of the size of numbers by comparing them to meaningful benchmark numbers.**The place value system we use is built on patterns to make our work with numbers more efficient.**
3. Decimals are an alternative representation to fractions, but one that allows for modeling, comparisons,

and calculations that are consistent with whole numbers; because decimals extend the pattern of the

base ten place value system.

4. A decimal can be read and interpreted in different ways; sometimes one representation is more useful

than another in interpreting or comparing decimals or for performing and explaining a computation.

**GOAL: I can demonstrate and explain equivalent representations using powers of ten**

- VIDEO: Comparing Place Values (whole numbers)
- VIDEO: Comparing Place Values (decimals)
- VIDEO: Regrouping Whole Numbers (3 videos, 1 practice quiz)
- QUIZ: Renaming Numbers
- QUIZ: Understanding Place Value
- QUIZ: Understanding Place Value when Multiplying or Dividing by 10

**GOAL: I can identify and explain patterns within our place value system (including decimals)**

- VIDEO: Finding a Number’s Place (whole numbers)
- VIDEO: Value of a Number
- VIDEO: Finding a Number’s Place (decimals)
- QUIZ: Decimal Hundredths
- QUIZ: Place Value Introduction
- GAME: Mystery Numbers
- GAME: Place Value Pirates
- GAME: Football Math

**GOAL: I can use these patterns to represent whole and decimals numbers in standard form,**

**expanded form, in pictures, and in words**

- VIDEO: Writing in Standard Form (from Words) (whole number)
- VIDEO: Writing in Expanded Form (whole number)
- VIDEO: Representing Numbers in Pictures and Models
- VIDEO: Writing Decimal Numbers in Words
- VIDEO: Writing in Expanded Form (decimals)
- QUIZ: Reading and Writing Numbers
- QUIZ: Exploring Equivalent Decimals
- GAME: Decimals of the Caribbean
- GAME: Eagle and Airplane

**GOAL: I can compare and order whole and decimals numbers and plot them on a number line**

- VIDEO: Comparing and Ordering Decimals (6 videos, 3 practice quizzes)
- QUIZ: Comparing and Ordering Numbers
- QUIZ: Comparing and Ordering Decimals
- GAME: Comparing Decimals
- GAME: Builder Ted

**GOAL: I can round whole and decimals numbers to meaningful benchmarks**

- VIDEO: Rounding Whole Numbers (3 videos, 1 practice quiz)
- QUIZ: Rounding Numbers
- QUIZ: Rounding Decimals
- GAME: Rounding Off

- represent, compare, and order whole numbers and decimal numbers from 0.001 to 1 000 000, using number lines with appropriate increments, base ten materials for decimals);
- demonstrate an understanding of place value in whole numbers and decimal numbers from 0.001 to 1 000 000, using base ten materials to represent the relationship between 1, 0.1, 0.01, and 0.001) (Sample problem: How many thousands cubes would be needed to make a base ten block for 1 000 000?);
- read and print in words whole numbers to one hundred thousand, using meaningful contexts
- solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 1 000 000 (Sample problem: How would you determine if a person could live to be 1 000 000 hours old?);
- identify composite numbers and prime numbers, and explain the relationship between them (i.e., any composite number can be factored into prime factors) (e.g., 42 = 2 x 3 x 7).

## ADDING AND SUBTRACTING

##
**BIG IDEAS****:**

**BIG IDEAS**

**:**

*(taken from “Big Ideas by Dr. Small”)*

**:**

- A personal “invented” algorithm is often more meaningful and sometimes equally efficient as a conventional algorithm.
- Decimals are an alternative representation to fractions, but one that allows for calculations that are consistent with whole numbers.

##
**STUDENT LEARNING GOALS:**

**GOAL: I can use strategies to estimate sums and differences of decimal numbers.**

- QUIZ: Adding and Subtracting using Mental Math
- QUIZ: Estimating Sums and Differences (Whole Numbers)

**GOAL: I can add whole and decimal numbers.**

- QUIZ: Adding Whole Numbers
- QUIZ: Adding Decimals
- QUIZ: Adding Money
- VIDEO: Adding Whole Numbers – with carrying (4 videos, 2 practice quizzes)
- VIDEO: Adding Decimals (3 videos, 3 practice quizzes)
- GAME: Math Soccer
- GAME: Hungry Puppies
- GAME: Decimal Addition – Matching
- GAME: Bubble Burst

**GOAL: I can subtract whole and decimal numbers.**

- QUIZ: Making Change
- QUIZ: Subtracting Decimals
- VIDEO: Subtracting Whole Numbers – with borrowing (12 videos, 2 practice quizzes)
- VIDEO: Subtracting Decimals (2 videos, 3 practice quizzes)
- GAME: Hotel Decimalfornia
- GAME: Hoop Shoot
- GAME: Decimal Subtraction – Matching

##
**CURRICULUM EXPECTATIONS:**

- add and subtract decimal numbers to thousandths, using concrete materials, estimation, algorithms, and calculators
- use estimation when solving problems involving the addition and subtraction of whole numbers and decimals, to help judge the reasonableness of a solution

## MULTIPLYING AND DIVIDING

##
**BIG IDEAS****:**

*(taken from “Big Ideas by Dr. Small”)*

**:**

- A personal “invented” algorithm is often more meaningful and sometimes equally efficient as a conventional algorithm.
- Thinking of numbers as factors or multiples of other numbers provides alternative representations of those numbers.
- Just as multiplication and division are intrinsically related, so are factors and multiples.

##
**STUDENT LEARNING GOALS:**

**GOAL: I can use strategies to estimate products and quotients.**

- QUIZ: Multiplying Tens
- QUIZ: Estimating Products
- QUIZ: Estimating Quotients
- QUIZ: Choosing Multiplication or Division
- VIDEO: Multiplying by Multiples of 10
- GAME: Farmer Multiplication (by 10, 100, 1000)
- GAME: MathMan Product Estimation
- GAME: Estimating Products Practice (IXL)

**GOAL: I can multiply two-digit numbers.**

- QUIZ: Multiplying using Arrays
- QUIZ: Multiplying Numbers
- VIDEO: What is Multiplication?
- VIDEO: Multiplication as Groups of Objects
- VIDEO: Multiplication as Partial Products and Area Model (skip to 1:38 mark)
- VIDEO: Multiplication Algorithm (2-digit x 1-digit numbers)
- VIDEO: Multiplication Algorithm (2-digit x 2-digit numbers)
- GAME: Multiplication Tables (a collection of games)
- GAME: Fruit Shoot (multiplication tables practice)
- GAME: Grand Prix Multiplication (multiplication tables practice)
- GAME: The Great Penguin Canoe Race

**GOAL: I can divide three-digit numbers by one-digit numbers.**

- QUIZ: Dividing Hundreds by One-Digit Numbers
- QUIZ: Dividing Thousands
- VIDEO: What is Division?
- VIDEO: Different ways of showing division
- VIDEO: Long Division
- VIDEO: Intro to Remainders
- VIDEO: Long Division with Remainders
- GAME: Monster Math Division (allows you to practice specific division tables)
- GAME: Pony Pull Division (division tables practice)
- GAME: Snork’s Long Division
- GAME: Division Millionaire

##
**CURRICULUM EXPECTATIONS:**

- multiply and divide decimal numbers to tenths by whole numbers, using concrete materials, estimation, algorithms, and calculators (e.g., calculate 4 x 1.4 using base ten materials; calculate 5.6 ÷ 4 using base ten materials)
- multiply whole numbers by 0.1, 0.01, and 0.001 using mental strategies (e.g., use a calculator to look for patterns and generalize to develop a rule);
- multiply and divide decimal numbers by 10, 100, 1000, and 10 000 using mental strategies (e.g.,“To convert 0.6 m2 to square centimetres, I calculated in my head 0.6 x 10 000 and got 6000 cm2.”)
- explain the need for a standard order for performing operations, by investigating the impact that changing the order has when performing a series of operations

## FRACTIONS, RATIOS AND RATES

##
**BIG IDEAS****:**

*(taken from “Big Ideas by Dr. Small”)*

**:**

- Fractions can represent parts of regions, parts of sets, parts of measures, division, or ratios. These meanings are equivalent.
- A fraction is not meaningful without knowing what the whole is.
- Renaming fractions is often the key to comparing them or computing with them. Every fraction can be renamed in an infinite number of ways.
- Ratio and rates, just like fractions and decimals, are comparisons of quantities.
- A ratio compares quantities with the same unit
- A rate compares quantities with different units

##
**STUDENT LEARNING GOALS:**

**GOAL: I can represent fractions and their equivalents.**

- QUIZ: Fractions Puzzles (representing fractions)
- QUIZ: Equivalent Fractions
- QUIZ: Improper Fractions and Mixed Numbers
- VIDEO: Introduction to Fractions
- VIDEO: Representing Fractions
- VIDEO: Numerators and Denominators
- VIDEO: Mixed Numbers to Improper Fractions
- VIDEO: Improper Fractions to Mixed Numbers
- VIDEO: Equivalent Fractions
- VIDEO: Fractions in Lowest Terms
- GAME: Representing Fractions
- GAME: Fractions Booster (representing)
- GAME: Thirteen Ways of Looking at a Half
- GAME: Melvin’s Match (representing)
- GAME: Fraction Flags (representing)
- GAME: Improper Fractions and Mixed Numbers
- GAME: Fresh Baked Fractions (equivalents)
- GAME: Fractions Monkeys (equivalents)

**GOAL: I can relate fractions to decimals.**

- QUIZ: Relating Fractions to Decimals
- QUIZ: Fraction Applications
- VIDEO: Converting Fractions to Decimals
- VIDEO: Converting Simple Decimal to Fraction
- GAME: Fruit Shoot
- GAME: Puppy Chase

**GOAL: I can order fractions and mixed numbers with like denominators.**

- QUIZ: Comparing Proper Fractions
- VIDEO: Comparing Fractions with Like Denominators
- GAME: Comparing Fractions
- GAME: Dirt Bike Comparing Fractions (more of a grade 6 concept)
- GAME: Ordering Fractions

**GOAL: I can identify and solve problems using ratios and rates.**

- QUIZ: Ratios
- QUIZ: Rates
- VIDEO: Ratios
- VIDEO: Rates
- GAME: Ratio Martian
- GAME: Thinking Block Ratios
- GAME: Ratio Rumble
- GAME: Ratio Stadium
- GAME: Matching Rates]
- GAME: Ratios and Rates Jeopardy

##
**CURRICULUM EXPECTATIONS:**

- represent, compare, and order fractional amounts with unlike denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, number lines, calculators) and using standard fractional notation (Sample problem: Use fraction strips to show that 1 is greater than .);
- estimate quantities using benchmarks of 10%, 25%, 50%, 75%, and 100% (e.g., the container is about 75% full; approximately 50% of our students walk to school)
- represent ratios found in real-life contexts, using concrete materials, drawings, and standard fractional notation (Sample problem: In a classroom of 28 students, 12 are female.What is the ratio of male students to female students?);
- determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among fractions (i.e., with denominators of 2, 4, 5, 10, 20, 25, 50, and 100), decimal numbers, and percents
- represent relationships using unit rates (Sample problem: If 5 batteries cost $4.75, what is the cost of 1 battery?).

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