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- Growth: Grades 6+ Math - Number Sense (2017)

# Growth: Grades 6+ Math - Number Sense (2017)

### 2: Number Sense

2.1: Whole Numbers: Place Value, Counting & Rounding

2.1.1: Whole Numbers: Counting and Cardinality

2.1.1.6: [RIT 152 - 165] Counts by 10s within 100

Whole Numbers with Base-10 Blocks

Use base-10 blocks to model, add, and subtract whole numbers. Learn about place value using flats (hundreds), rods (tens), and cubes (ones). Group or ungroup blocks as needed to add or subtract. This regrouping is often called "carrying" when adding, and "borrowing" when subtracting. 5 Minute Preview

2.1.1.7: [RIT 160 - 181] Counts by 2s within 100

Pattern Flip (Patterns)

In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck! 5 Minute Preview

2.1.1.10: [RIT 163 - 164] Represents groups of 10 objects as a numeral within 100

Whole Numbers with Base-10 Blocks

Use base-10 blocks to model, add, and subtract whole numbers. Learn about place value using flats (hundreds), rods (tens), and cubes (ones). Group or ungroup blocks as needed to add or subtract. This regrouping is often called "carrying" when adding, and "borrowing" when subtracting. 5 Minute Preview

2.1.1.11: [RIT 165 - 175] Counts by 10s within 1,000

Whole Numbers with Base-10 Blocks

Use base-10 blocks to model, add, and subtract whole numbers. Learn about place value using flats (hundreds), rods (tens), and cubes (ones). Group or ungroup blocks as needed to add or subtract. This regrouping is often called "carrying" when adding, and "borrowing" when subtracting. 5 Minute Preview

2.1.1.14: [RIT 177 - 187] Counts by 5s within 100

Pattern Flip (Patterns)

In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck! 5 Minute Preview

2.1.2: Whole Numbers and Decimals: Rounding/Estimation

2.1.2.1: [RIT 179 - 202] Rounds whole numbers within 100

Rounding Whole Numbers (Number Line)

Place points on a number line. Round these values to the nearest ten or hundred. Visualize rounding by showing the number line as a hill or series of hills. These hills cause the points to roll to the nearest valley (nearest multiple of ten or one hundred). 5 Minute Preview

2.1.2.2: [RIT 186 - 204] Rounds whole numbers within 1,000

Rounding Whole Numbers (Number Line)

Place points on a number line. Round these values to the nearest ten or hundred. Visualize rounding by showing the number line as a hill or series of hills. These hills cause the points to roll to the nearest valley (nearest multiple of ten or one hundred). 5 Minute Preview

2.1.2.3: [RIT 197 - 229] Rounds whole numbers within 1,000,000

Rounding Whole Numbers (Number Line)

Place points on a number line. Round these values to the nearest ten or hundred. Visualize rounding by showing the number line as a hill or series of hills. These hills cause the points to roll to the nearest valley (nearest multiple of ten or one hundred). 5 Minute Preview

2.1.2.4: [RIT 204 - 227] Rounds whole numbers greater than 1,000,000

Rounding Whole Numbers (Number Line)

2.1.3: Exponents

2.1.3.1: [RIT 220 - 232] Reads and writes whole numbers within 100,000 using powers of 10 in exponential form

Number Systems

Explore number systems and convert numbers from one base to another using counter beads in place-value columns. 5 Minute Preview

2.1.3.2: [RIT 232 - 246] Reads and writes whole numbers greater than 100,000 using powers of 10 in exponential form

Number Systems

Explore number systems and convert numbers from one base to another using counter beads in place-value columns. 5 Minute Preview

2.1.5: Whole Numbers: Place Value

2.1.5.1: [RIT 158 - 166] Represents whole numbers within 20 with models

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Model numbers with base-10 blocks. Drag flats, rods, and individual cubes onto a mat to model a number. Blocks can be exchanged from one area of the mat to the other. Four sets of blocks are available to model a variety of whole numbers and decimals. 5 Minute Preview

Whole Numbers with Base-10 Blocks

2.1.5.2: [RIT 161 - 180] Represents whole numbers within 100 with models

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Model numbers with base-10 blocks. Drag flats, rods, and individual cubes onto a mat to model a number. Blocks can be exchanged from one area of the mat to the other. Four sets of blocks are available to model a variety of whole numbers and decimals. 5 Minute Preview

Whole Numbers with Base-10 Blocks

2.1.5.3: [RIT 162 - 187] Reads and writes whole numbers within 1,000 as hundreds, tens, and ones

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Model numbers with base-10 blocks. Drag flats, rods, and individual cubes onto a mat to model a number. Blocks can be exchanged from one area of the mat to the other. Four sets of blocks are available to model a variety of whole numbers and decimals. 5 Minute Preview

Whole Numbers with Base-10 Blocks

2.1.5.5: [RIT 162 - 192] Represents whole numbers within 1,000 with models

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Whole Numbers with Base-10 Blocks

2.1.5.8: [RIT 171 - 204] Knows place-value names in numbers through the hundred thousands

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Whole Numbers with Base-10 Blocks

2.1.5.9: [RIT 175 - 197] Reads and writes whole numbers within 1,000 in expanded form

Number Systems

Explore number systems and convert numbers from one base to another using counter beads in place-value columns. 5 Minute Preview

2.1.5.10: [RIT 175 - 180] Reads and writes whole numbers within 100 in expanded form

Number Systems

2.1.5.11: [RIT 176 - 184] Understands the value of a digit in whole numbers within 1,000

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Number Systems

Whole Numbers with Base-10 Blocks

2.1.5.12: [RIT 177 - 194] Reads and writes whole numbers within 10,000 in expanded form

Number Systems

2.1.5.13: [RIT 177 - 199] Reads and writes whole numbers within 100 as tens and ones

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Number Line Frog Hop (Addition and Subtraction)

Live a frog's life as you hop along a number line in search of flies. Learn how addition and subtraction can be represented as movement along a number line. Fred the frog may even help you get better at adding and subtracting two-digit numbers in your head by decomposing them into tens and ones. 5 Minute Preview

2.1.5.15: [RIT 179 - 189] Identifies the number of tens and ones in a model

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Whole Numbers with Base-10 Blocks

2.1.5.16: [RIT 180 - 180] Composes or decomposes tens in a model to represent whole numbers within 20 in multiple ways

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Whole Numbers with Base-10 Blocks

2.1.5.18: [RIT 184 - 199] Understands the value of a digit in whole numbers within 1,000,000

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Number Systems

Whole Numbers with Base-10 Blocks

2.1.5.19: [RIT 191 - 191] Composes or decomposes tens in a model to represent whole numbers within 100 in multiple waysÂ

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Whole Numbers with Base-10 Blocks

2.1.5.20: [RIT 194 - 220] Reads and writes whole numbers within 100,000 in expanded form

Number Systems

2.1.5.23: [RIT 199 - 214] Understands that 10 ones is the same as 1 ten

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Whole Numbers with Base-10 Blocks

2.1.5.24: [RIT 200 - 205] Represents whole numbers greater than 1,000 with models

Number Systems

2.1.5.25: [RIT 202 - 202] Understands the value of a digit in whole numbers greater than 1,000,000

Number Systems

2.1.5.26: [RIT 202 - 212] Decomposes whole numbers within 100 into tens and ones in multiple ways

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Whole Numbers with Base-10 Blocks

2.1.5.28: [RIT 203 - 203] Reads and writes whole numbers within 1,000,000 in expanded form

Number Systems

2.1.5.29: [RIT 204 - 209] Reads and writes whole numbers within 10,000 as thousands, hundreds, tens, and ones

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Whole Numbers with Base-10 Blocks

2.1.5.30: [RIT 205 - 205] Understands that 10 tens is the same as 1 hundred

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Whole Numbers with Base-10 Blocks

2.1.5.31: [RIT 207 - 247] Understands that the same digit, moved one place to the left, now represents 10 times the value

Number Systems

2.1.5.33: [RIT 215 - 245] Understands that the same digit, moved one place to the right, now represents 1/10 the value

Number Systems

2.1.5.34: [RIT 220 - 232] Reads and writes whole numbers within 100,000 using powers of 10 in exponential form

Number Systems

2.1.5.35: [RIT 222 - 232] Decomposes whole numbers within 1,000 into hundreds, tens, and ones, in multiple ways

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Whole Numbers with Base-10 Blocks

2.1.5.36: [RIT 231 - 231] Understands whole-number place-value relationships

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Whole Numbers with Base-10 Blocks

2.1.5.37: [RIT 232 - 246] Reads and writes whole numbers greater than 100,000 using powers of 10 in exponential form

Number Systems

2.2: Fractions, Decimals, and Percents: Concepts

2.2.1: Decimals: Compare/Order

2.2.1.1: [RIT 167 - 167] Compares decimals to the hundredths, with the same number of digits after the decimal point, using terms

Comparing and Ordering Decimals

Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line. 5 Minute Preview

Ordering Percents, Fractions, and Decimals Greater Than 1

Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview

Treasure Hunter (Decimals on the Number Line)

Drive a desert highway searching for buried treasure. Learn to use the car's tens, ones, tenths, and hundredths gears, along with a GPS system (number line), to find the right place to dig. Plot your findings on a zoomable number line map. Can you become a master Treasure Hunter? 5 Minute Preview

2.2.1.2: [RIT 173 - 173] Compares decimals to the hundredths using symbols, given models

Comparing and Ordering Decimals

Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line. 5 Minute Preview

Ordering Percents, Fractions, and Decimals Greater Than 1

Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview

2.2.1.3: [RIT 174 - 190] Orders decimals to the hundredths, with the same number of digits after the decimal point

Comparing and Ordering Decimals

Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line. 5 Minute Preview

Treasure Hunter (Decimals on the Number Line)

Drive a desert highway searching for buried treasure. Learn to use the car's tens, ones, tenths, and hundredths gears, along with a GPS system (number line), to find the right place to dig. Plot your findings on a zoomable number line map. Can you become a master Treasure Hunter? 5 Minute Preview

2.2.1.4: [RIT 191 - 191] Compares decimals to the thousandths, with the same number of digits after the decimal point, using symbols

Comparing and Ordering Decimals

Ordering Percents, Fractions, and Decimals Greater Than 1

Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview

2.2.1.5: [RIT 191 - 191] Compares decimals to the hundredths, with the same number of digits after the decimal point, using symbols

Comparing and Ordering Decimals

Ordering Percents, Fractions, and Decimals Greater Than 1

2.2.1.6: [RIT 210 - 227] Compares decimals to the hundredths, with a different number of digits after the decimal point, using terms

Comparing and Ordering Decimals

Ordering Percents, Fractions, and Decimals Greater Than 1

Treasure Hunter (Decimals on the Number Line)

Drive a desert highway searching for buried treasure. Learn to use the car's tens, ones, tenths, and hundredths gears, along with a GPS system (number line), to find the right place to dig. Plot your findings on a zoomable number line map. Can you become a master Treasure Hunter? 5 Minute Preview

2.2.1.7: [RIT 211 - 235] Compares decimals to the thousandths, with a different number of digits after the decimal point, using symbols

Comparing and Ordering Decimals

Ordering Percents, Fractions, and Decimals Greater Than 1

2.2.1.8: [RIT 219 - 229] Compares decimals to the hundredths, with a different number of digits after the decimal point, using symbols

Comparing and Ordering Decimals

Ordering Percents, Fractions, and Decimals Greater Than 1

2.2.1.10: [RIT 221 - 221] Orders decimals to the thousandths, with the same number of digits after the decimal point

Comparing and Ordering Decimals

Treasure Hunter (Decimals on the Number Line)

2.2.1.11: [RIT 221 - 221] Compares decimals to the thousandths, with a different number of digits after the decimal point, using terms

Comparing and Ordering Decimals

Ordering Percents, Fractions, and Decimals Greater Than 1

Treasure Hunter (Decimals on the Number Line)

2.2.1.12: [RIT 223 - 226] Orders decimals to the hundredths, with a different number of digits after the decimal point

Comparing and Ordering Decimals

Treasure Hunter (Decimals on the Number Line)

2.2.1.14: [RIT 227 - 232] Orders decimals to the thousandths, with a different number of digits after the decimal point

Comparing and Ordering Decimals

Treasure Hunter (Decimals on the Number Line)

2.2.2: Decimals: Represent/Model

2.2.2.2: [RIT 209 - 221] Locates decimals to the hundredths on a number line

Modeling Decimals (Area and Grid Models)

Model and compare decimals using area models. Set the number of sections in each model to 1, 10, or 100, and then click in the models to shade sections. Compare decimals visually and on a number line. 5 Minute Preview

Treasure Hunter (Decimals on the Number Line)

2.2.2.3: [RIT 213 - 226] Knows decimal place-value names through hundredths

Modeling Decimals (Area and Grid Models)

Model and compare decimals using area models. Set the number of sections in each model to 1, 10, or 100, and then click in the models to shade sections. Compare decimals visually and on a number line. 5 Minute Preview

Modeling Whole Numbers and Decimals (Base-10 Blocks)

2.2.2.5: [RIT 224 - 229] Represents decimals to the hundredths with models

Modeling Decimals (Area and Grid Models)

Model and compare decimals using area models. Set the number of sections in each model to 1, 10, or 100, and then click in the models to shade sections. Compare decimals visually and on a number line. 5 Minute Preview

Modeling Whole Numbers and Decimals (Base-10 Blocks)

2.2.2.6: [RIT 228 - 228] Knows decimal place-value names through thousandths

Modeling Decimals (Area and Grid Models)

Modeling Whole Numbers and Decimals (Base-10 Blocks)

2.2.3: Whole Numbers and Decimals: Rounding/Estimation

2.2.3.1: [RIT 200 - 218] Rounds decimals to nearest whole number

Estimating Sums and Differences

Estimate the sum or difference of two fractions using area models. Compare estimates to exact sums and differences. 5 Minute Preview

2.2.3.2: [RIT 202 - 223] Rounds dollars and cents

Estimating Sums and Differences

Estimate the sum or difference of two fractions using area models. Compare estimates to exact sums and differences. 5 Minute Preview

2.2.4: Fractions: Compare/Order

2.2.4.1: [RIT 164 - 176] Orders fraction models with like denominators

Equivalent Fractions (Fraction Tiles)

Explore fractions using the Fractionator, the machine that makes fraction tiles. Compare fractions and find equivalent fractions by arranging the tiles on two horizontal rows. Explore simplifying fractions. Add fractions and express sums as improper fractions or mixed numbers. 5 Minute Preview

Fraction Garden (Comparing Fractions)

Plant flowers in two gardens to help develop fraction sense. The two gardens act as number lines, from 0 to 1. Use the flowers in the gardens to compare fractions and to explore equivalent fractions. Chalk marks can be drawn to divide the garden into equal sections. 5 Minute Preview

2.2.4.2: [RIT 176 - 204] Compares fraction models with unlike numerators and denominators using words

Fraction Artist 1 (Area Models of Fractions)

Develop understanding of fractions by making modern paintings. Find different ways to divide a canvas into equal-sized sections. Make paintings to represent simple fractions and to find fractions that are equivalent to one-half. 5 Minute Preview

Modeling Fractions (Area Models)

Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview

2.2.4.3: [RIT 182 - 208] Compares fraction models with like numerators or denominators using words

Fraction Artist 1 (Area Models of Fractions)

Develop understanding of fractions by making modern paintings. Find different ways to divide a canvas into equal-sized sections. Make paintings to represent simple fractions and to find fractions that are equivalent to one-half. 5 Minute Preview

Modeling Fractions (Area Models)

Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview

2.2.4.4: [RIT 201 - 213] Compares fraction models with like numerators or denominators using symbols

Modeling Fractions (Area Models)

Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview

2.2.4.5: [RIT 204 - 208] Compares unit fractions using words

Fraction Artist 1 (Area Models of Fractions)

Develop understanding of fractions by making modern paintings. Find different ways to divide a canvas into equal-sized sections. Make paintings to represent simple fractions and to find fractions that are equivalent to one-half. 5 Minute Preview

2.2.4.6: [RIT 205 - 216] Orders fractions with like numerators or denominators using models

Fraction Garden (Comparing Fractions)

Plant flowers in two gardens to help develop fraction sense. The two gardens act as number lines, from 0 to 1. Use the flowers in the gardens to compare fractions and to explore equivalent fractions. Chalk marks can be drawn to divide the garden into equal sections. 5 Minute Preview

2.2.4.7: [RIT 213 - 225] Compares fractions with like numerators or denominators using words

Fraction Artist 1 (Area Models of Fractions)

2.2.4.8: [RIT 213 - 229] Compares fraction models with unlike numerators and denominators using symbols

Modeling Fractions (Area Models)

2.2.4.9: [RIT 214 - 222] Compares fractions with unlike numerators and denominators using words

Modeling Fractions (Area Models)

2.2.4.10: [RIT 226 - 226] Orders fractions with unlike numerators and denominators using models

Fraction Garden (Comparing Fractions)

Plant flowers in two gardens to help develop fraction sense. The two gardens act as number lines, from 0 to 1. Use the flowers in the gardens to compare fractions and to explore equivalent fractions. Chalk marks can be drawn to divide the garden into equal sections. 5 Minute Preview

2.2.4.11: [RIT 228 - 229] Orders fractions with unlike numerators and/or denominators

Fraction Garden (Comparing Fractions)

2.2.5: Fractions: Represent/Model

2.2.5.1: [RIT 151 - 188] Identifies shapes that are divided into equal parts

Fraction Artist 1 (Area Models of Fractions)

2.2.5.2: [RIT 161 - 179] Identifies shapes that are divided into fourths

Fraction Artist 1 (Area Models of Fractions)

2.2.5.3: [RIT 162 - 180] Identifies shapes that are divided into halves

Fraction Artist 1 (Area Models of Fractions)

Fraction Artist 2 (Area Models of Fractions)

Extend understanding of fractions by making modern paintings in the style of Piet Mondrian. Create and analyze paintings with different-sized sections. Compare the sizes of unit fractions. Find creative ways to color one-half of a painting. This can be a nice introduction to adding fractions with unlike denominators. 5 Minute Preview

2.2.5.4: [RIT 163 - 163] Identifies shapes that are divided into thirds

Fraction Artist 1 (Area Models of Fractions)

2.2.5.5: [RIT 171 - 209] Models non-unit fractions using set models

Toy Factory (Set Models of Fractions)

Create a set of stuffed animals: monkeys, giraffes, and rabbits. Toys can be painted red, green, or blue. Describe the makeup of the set (animals or colors) with fractions. Arrange the toys into groups to simplify the fractions. 5 Minute Preview

2.2.5.6: [RIT 174 - 197] Models unit fractions using area models

Fraction Artist 1 (Area Models of Fractions)

Fraction Artist 2 (Area Models of Fractions)

Extend understanding of fractions by making modern paintings in the style of Piet Mondrian. Create and analyze paintings with different-sized sections. Compare the sizes of unit fractions. Find creative ways to color one-half of a painting. This can be a nice introduction to adding fractions with unlike denominators. 5 Minute Preview

Modeling Fractions (Area Models)

2.2.5.7: [RIT 178 - 205] Models unit fractions using set models

Toy Factory (Set Models of Fractions)

Create a set of stuffed animals: monkeys, giraffes, and rabbits. Toys can be painted red, green, or blue. Describe the makeup of the set (animals or colors) with fractions. Arrange the toys into groups to simplify the fractions. 5 Minute Preview

2.2.5.8: [RIT 178 - 208] Models non-unit fractions using area models

Fraction Artist 1 (Area Models of Fractions)

Fraction Artist 2 (Area Models of Fractions)

Extend understanding of fractions by making modern paintings in the style of Piet Mondrian. Create and analyze paintings with different-sized sections. Compare the sizes of unit fractions. Find creative ways to color one-half of a painting. This can be a nice introduction to adding fractions with unlike denominators. 5 Minute Preview

Modeling Fractions (Area Models)

2.2.5.9: [RIT 180 - 190] Reads and writes fractions in word form

Fraction Artist 2 (Area Models of Fractions)

2.2.5.10: [RIT 183 - 183] Understands the meaning of the numerator and the denominator in a fraction

Fraction Artist 1 (Area Models of Fractions)

Fraction Artist 2 (Area Models of Fractions)

Fractions Greater than One (Fraction Tiles)

Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as improper fractions on the top number line, and as mixed numbers on the bottom number line. 5 Minute Preview

Modeling Fractions (Area Models)

Toy Factory (Set Models of Fractions)

Create a set of stuffed animals: monkeys, giraffes, and rabbits. Toys can be painted red, green, or blue. Describe the makeup of the set (animals or colors) with fractions. Arrange the toys into groups to simplify the fractions. 5 Minute Preview

2.2.5.11: [RIT 187 - 204] Identifies the fractional parts of shapes

Fraction Artist 1 (Area Models of Fractions)

Fraction Artist 2 (Area Models of Fractions)

Improper Fractions and Mixed Numbers

Represent a quantity given by a shaded region as an improper fraction and as a mixed number. Experiment with different shaded regions sliced differently. 5 Minute Preview

2.2.5.12: [RIT 192 - 208] Identifies shapes that are divided into quarters

Fraction Artist 1 (Area Models of Fractions)

2.2.5.13: [RIT 196 - 238] Locates non-unit proper fractions on a number line

Fraction Garden (Comparing Fractions)

Improper Fractions and Mixed Numbers

Represent a quantity given by a shaded region as an improper fraction and as a mixed number. Experiment with different shaded regions sliced differently. 5 Minute Preview

2.2.5.14: [RIT 202 - 224] Identifies fractions which represent given situations

Equivalent Fractions (Fraction Tiles)

Explore fractions using the Fractionator, the machine that makes fraction tiles. Compare fractions and find equivalent fractions by arranging the tiles on two horizontal rows. Explore simplifying fractions. Add fractions and express sums as improper fractions or mixed numbers. 5 Minute Preview

Fraction Artist 1 (Area Models of Fractions)

Fractions Greater than One (Fraction Tiles)

Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as improper fractions on the top number line, and as mixed numbers on the bottom number line. 5 Minute Preview

Improper Fractions and Mixed Numbers

Represent a quantity given by a shaded region as an improper fraction and as a mixed number. Experiment with different shaded regions sliced differently. 5 Minute Preview

Toy Factory (Set Models of Fractions)

2.2.5.15: [RIT 205 - 214] Identifies the mixed number represented by a fraction model

Fractions Greater than One (Fraction Tiles)

Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as improper fractions on the top number line, and as mixed numbers on the bottom number line. 5 Minute Preview

2.2.5.16: [RIT 211 - 223] Locates unit fractions on a number line

Fraction Garden (Comparing Fractions)

Improper Fractions and Mixed Numbers

2.2.5.18: [RIT 217 - 244] Locates mixed numbers on a number line

Improper Fractions and Mixed Numbers

2.2.5.19: [RIT 222 - 232] Identifies the improper fraction represented by a fraction model

Fractions Greater than One (Fraction Tiles)

Improper Fractions and Mixed Numbers

2.2.6: Rates/Ratios/Proportions/Percents

2.2.6.1: [RIT 156 - 157] Represents 100% using models

Fraction, Decimal, Percent (Area and Grid Models)

Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview

Ordering Percents, Fractions, and Decimals Greater Than 1

Part-to-part and Part-to-whole Ratios

Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

Percents, Fractions, and Decimals

Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

2.2.6.2: [RIT 185 - 226] Represents percents less than 100% using models

Fraction, Decimal, Percent (Area and Grid Models)

Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview

Ordering Percents, Fractions, and Decimals Greater Than 1

Part-to-part and Part-to-whole Ratios

Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

Percents, Fractions, and Decimals

Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

2.3: Fractions, Decimals, and Percents: Equivalency

2.3.1: Fractions: Equivalence

2.3.1.1: [RIT 157 - 186] Identifies fractions equivalent to 1 using area or set models

Fraction Artist 1 (Area Models of Fractions)

Fraction Artist 2 (Area Models of Fractions)

Modeling Fractions (Area Models)

Toy Factory (Set Models of Fractions)

2.3.1.2: [RIT 174 - 220] Identifies equivalent fraction models

Equivalent Fractions (Fraction Tiles)

Explore fractions using the Fractionator, the machine that makes fraction tiles. Compare fractions and find equivalent fractions by arranging the tiles on two horizontal rows. Explore simplifying fractions. Add fractions and express sums as improper fractions or mixed numbers. 5 Minute Preview

Fraction Artist 1 (Area Models of Fractions)

Fraction Garden (Comparing Fractions)

Modeling Fractions (Area Models)

Toy Factory (Set Models of Fractions)

2.3.1.3: [RIT 192 - 221] Writes equivalent fractions for given area or set models

Equivalent Fractions (Fraction Tiles)

Fraction Artist 1 (Area Models of Fractions)

Modeling Fractions (Area Models)

Toy Factory (Set Models of Fractions)

2.3.1.4: [RIT 194 - 223] Understands that fractions that occupy the same position on a number line are equivalent

Fraction Garden (Comparing Fractions)

Modeling Fractions (Area Models)

2.3.1.5: [RIT 198 - 213] Converts between fractions with denominators of 10 and 100

Fraction, Decimal, Percent (Area and Grid Models)

Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview

2.3.1.6: [RIT 202 - 233] Writes equivalent fractions

Equivalent Fractions (Fraction Tiles)

Fraction Artist 1 (Area Models of Fractions)

Fraction Garden (Comparing Fractions)

Modeling Fractions (Area Models)

Toy Factory (Set Models of Fractions)

2.3.1.7: [RIT 207 - 235] Writes fractions in simplest form

Equivalent Fractions (Fraction Tiles)

2.3.1.8: [RIT 207 - 207] Identifies fractions equivalent to 1

Fraction Artist 1 (Area Models of Fractions)

Fraction Artist 2 (Area Models of Fractions)

Fraction Garden (Comparing Fractions)

Modeling Fractions (Area Models)

Toy Factory (Set Models of Fractions)

2.3.1.9: [RIT 207 - 229] Converts between mixed numbers and improper fractions

Fractions Greater than One (Fraction Tiles)

Improper Fractions and Mixed Numbers

2.3.1.10: [RIT 216 - 216] Identifies fractions equivalent to 1 using number lines

Fraction Garden (Comparing Fractions)

2.3.1.11: [RIT 217 - 217] Divides two whole numbers given in the form of a fraction, with a whole number quotient

Dividing Fractions

Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. 5 Minute Preview

2.3.1.12: [RIT 219 - 219] GeneratesÂ equations to show two fractions are equivalentÂ

Fractions Greater than One (Fraction Tiles)

Modeling Fractions (Area Models)

Toy Factory (Set Models of Fractions)

2.3.1.13: [RIT 222 - 237] Determines common or least common denominators of fractions

Adding Fractions (Fraction Tiles)

Add fractions with the help of the Fractionator, a fraction-tile-making machine in the Gizmo. Model sums by placing the tiles on side-by-side number lines. Explore the usefulness of common denominators in adding. Express sums as improper fractions or mixed numbers. 5 Minute Preview

Fractions Greater than One (Fraction Tiles)

Fractions with Unlike Denominators

Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically. 5 Minute Preview

2.3.1.14: [RIT 223 - 228] Identifies fractions equivalent to whole numbers greater than 1

Fractions Greater than One (Fraction Tiles)

Improper Fractions and Mixed Numbers

2.3.1.15: [RIT 227 - 227] Identifies fractions equivalent to whole numbers greater than 1 using area or set models

Improper Fractions and Mixed Numbers

2.3.1.16: [RIT 227 - 227] Identifies both the improper fraction and the mixed number represented by a fraction model

Fractions Greater than One (Fraction Tiles)

Improper Fractions and Mixed Numbers

2.3.1.17: [RIT 238 - 238] Writes equivalent fractions for given points on a number line

Fraction Garden (Comparing Fractions)

2.3.2: Fractions: Represent and Solve Word Problems

2.3.2.1: [RIT 193 - 211] Solves word problems about finding equivalent fractions

Equivalent Fractions (Fraction Tiles)

Fraction Artist 1 (Area Models of Fractions)

Modeling Fractions (Area Models)

Toy Factory (Set Models of Fractions)

2.3.3: Rational Numbers: Equivalence

2.3.3.1: [RIT 196 - 226] Converts between percents and fractions with denominators of 10 or 100

Fraction, Decimal, Percent (Area and Grid Models)

Percents, Fractions, and Decimals

Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

2.3.3.2: [RIT 203 - 239] Converts between decimals and percents less than 100%

Fraction, Decimal, Percent (Area and Grid Models)

Percents, Fractions, and Decimals

2.3.3.3: [RIT 207 - 232] Converts between decimals and fractions with denominators of 10 or 100

Fraction, Decimal, Percent (Area and Grid Models)

Percents, Fractions, and Decimals

2.3.3.4: [RIT 208 - 233] Converts between percents and fractions with denominators other than 10 and 100

Fraction, Decimal, Percent (Area and Grid Models)

Percents, Fractions, and Decimals

2.3.3.5: [RIT 209 - 237] Converts between decimals and fractions with denominators of 2, 4, or 5

Fraction, Decimal, Percent (Area and Grid Models)

Percents, Fractions, and Decimals

2.3.3.6: [RIT 212 - 212] Determines equivalence between fractions, decimals, and percents

Fraction, Decimal, Percent (Area and Grid Models)

Percents, Fractions, and Decimals

2.3.3.7: [RIT 214 - 214] Determines equivalence between fractions and percents using models

Fraction, Decimal, Percent (Area and Grid Models)

Percents, Fractions, and Decimals

2.3.3.8: [RIT 218 - 218] Determines equivalence between decimals and percents using models

Fraction, Decimal, Percent (Area and Grid Models)

Percents, Fractions, and Decimals

2.3.3.12: [RIT 227 - 238] Converts between decimals and fractions with a denominator of 3

Fraction, Decimal, Percent (Area and Grid Models)

2.4: Integer, Rational, and Real Number: Concepts

2.4.1: Absolute Value: Concepts/Properties

2.4.1.1: [RIT 228 - 234] Evaluates the absolute value of a number

Integers, Opposites, and Absolute Values

Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview

Rational Numbers, Opposites, and Absolute Values

Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview

2.4.1.3: [RIT 241 - 245] Interprets the absolute value of rational numbers in terms of their relative position to 0 in a given real-world situation

Rational Numbers, Opposites, and Absolute Values

Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview

2.4.2: Properties and Relationships of Operations

2.4.2.1: [RIT 184 - 214] Identifies the missing value in an equation to show that a number and its opposite have a sum of 0

Solving Algebraic Equations II

Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview

2.4.2.3: [RIT 209 - 217] Understands that a number and its opposite are the same distance from 0 on a number line

Integers, Opposites, and Absolute Values

Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview

2.4.2.4: [RIT 222 - 231] Locates the additive inverse of a number on a number line

Integers, Opposites, and Absolute Values

Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview

2.4.2.5: [RIT 228 - 242] Understands the additive inverse property

Integers, Opposites, and Absolute Values

Solving Algebraic Equations I

Are there times when you wish you could escape from everyone and just be alone? Meet our variable friend, a real loner who doesn't like coefficients and neighboring terms. Learn how to use inverses to isolate a variable â€“ a foundational skill for solving algebraic equations. 5 Minute Preview

Solving Algebraic Equations II

Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview

2.4.2.6: [RIT 242 - 242] Determines the distance between two integers on a number line

Adding and Subtracting Integers

Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview

2.4.2.7: [RIT 243 - 243] Understands the multiplicative inverse property

Solving Algebraic Equations I

Are there times when you wish you could escape from everyone and just be alone? Meet our variable friend, a real loner who doesn't like coefficients and neighboring terms. Learn how to use inverses to isolate a variable â€“ a foundational skill for solving algebraic equations. 5 Minute Preview

Solving Algebraic Equations II

Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview

2.4.2.8: [RIT 243 - 243] Understands a negative number is less than its opposite

Integers, Opposites, and Absolute Values

2.4.2.9: [RIT 245 - 245] Understands that the product of two negative numbers is positive

Adding and Subtracting Integers

Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview

2.4.2.10: [RIT 245 - 245] Understands the multiplicative identity property

Solving Algebraic Equations I

Are there times when you wish you could escape from everyone and just be alone? Meet our variable friend, a real loner who doesn't like coefficients and neighboring terms. Learn how to use inverses to isolate a variable â€“ a foundational skill for solving algebraic equations. 5 Minute Preview

2.4.3: Real/Complex Numbers: Concepts/Properties

2.4.3.2: [RIT 227 - 260] Approximates the value of an irrational number

Square Roots

Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview

2.4.3.3: [RIT 231 - 261] Compares and orders real numbers

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview

2.4.4: Rational Numbers: Compare/Order

2.4.4.3: [RIT 202 - 221] Compares integers that represent quantities in a real-world context

Integers, Opposites, and Absolute Values

2.4.4.5: [RIT 207 - 211] Compares two rational numbers shown on a number line

Rational Numbers, Opposites, and Absolute Values

2.4.4.6: [RIT 210 - 210] Justifies a comparison of two rational numbers using a number line

Rational Numbers, Opposites, and Absolute Values

2.4.4.7: [RIT 211 - 218] Compares integers

Integers, Opposites, and Absolute Values

2.4.4.8: [RIT 218 - 255] Orders positive and negative rational numbers

Rational Numbers, Opposites, and Absolute Values

2.4.4.9: [RIT 218 - 230] Compares two rational numbers using a number line

Rational Numbers, Opposites, and Absolute Values

2.4.4.10: [RIT 224 - 239] Compares integers given the meaning of zero within a real-world situation

Integers, Opposites, and Absolute Values

2.4.4.11: [RIT 224 - 230] Compares positive rational numbers represented in multiple forms

Ordering Percents, Fractions, and Decimals Greater Than 1

2.4.4.12: [RIT 230 - 230] Orders positive rational numbers represented in multiple forms

Ordering Percents, Fractions, and Decimals Greater Than 1

2.4.5: Rational Numbers: Represent/Model

2.4.5.1: [RIT 197 - 219] Understands positive and negative numbers in terms of real-world situations

Integers, Opposites, and Absolute Values

2.4.5.2: [RIT 200 - 220] Locates integers on a number line

Integers, Opposites, and Absolute Values

2.4.5.3: [RIT 204 - 204] Locates positive and negative rational numbers on a number line

Rational Numbers, Opposites, and Absolute Values

2.4.5.4: [RIT 214 - 232] Locates negative rational numbers on a number line

Rational Numbers, Opposites, and Absolute Values

2.4.5.5: [RIT 229 - 246] Identifies values that are a given distance from a point on a number line

Integers, Opposites, and Absolute Values

2.4.5.6: [RIT 233 - 233] Locates the opposite of a negative rational number on a number line

Rational Numbers, Opposites, and Absolute Values

2.5: Rate, Ratio, Proportion, and Percent

2.5.1: Rates/Ratios/Proportions/Percents

2.5.1.2: [RIT 204 - 204] Understands percentage parts add up to 100

Percent of Change

Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview

Percents and Proportions

Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview

2.5.1.3: [RIT 206 - 231] Converts between percents and ratios expressed verbally or in the form a:b

Part-to-part and Part-to-whole Ratios

Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

Percents, Fractions, and Decimals

2.5.1.4: [RIT 207 - 212] Identifies ratios between two quantities not from the same whole

Part-to-part and Part-to-whole Ratios

2.5.1.5: [RIT 209 - 209] Recognizes a ratio within a context

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

2.5.1.8: [RIT 217 - 247] Compares unit rates within a real-world context

Road Trip (Problem Solving)

Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview

2.5.1.9: [RIT 218 - 246] Identifies the part-to-whole ratio between two quantities

Part-to-part and Part-to-whole Ratios

2.5.1.10: [RIT 219 - 249] Determines equivalent ratios

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

2.5.1.11: [RIT 219 - 239] Identifies the part-to-part ratio between two quantities

Part-to-part and Part-to-whole Ratios

2.5.1.12: [RIT 225 - 225] Writes a different ratio using the same quantities as a given ratio expressed either verbally, as a fraction, or in the form a:b

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

2.5.1.13: [RIT 251 - 255] Compares ratios within a real-world context

Part-to-part and Part-to-whole Ratios

2.6: Exponents, Radicals, and Scientific Notation

2.6.1: Exponents

2.6.1.2: [RIT 221 - 237] Represents a whole number as a power of a whole number

Finding Factors with Area Models

Find factors of a number using an area model. Reshape the area rectangle to see different factorizations of the number. Find the prime factorization using a factor tree. 5 Minute Preview

2.6.1.3: [RIT 225 - 232] Represents the value of digits in whole numbers using powers of 10 in exponential form

Number Systems

2.6.2: Scientific Notation

2.6.2.1: [RIT 213 - 230] Converts a number from scientific notation to standard form

Unit Conversions 2 - Scientific Notation and Significant Digits

Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview

2.6.2.2: [RIT 229 - 250] Converts a number from standard form to scientific notation

Number Systems

Unit Conversions 2 - Scientific Notation and Significant Digits

Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview

2.7: Number Theory

2.7.1: Whole Numbers: Concepts/Properties

2.7.1.2: [RIT 179 - 206] Determines if a number or set of numbers is even or odd

Factor Trees (Factoring Numbers)

The Factor Trees Gizmo has two modes. In Factor mode, you can create factor trees to factor composite numbers into primes. In Build mode, you can build numbers by multiplying primes together. Can you build all composite numbers up to 50? Any whole composite number up to 999 can be factored or built with the Gizmo. 5 Minute Preview

Finding Factors with Area Models

Find factors of a number using an area model. Reshape the area rectangle to see different factorizations of the number. Find the prime factorization using a factor tree. 5 Minute Preview

2.7.1.3: [RIT 194 - 230] Identifies factors of numbers less than 100

Factor Trees (Factoring Numbers)

The Factor Trees Gizmo has two modes. In Factor mode, you can create factor trees to factor composite numbers into primes. In Build mode, you can build numbers by multiplying primes together. Can you build all composite numbers up to 50? Any whole composite number up to 999 can be factored or built with the Gizmo. 5 Minute Preview

Finding Factors with Area Models

Find factors of a number using an area model. Reshape the area rectangle to see different factorizations of the number. Find the prime factorization using a factor tree. 5 Minute Preview

2.7.1.4: [RIT 203 - 203] Applies the tests for divisibility by 2, 5, and 10

Factor Trees (Factoring Numbers)

The Factor Trees Gizmo has two modes. In Factor mode, you can create factor trees to factor composite numbers into primes. In Build mode, you can build numbers by multiplying primes together. Can you build all composite numbers up to 50? Any whole composite number up to 999 can be factored or built with the Gizmo. 5 Minute Preview

2.7.1.5: [RIT 208 - 217] Solves problems involving factors and multiples

Factor Trees (Factoring Numbers)

Finding Factors with Area Models

Pattern Flip (Patterns)

In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck! 5 Minute Preview

2.7.1.6: [RIT 210 - 220] Determines greatest common factors

Factor Trees (Factoring Numbers)

2.7.1.7: [RIT 211 - 253] Solves real-world problems involving the least common multiple

Pattern Flip (Patterns)

2.7.1.8: [RIT 212 - 212] Determines prime factorization of a number using a factor tree

Factor Trees (Factoring Numbers)

Finding Factors with Area Models

2.7.1.9: [RIT 213 - 256] Determines least common multiples

Pattern Flip (Patterns)

2.7.1.10: [RIT 218 - 245] Determines the prime factorization of a number

Factor Trees (Factoring Numbers)

Finding Factors with Area Models

2.7.1.12: [RIT 219 - 219] Identifies multiples of two-digit numbers

Factor Trees (Factoring Numbers)

Finding Factors with Area Models

2.7.1.13: [RIT 219 - 243] Determines common factors

Pattern Flip (Patterns)

2.7.1.14: [RIT 222 - 223] Identifies prime and composite numbers

Factor Trees (Factoring Numbers)

Finding Factors with Area Models

2.7.1.15: [RIT 223 - 239] Applies multiple tests for divisibility

Factor Trees (Factoring Numbers)

Finding Factors with Area Models

2.7.1.16: [RIT 224 - 242] Determines common multiples

Pattern Flip (Patterns)

2.7.1.17: [RIT 235 - 236] Identifies true statements about number-theory concepts, including prime, composite, multiples, factors, least common multiples, and greatest common factors

Factor Trees (Factoring Numbers)

Finding Factors with Area Models

Pattern Flip (Patterns)

2.7.1.18: [RIT 237 - 237] Identifies factors of numbers greater than 100

Finding Factors with Area Models

2.7.1.20: [RIT 259 - 259] Solves problems by applying multiple number-theory concepts, including prime numbers, multiples, factors, least common multiples, and greatest common factors

Factor Trees (Factoring Numbers)