The middle years span from grades six through nine and move students from whole numbers, fractions and decimals into the world of integers, rational and irrational numbers. They utilize greater understanding of whole numbers to work with exponents and radicals. Understanding fractions and decimals becomes ratios, rates and percentages. Students can use number lines and inequalities with greater precision. Students work with integers understanding negative numbers and how they relate to quantities or lack thereof. At this level students are beginning to have a sophisticated understanding of numbers that allows them to work flexibly with all types of numbers.
| Domain | skill group | skill descriptor | 9 | 10 | 11 | 12 |
| Numbers | recognizes numbers | spoken | 1 000 000 | 1 000 000 | 1 000 000 | |
| mixed numbers | positive integers | square numbers | whole number exponents | |||
| improper fractions | negative integers | cube numbers | positive exponents | |||
| square roots | ||||||
| cube roots | ||||||
| written | 1 000 000 | 1 000 000 | 1 000 000 | |||
| mixed numbers | positive integers | square numbers | ||||
| improper fractions | negative integers | cube numbers | ||||
| square roots | ||||||
| cube roots | ||||||
| Fractions | identify fractions | improper fractions | ||||
| mixed numbers | ||||||
| rational and irrational numbers | rational numbers | square numbers | exponents with varied bases | |||
| cube numbers | ||||||
| irrational numbers | pi | square roots | ||||
| cube roots | ||||||
| Representing Numbers | whole numbers | with objects | 1 000 000 | 1 000 000 | 1 000 000 | |
| with drawings | 1 000 000 | 1 000 000 | 1 000 000 | |||
| with numerals | 1 000 000 | 1 000 000 | 1 000 000 | |||
| represent fractions… | improper fractions with objects | |||||
| improper fractions with drawing | ||||||
| improper fractions with numerals | ||||||
| mixed numbers with objects | ||||||
| mixed numbers with drawings | ||||||
| mixed numbers with numerals | ||||||
| integers | represent positive integers …. | with objects | ||||
| with drawings | ||||||
| with numerals | ||||||
| represent negative integers | with objects | |||||
| with drawings | ||||||
| with numerals | ||||||
| rational and irrational numbers | represent rational numbers | squares with objects | represent exponents with drawings | |||
| squares with drawings | represent exponents with numerals | |||||
| squares with numerals | represent numerals with mathematical notation | |||||
| cubes with objects | ||||||
| cubes with drawings | ||||||
| cubes with numerals | ||||||
| represent irrational numbers | square roots with objects | |||||
| square roots with drawings | ||||||
| square roots with numerals | ||||||
| cube roots with objects | ||||||
| cube roots with drawings | ||||||
| cube roots with numerals | ||||||
| Place Value | base 10 numeration – whole numbers | represents numbers with base ten blocks to | ||||
| uses a place value chart to represent numbers to | 1 000 000 | 1 000 000 | ||||
| identifies the value of the numbers in each place to | 1 000 000 | 1 000 000 | ||||
| record numbers in standard notation from a place value chart | 1 000 000 | 1 000 000 | ||||
| Base 10 numeration – decimals | represents numbers with base ten blocks to | 4 decimal places | ||||
| uses a place value chart to represent numbers to | 4 decimal places | |||||
| identifies the value of the numbers in each place to | 4 decimal places | |||||
| record numbers in standard notation from a place value chart | 4 decimal places | |||||
| Number Relationships | composition and decomposition | composes numbers to___ in many ways using objects | 1 000 000 | |||
| composes numbers to___ in many ways using pictures | 1 000 000 | |||||
| compose numbers to____ using numerals and mathematical notation | 1 000 000 | |||||
| decomposes numbers to___ in many ways using objects | 1 000 000 | |||||
| decomposes numbers to___ in many ways using pictures | 1 000 000 | |||||
| decompose numbers to____ using numerals and mathematical notation | 1 000 000 | |||||
| composes numbers to___ in many ways using objects | 4 decimal places | |||||
| composes numbers to___ in many ways using pictures | 4 decimal places | |||||
| compose numbers to____ using numerals and mathematical notation | 4 decimal places | |||||
| decomposes numbers to___ in many ways using objects | 4 decimal places | |||||
| decomposes numbers to___ in many ways using pictures | 4 decimal places | |||||
| decompose numbers to____ using numerals and mathematical notation | 4 decimal places | |||||
| comparing and ordering – base 10 numeration | compares quantities to | 1 000 000 | ||||
| compare pairs of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to) | 1 000 000 | |||||
| compare groups of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to) | 1 000 000 | |||||
| uses place value to compare numbers | 1 000 000 | 1 000 000 | ||||
| uses place value to order numbers | 1 000 000 | 1 000 000 | ||||
| order numbers to ___ | 1 000 000 | |||||
| place numbers to ___ on a number line | 1 000 000 | |||||
| uses benchmarks to compare and order numbers | 100 000 | |||||
| 500 000 | ||||||
| compare pairs of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to) | 4 decimal places | |||||
| decimal places | ||||||
| compare groups of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to) | 4 decimal places | |||||
| decimal places | ||||||
| order numbers to ___ | 4 decimal places | |||||
| decimal places | ||||||
| place numbers to ___ on a number line | 4 decimal places | |||||
| decimal places | ||||||
| compare pairs of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to) | positive and negative integers | |||||
| compare groups of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to) | positive and negative integers | |||||
| order numbers to ___ | positive and negative integers | |||||
| place numbers to ___ on a number line | positive and negative integers | |||||
| comparing and ordering – fractions | compares fractions to benchmarks | x/2 | ||||
| orders fractions on a number line | mixed numbers | |||||
| compare pairs of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to) | mixed numbers | |||||
| compare groups of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to) | mixed numbers | |||||
| using fractions | convert between fractions and decimals | simplifying fractions | ||||
| Proportional sharing based on changing group size | ||||||
| Ratios and Percentages | represent ratios using | pictures | ||||
| objects | ||||||
| numerals | ||||||
| fractions | ||||||
| decimals | ||||||
| represent percentages using | pictures | |||||
| objects | ||||||
| numerals | ||||||
| fractions | ||||||
| decimals | ||||||
| comparing and ordering | compare ratios using inequalities notation | |||||
| order ratios | ||||||
| compare percentages using inequalities notation | ||||||
| order percentages | ||||||
| use of ratios and percentages | two and three term ratios | |||||
| use in mechanics | ||||||
| use in architecture | ||||||
| percentage increase | ||||||
| percentage decrease | ||||||
| equivalency | Fractions | mixed numbers | fractions to ratios | |||
| fractions to percentages | ||||||
| decimals | Ratios tenths to decimal tenths | decimals to ratios | ||||
| Ratio hundredths to decimal hundredths | decimals to percentages |