Common Sense Review
Updated December 2012
Math Blaster HyperBlast
Common Sense Rating
3
Teacher Rating
(3 Teacher Reviews)
4
Price
Free to Try, Paid
This grade range is a recommendation by the Common Sense Education editorial team, not the developer/publisher.
Grades
2-8 Platforms
Android, iPad, iPhone, iPod Touch, Kindle Fire, Nook HD Subjects
Math
- addition
- division
- multiplication
- subtraction
Skills
Critical Thinking
- problem solving
Purpose
Targeted Practice Standards
Common Core State Standards 
Before starting their mission, kids can choose which mathematical operation to work on.
When players encounter the alien-robot, they answer as many math problems as possible before time runs out.
Players blast through hyperspace, shooting objects that get in their way to accumulate points.
Hitting obstacles slows down the progress.
Pros
Many levels and function choices accommodate a broad range of use for kids with varying skill levels.Cons
Gameplay can stray from math-focused learning into pure arcade entertainment.Bottom Line
A versatile tool to build and practice basic math skills, though it could better integrate learning and fun.
Common Sense Rating
3
Engagement
Is the product stimulating, entertaining, and engrossing? Will kids want to return?
4
The game is fun and challenging, with colorful space-age graphics kids will appreciate. With the feel and speed of a video game, it'll draw kids in and encourage them to stick around for the math.
Pedagogy
Is learning content seamlessly baked-in, and do kids build conceptual understanding? Is the product adaptable and empowering? Will skills transfer?
3
Fast-paced gameplay encourages both speed and accuracy in math calculations, although the learning isn't very baked-in (kids play the game, then do some math problems, etc.). There are a variety of operations to integrate into the gameplay.
Support
Does the product take into account learners of varying abilities, skill levels, and learning styles? Does it address both struggling and advanced students?
4
The developer's website offers more games and extensive resources for teachers. In the app, kids will see immediately whether they've missed a problem and will see their scores after each level.
How Can Teachers Use It?
Its versatility makes Math Blaster Hyperblast a fun supplement to classroom work. The app tracks scores for up to six kids with one email address. Unfortunately, high scores reflect a combination of kids’ performance on math problems as well as points earned shooting objects in the game. Teachers will appreciate the developer's website, which includes online games and extensive resources such as worksheets and lesson plans.
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What's It Like?
Math Blaster Hyperblast is an arcade-style game where kids can develop speed in math recall as they answer problems in addition, subtraction, multiplication, division, fractions, or standard form. The different skill choices and customizable number ranges make this app playable for a variety of ages and skills, from elementary through middle school.
In the game, kids blast through space, shooting objects that get in their way, and when a multi-legged robot appears, they answer a few math problems, practicing a variety of concepts while fighting off this alien-robot. Play offers challenges for a wide range of math abilities, even within each skill. Kids can choose the range of numbers (like sums to eight) within the skill and can test combined skills such as addition/subtraction or multiplication/division. Challenge levels can also be set to easy, medium, or hard. The game ends after a round with multiple incorrect answers.
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Is It Good For Learning?
The “hyperblasting” portion of the game is pure arcade-like fun, and kids can develop some speedy reflexes as they maneuver through space, tilting the device to dodge obstacles and pressing the button on the screen to shoot aliens. However, the educational thrust of the app appears in the math quizzes for each mission. When they encounter the many-legged robot, students have to choose the correct answer to the given problem on one of the legs. The legs are moving a bit, though, which can make identifying the right answer difficult. And the touch screen doesn’t always register the tap on the chosen answer. When kids choose a wrong answer, they see the correct answer before the next problem appears, but they get no instruction or explanation of the underlying concepts.
Read More Read LessKey Standards Supported
Number And Operations In Base Ten | |
| 1.NBT: Extend The Counting Sequence. | |
| 1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. |
| Understand Place Value. | |
| 1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: |
| 1.NBT.2.a | 10 can be thought of as a bundle of ten ones — called a “ten.” b. |
| 1.NBT.2.b | The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. |
| 1.NBT.2.c | The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). |
| 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. |
| Use Place Value Understanding And Properties Of Operations To Add And Subtract. | |
| 1.NBT.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. |
| 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. |
| 1.NBT.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), 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. |
| 2.NBT: Understand Place Value. | |
| 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: |
| 2.NBT.1.a | 100 can be thought of as a bundle of ten tens — called a “hundred.” |
| 2.NBT.1.b | The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). |
| 2.NBT.2 | Count within 1000; skip-count by 5s, 10s, and 100s. |
| 2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. |
| 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. |
| Use Place Value Understanding And Properties Of Operations To Add And Subtract. | |
| 2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. |
| 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. |
| 2.NBT.7 | Add and subtract within 1000, 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. Understand that in adding or subtracting three- digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. |
| 2.NBT.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. |
| 2.NBT.9 | Explain why addition and subtraction strategies work, using place value and the properties of operations.3 |
| 4.NBT: Generalize Place Value Understanding For Multi-Digit Whole Numbers. | |
| 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. |
| 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. |
| 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. |
| Use Place Value Understanding And Properties Of Operations To Perform Multi-Digit Arithmetic. | |
| 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. |
| 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. |
| 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. |
| 3.NBT: Use Place Value Understanding And Properties Of Operations To Perform Multi-Digit Arithmetic.4 | |
| 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. |
| 3.NBT.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. |
| 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. |
| 5.NBT: Perform Operations With Multi-Digit Whole Numbers And With Decimals To Hundredths. | |
| 5.NBT.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. |
| 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. |
| 5.NBT.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. |
| Understand The Place Value System. | |
| 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. |
| 5.NBT.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. |
| 5.NBT.3 | Read, write, and compare decimals to thousandths. |
| 5.NBT.3.a | Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). |
| 5.NBT.3.b | Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. |
| 5.NBT.4 | Use place value understanding to round decimals to any place. |
| 4.NF: Build Fractions From Unit Fractions By Applying And Extending Previous Understandings Of Operations On Whole Numbers. | |
| 4.NF.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. |
| 4.NF.3.a | Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. |
| 4.NF.3.b | Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. |
| 4.NF.3.c | Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. |
| 4.NF.3.d | Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. |
| 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. |
| 4.NF.4.a | Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). |
| 4.NF.4.b | Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) |
| 4.NF.4.c | Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? |
| Extend Understanding Of Fraction Equivalence And Ordering. | |
| 4.NF.1 | Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. |
| 4.NF.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. |
| Understand Decimal Notation For Fractions, And Compare Decimal Fractions. | |
| 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. |
| 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. |
| 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. |
Number And Operations—Fractions | |
| 5.NF: Apply And Extend Previous Understandings Of Multiplication And Division To Multiply And Divide Fractions. | |
| 5.NF.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. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? |
| 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. |
| 5.NF.4.a | Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) |
| 5.NF.4.b | Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. |
| 5.NF.5 | Interpret multiplication as scaling (resizing), by: |
| 5.NF.5.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. |
| 5.NF.5.b | Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); 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 = (n×a)/(n×b) to the effect of multiplying a/b by 1. |
| 5.NF.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. |
| 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1 |
| 5.NF.7.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) × 4 = 1/3. |
| 5.NF.7.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 × (1/5) = 4. |
| 5.NF.7.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 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? |
| Use Equivalent Fractions As A Strategy To Add And Subtract Fractions. | |
| 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) |
| 5.NF.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 |
| 3.NF: Develop Understanding Of Fractions As Numbers. | |
| 3.NF.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. |
| 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. |
| 3.NF.2.a | Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. |
| 3.NF.2.b | Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. |
| 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. |
| 3.NF.3.a | Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. |
| 3.NF.3.b | Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. |
| 3.NF.3.c | Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. |
| 3.NF.3.d | Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. |
Operations And Algebraic Thinking | |
| 1.OA: Add And Subtract Within 20. | |
| 1.OA.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). |
| 1.OA.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). |
| Represent And Solve Problems Involving Addition And Subtraction. | |
| 1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.2 |
| 1.OA.2 | Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. |
| Understand And Apply Properties Of Operations And The Relationship Between Addition And Subtraction. | |
| 1.OA.3 | Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) |
| 1.OA.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. |
| Work With Addition And Subtraction Equations. | |
| 1.OA.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. |
| 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = � – 3, 6 + 6 = �. |
| 2.OA: Add And Subtract Within 20. | |
| 2.OA.2 | Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers. |
| Represent And Solve Problems Involving Addition And Subtraction. | |
| 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 |
| Work With Equal Groups Of Objects To Gain Foundations For Multiplication. | |
| 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. |
| 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. |
| 3.OA: Multiply And Divide Within 100. | |
| 3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. |
| Represent And Solve Problems Involving Multiplication And Division. | |
| 3.OA.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. |
| 3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. |
| 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 |
| 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = � ÷ 3, 6 × 6 = ?. |
| Solve Problems Involving The Four Operations, And Identify And Explain Patterns In Arithmetic. | |
| 3.OA.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3 |
| 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. |
| Understand Properties Of Multiplication And The Relationship Between Multiplication And Division. | |
| 3.OA.5 | Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) |
| 3.OA.6 | Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. |
The Number System | |
| 6.NS: Apply And Extend Previous Understandings Of Multiplication And Division To Divide Fractions By Fractions. | |
| 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? |
| Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers. | |
| 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. |
| 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. |
| 6.NS.6.a | Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. |
| 6.NS.6.b | Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. |
| 6.NS.6.c | Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. |
| 6.NS.7 | Understand ordering and absolute value of rational numbers. |
| 6.NS.7.a | Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. |
| 6.NS.7.b | Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC. |
| 6.NS.7.c | Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. |
| 6.NS.7.d | Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. |
| 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. |
| Compute Fluently With Multi-Digit Numbers And Find Common Factors And Multiples. | |
| 6.NS.2 | Fluently divide multi-digit numbers using the standard algorithm. |
| 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. |
| 6.NS.4 | Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). |
| 7.NS: Apply And Extend Previous Understandings Of Operations With Fractions To Add, Subtract, Multiply, And Divide Rational Numbers. | |
| 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. |
| 7.NS.1.a | Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. |
| 7.NS.1.b | Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. |
| 7.NS.1.c | Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. |
| 7.NS.1.d | Apply properties of operations as strategies to add and subtract rational numbers. |
| 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. |
| 7.NS.2.a | Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. |
| 7.NS.2.b | Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real- world contexts. |
| 7.NS.2.c | Apply properties of operations as strategies to multiply and divide rational numbers. |
| 7.NS.2.d | Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. |
| 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. |
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