# Zap Zap Math - K6 Math Games

- addition
- fractions
- geometry
- measurement

- applying information
- memorization
- thinking critically

###### Pros

Games are beautifully designed and target essential Common Core standards.###### Cons

Some of the games are a bit cumbersome, so it takes a long time to get to the actual math.###### Bottom Line

These interactive games give kids plenty of practice, so long as they can focus on the math and not the paid upgrades and rewards.An easy-to-use dashboard allows teachers to track individual student progress.

Graphics and rewards pull kids in, and the variety of interactive games should keep them going.

Students play games to practice skills and then apply what they practiced to solve higher-order thinking problems. The reward system is motivating but could distract some kids from learning.

Not all the games are intuitive, but animated instructions help. Instructional feedback for incorrect answers, at least at the training skill level, would improve support.

Teachers can use Zap Zap Math for targeted practice in the classroom. The games align very well with Common Core math standards and could serve as a pre-assessment tool, giving kids practice before a high-stakes exam. Choose a standard to practice from the appropriate grade level, and then choose a skill. Have kids complete a skill and track their progress on the teacher dashboard. Instructional feedback is not built into the games, so teachers need to provide their own remediation if needed.

Read more Read lessKids start playing Zap Zap Math games by selecting a grade and a skill: training, accuracy, speed, or mission. The games default to the first set of Common Core standards listed, but these can also be selected before playing a game if kids want to practice a specific standard. Each skill takes a different approach on a standard, with the mission skill being the most challenging. In this skill, kids must apply what they've learned to complete a task. A web-based teacher dashboard allows for progress tracking once kids enter a code from the app.

For each level within a skill, kids earn points and rewards they can use to decorate rooms inside a spaceship. It's always nice to have motivating rewards, but the reward window pops up after kids complete a level. This, along with the frequently busy screen, might distract some kids who just want to get stuff.

Read more Read lessWith Zap Zap Math, kids can learn about many concepts covered by Common Core math standards. These standards are sometimes hard to break down into meaningful, kid-friendly lessons, but the app does an excellent job of addressing this challenge; kids could benefit from the practice that the games provide. Having four skills within the same set of standards is also a great way for kids to deepen their understanding of the standards. Since kids do not receive instructional feedback for incorrect answers, it's important that teachers use the dashboard to monitor progress and provide reinforcement as needed.

The game is filled with lots of bells and whistles, which could be engaging and motivational to some kids. However, the constant music and reward and purchase pop-ups are a bit much. The graphics are fun, but some take a while to load. Overall, Zap Zap Math offers plenty of practice for kids who are trying to master Common Core math standards.

Read more Read less## Key Standards Supported

## Counting And Cardinality | |

K.CC: Count To Tell The Number Of Objects. | |

K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. |

K.CC.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. |

Compare Numbers. | |

K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.1 |

K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. |

## Expressions And Equations | |

6.EE: Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions. | |

6.EE.3 | Apply the properties of operations to generate equivalent expressions. |

Reason About And Solve One-Variable Equations And Inequalities. | |

6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. |

## Geometry | |

1.G: Reason With Shapes And Their Attributes. | |

1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. |

1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.4 |

1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. |

2.G: Reason With Shapes And Their Attributes. | |

2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. |

2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. |

4.G: Draw And Identify Lines And Angles, And Classify Shapes By Properties Of Their Lines And Angles. | |

4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. |

4.G.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. |

5.G: Graph Points On The Coordinate Plane To Solve Real-World And Mathematical Problems. | |

5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). |

6.G: Solve Real-World And Mathematical Problems Involving Area, Surface Area, And Volume. | |

6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. |

## Measurement And Data | |

K.MD: Describe And Compare Measurable Attributes. | |

K.MD.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. |

K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. |

Classify Objects And Count The Number Of Objects In Each Category. | |

K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.3 |

1.MD: Measure Lengths Indirectly And By Iterating Length Units. | |

1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. |

1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. |

Tell And Write Time. | |

1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. |

Represent And Interpret Data. | |

1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. |

2.MD: Represent And Interpret Data. | |

2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put- together, take-apart, and compare problems4 using information presented in a bar graph. |

2.MD.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. |

Measure And Estimate Lengths In Standard Units. | |

2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. |

2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. |

2.MD.3 | Estimate lengths using units of inches, feet, centimeters, and meters. |

2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. |

Relate Addition And Subtraction To Length. | |

2.MD.6 | Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. |

Work With Time And Money. | |

2.MD.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? |

3.MD: Represent And Interpret Data. | |

3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. |

3.MD.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters. |

Solve Problems Involving Measurement And Estimation Of Intervals Of Time, Liquid Volumes, And Masses Of Objects. | |

3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. |

3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.7 |

Geometric Measurement: Understand Concepts Of Area And Relate Area To Multiplication And To Addition. | |

3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. |

3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). |

3.MD.7 | Relate area to the operations of multiplication and addition. |

Geometric Measurement: Recognize Perimeter As An Attribute Of Plane Figures And Distinguish Between Linear And Area Measures. | |

3.MD.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. |

4.MD: Solve Problems Involving Measurement And Conversion Of Measurements From A Larger Unit To A Smaller Unit. | |

4.MD.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... |

4.MD.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. |

Geometric Measurement: Understand Concepts Of Angle And Measure Angles. | |

4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: |

4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. |

4.MD.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. |

5.MD: Convert Like Measurement Units Within A Given Measurement System. | |

5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. |

Geometric Measurement: Understand Concepts Of Volume And Relate Volume To Multiplication And To Addition. | |

5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. |

5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. |

5.MD.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. |

## Number And Operations In Base Ten | |

K.NBT: Work With Numbers 11–19 To Gain Foundations For Place Value. | |

K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. |

## 1.NBT | |

Extend The Counting Sequence.: 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.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.2 | Count within 1000; skip-count by 5s, 10s, and 100s. |

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. |

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. |

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. |

5.NBT: 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.4 | Use place value understanding to round decimals to any place. |

## Number And Operations—Fractions | |

3.NF: Develop Understanding Of Fractions As Numbers. | |

3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. |

3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. |

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. |

Understand Decimal Notation For Fractions, And Compare Decimal Fractions. | |

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. |

5.NF: 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.) |

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? |

## Operations And Algebraic Thinking | |

K.OA: Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From. | |

K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. |

K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). |

K.OA.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. |

K.OA.5 | Fluently add and subtract within 5. |

1.OA: 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. |

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). |

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: 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: 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.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 = ?. |

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. |

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. |

Solve Problems Involving The Four Operations, And Identify And Explain Patterns In Arithmetic. | |

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. |

4.OA: Gain Familiarity With Factors And Multiples. | |

4.OA.4 | Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. |

Generate And Analyze Patterns. | |

4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. |

5.OA: Write And Interpret Numerical Expressions. | |

5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. |

5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. |

## Ratios And Proportional Relationships | |

6.RP: Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems. | |

6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” |

6.RP.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1 |

6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. |

## The Number System | |

6.NS: Compute Fluently With Multi-Digit Numbers And Find Common Factors And Multiples. | |

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). |

Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers. | |

6.NS.7 | Understand ordering and absolute value of rational numbers. |

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