# 4th Grade Topic 1 - Multiplication and Division: Meanings and Facts

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1 4th Grade Topic 1 - Multiplication and Division: Meanings and Facts Approximately 9 days Standard Objective Notes 1-1 OA1 recognize multiplication as repeated addition G21, G22, G23, G OA5 use patterns to find products G25, G OA1 1-4 OA4 OPTIONAL 1-5 OA3 use multiplication properties to simplify computation recognize and extend patterns to solve word problems 1-6 OA2 use models to solve division problems Combine 1-7 & 1-8 OA1 & OA2 use fact families to solve multiplication and division problems F37 G28, G29, G30,G31 J16 G21, G22, G23, G35 G37 TO G41 All questions on the re-teach Topic 1 practice test and Topic 1 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. OA1 OA2 Interpret a multiplication equation as a comparision, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. OA3 OA4 OA5 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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. Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the rage is a multiple of a given one-digit number. Determine whetehr a given whole number in the range is prime or composite 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.

2 4th Grade Topic 2 - Generate and Analyze Patterns Approximately 5 days Standard Objective Notes Combine 2-1 & 2-2 Combine 2-3 & 2-4 OA5 identify and extend number and shape patterns; and generate numerical rules OA5 extend tables to represent a pattern F OA5 extend patterns of geometric solids F25 F22, F OMIT All questions on the re-teach Topic 2 practice test and Topic 2 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. OA5 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.

3 4th Grade Topic 3 - Place Value Approximately 8 days Standard Objective Notes 3-1 NBT2 read and write 3- & 4-digit numbers in standard, word, and expanded form 3-2 NBT1 recognize that the value of a digit is ten times the place to the right F3 3-3 NBT2 compare numbers through the hundred thousands F5 3-4 NBT2 order numbers through hundred thousands F9, F (2 days) NBT3 round whole numbers to any place Students probably need more than one day to master this concept. F8 3-6 OPTIONAL J6 All questions on the re-teach Topic 3 practice test and Topic 3 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. NBT1 NBT2 NBT3 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 = 10 by applying concepts of place value and division. 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. Use place value understanding to round multi-digit whole numbers to any place.

4 4th Grade Topic 4 - Add Subtract Whole Numbers Approximately 6 days Standard Objective Notes 4-1 OMIT G5, G6, G11 Combine 4-2 & 4-3 NBT3 & NBT4 4-4 NBT4 estimate to find sums and differences and add numbers to the thousands using the standard algorithm subtract with regrouping using the standard algorithm 4-5 NBT4 subtract across zeros using standard algorithm Encourage students to continue to use estimation daily. G7, G8, G15 G12, G16, G19 G13, G17, G18, G NBT4 & OA3 J8 All questions on the re-teach Topic 3 practice test and Topic 3 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. NBT3 NBT4 Use place value understanding to round multi-digit whole numbers to any place. Fluently add and subtract multi-digit whole numbers using the standard algorithm. OA3 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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.

5 4th Grade Topic 5 -Number Sense: Multiplying by 1-Digit Numbers Approximately 6 days Standard Objective Notes Combine 5-1 & 5-2 NBT5 use arrays and basic facts to multiply by 10, 100, or 1000 G32, G NBT5 use distributive property and arrays to multiply 2- digit numbers by 1-digit numbers G NBT5 OPTIONAL G NBT5 use estimation to solve multiplication problems Encourage students to continue to use estimation daily. G NBT5 check reasonableness using estimation strategies All questions on the re-teach Topic 5 practice test and Topic 5 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. NBT5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two 2-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.

6 4th Grade Topic 6 - Developing Fluency: Multiplying by 1-Digit Numbers Approximately 8 days Standard Objective Notes 6-1 NBT5 use partial products to multiply a 2-digit number by a 1-digit number G NBT5 & OA3 standard multiplication algorithm G NBT5 & OA3 multiply a 2-digit number by 1-digit number G NBT5 multiply 3- and 4-digit numbers by a 1-digit number 6-5 NBT5 & OA3 word problems (multiply by a 1-digit number) 6-6 NBT5 identify missing or extra information in word problems G52 G49, G50, G52 J1 All questions on the re-teach Topic 6 practice test and Topic 6 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. NBT5 OA3 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two 2-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. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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.

7 4th Grade Topic 7 - Number Sense: Multiplying by 2-Digit Numbers Approximately 9 days Standard Objective Notes 7-1 NBT5 multiply 2-digits by multiples of ten using arrays G66 Combine 7-2 & 7-3 NBT5 use basic facts to multiply larger numbers and round 2-digit numbers to multiply with basic facts Encourage students to continue to use estimation daily. G NBT5 OPTIONAL G NBT5 solve multi-step problems J3 All questions on the re-teach Topic 7 practice test and Topic 7 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. NBT5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two 2-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.

8 4th Grade Topic 8 - Developing Fluency Multiplying by 2-Digit Numbers Approximately 9 days Standard Objective Notes 8-1 NBT5 use arrays to multiply a 2-digit number by a 2-digit number G NBT5 use the expanded algorithm for multiplication G NBT5 multiply a 2-digit number by multiples of ten G NBT5 multiply a 2-digit number by a 2-digit number with the standard algorithm It's very important to focus on connecting the strategies in Topic 7 and Topic 8 to the traditional algorithm. It is suggested that you supplement and spend more time on working with the algorithm for those students that are ready; however it is NOT expected that students master it in 4th grade. G NBT5 solve two-question problems J2 All questions on the re-teach Topic 8 practice test and Topic 8 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. NBT5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two 2-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.

9 4th Grade Topic 9 - Number Sense: Dividing by 1-Digit Divisors Approximately 5 days Standard Objective Notes 9-1 NBT6 use mental math to divide G44 Combine 9-2 & OMIT NBT6 estimate quotients Estimation should be reviewed throughout the year. G46 See unpacked standard to show various examples with algorithm. 9-5 OMIT G NBT6 OPTIONAL G42 All questions on the re-teach Topic 9 practice test and Topic 9 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. NBT6 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.

10 4th Grade Topic 10 - Developing Fluency Dividing by 1- Digit Numbers Approximately 8 days Standard Objective Notes 10-1 NBT6 use repeated subtraction to show division G NBT6 use repeated subtraction to show division G NBT6 use objects to divide: division as sharing G53 Additional NBT6 SUPPLEMENTAL Use Common Core Progress OMIT LONG DIVISION ALGORITHM 10-5 OMIT IS NOT IN THE 10-6 OMIT COMMON CORE UNTIL 6th GRADE, 10-7 OMIT so save it for the end of the year or use with advanced students who are ready OA3 solve multi-step problems G55, G56, G58 All questions on the re-teach Topic 10 practice test and Topic 10 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. NBT6 OA3 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. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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.

11 4th Grade Topic 11 - Fraction Equivalence and Ordering Approximately 10 days Standard Objective Notes 11-1 OA4 find factors of whole numbers G OA4 identify prime and composite numbers G OA4 find multiples of a number 11-4 NF NF NF NF2 use models and computations to show equivalent fractions use number line to identify and write equivalent fractions use benchmark fractions to compare fractions with unlike denominators use common denominators to order fractions with unlike denominators PLEASE NOTE: SIMPLEST FORM IS NOT IN THE STANDARD. It's fine to discuss throughout the fraction topics, but not expected to be mastered. H7, H14 H5 H6, H9, H19 H NF2 solve fraction word problems J37 All questions on the re-teach Topic 11 practice test and Topic 11 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. OA4 NF1 NF2 Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whol e number in the rage is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite. 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. 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.

13 4th Grade Topic 13 - Extending Fraction Concepts Approximately 10 days Standard Objective Notes 13-1 NF4a use multiplication to write a fraction as the product of a whole number and a unit fraction 13-2 NF4b multiply fractions by a whole number using models H NF4c multiply fractions by a whole number using symbols H45 H NF6 write fractions as decimals and decimals as fractions H10, H NF5 OMIT REPLACE with CC Progress 24 H5, H8, H20 TO H23 H34, H NF6 & NF7 OMIT REPLACE with CC Progress OMIT 13-8 NF7 compare and order decimals to the hundredths H MD2 solve word problems with money H OMIT All questions on the re-teach Topic 16 practice test and Topic 16 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. NF4a NF4b NF4c NF5 NF6 NF7 MD.2 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). 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.) 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? 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 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100 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. 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. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

14 4th Grade Topic 14 - Measurement Units and Conversions Approximately 12 days Standard Objective Notes 14-1 MD1 estimate and measure customary units of length I MD1 estimate with customary units of capacity I MD1 estimate with customary units of weight I MD1 REPLACE with CC Progress MD1 solve word problems using measurement I33, I34, I MD1 estimate and measure metric units of length J MD.1 estimate with metric units of capacity I MD1 estimate and measure units of mass I MD1 REPLACE with CC Progress 27 I OMIT MD2 solve word problems with intervals of time J27 All questions on the re-teach Topic 14 practice test and Topic 14 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. MD1 MD2 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),... Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

15 4th Grade Topic 15 - Solving Measurement Problems Approximately 7 days Standard Objective Notes 15-1 (2 days) MD3 solve perimeter and area problems for rectangles Supplement a 2nd day with CC Progress 29 I OPTIONAL 15-3 MD2 solve problems with money H11, H (2 days) MD4 solve problems with fractional line plots Supplement a 2nd day with CC Progress 30 I62, J OPTIONAL All questions on the re-teach Topic 1 practice test and Topic 1 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. MD2 MD3 MD4 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 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. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

16 4th Grade Topic 16 - Lines, Angles, and Shapes Approximately 11 days Standard Objective Notes 16-1 G1 identify and describe points and lines I G2 describe lines and angles I3, I MD5a relate measures of angles to fractions of circles and use those fractions of circles to determine the measure of angle in degrees 16-4 OMIT 16-5 MD5b & MD6 measure and draw angles I MD7 add and subtract angle measures 16-7 G2 identify polygons This lesson should not take a whole day. You may opt to combine it with 16-8 or introduce the concept earlier in the Topic. I G2 identify and classify triangles I G2 identify quadrilaterals I G3 line of symmetry I OPTIONAL J32 All questions on the re-teach Topic 16 practice test and Topic 16 assessment will not apply because lessons were excluded. Additional questions may be added to assess the additional lesson included to thoroughly cover the standards. G1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. G2 G.3 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. 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 linesymmetric figures and draw lines of symmetry. MD.5a MD.5b An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 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.

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