Methods of Multiplication
10/9/2015
Dear Parents,
We began our next unit of study this week: methods of multiplication. The information below will serve as an overview of the unit as you work to support your child at home. Please note that the methods being taught are probably different than the typical strategy you are familiar with. The standard algorithm isn't tested until 5th grade. It will be covered, but not to the same degree as the strategies listed below. If you have any questions, please feel free to contact me. I appreciate your on-going support. Strategies for Multiplication Common Core State Standards: 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. Essential Vocabulary: • multiplication/multiply • division/divide • area • array • factor • square unit • product • area model • expanded notation • algebraic notation Unit Overview: In this unit, students will apply their understanding of place value to help them explore multiple groups or multiplication. Students will utilize their knowledge of base ten and groups of numbers within another number to help them solve for multi-digit multiplication. Students will use their knowledge from 3rd grade with multiplication factors to help them solve larger multi-digit problems. Students will solve multi-digit multiplication problems with the use of various strategies listed below. Students will not be required to use the standard algorithm until 5th grade. Strategies/Skills: Students will build on their understanding of addition and subtraction by using place value strategies to make sense of the standard algorithms. They are expected to use a variety of models to support their reasoning about numbers. • Rectangular Section/Arrays • Area Models • Base Ten blocks • Expanded notation • Algebraic notation Video Support: Video support can be found on The WCPSS Academics YouTube Channel. • http://tinyurl.com/WCPSSAcademicsYouTube o ES 4 Math Whole Number Multiplication w/ Expanded Notation https://www.youtube.com/watch?v=- 8PK7vsIF2Q&list=PLNDkuWRw1gGRpuFSgmHjf07KamFfjq8Gz&index=32 o ES 4 Math Whole Number Multiplication w/ Area Model https://www.youtube.com/watch?v=3TJ9KdEhUbU&list=PLNDkuWRw1gGRpuFSgm Hjf07KamFfjq8Gz&index=6 o ES 4 Math Whole Number Multiplication w/ Base Ten Blocks https://www.youtube.com/watch?v=c6MRuNTwZi8&list=PLNDkuWRw1gGRpuFSgm Hjf07KamFfjq8Gz&index=5
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Factors
9/28/2015
Factors
Common Core State Standards: 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. Essential Vocabulary: • multiplication/multiply • division/divide • area • array • factor pair • factor • prime • composite • product • area model Unit Overview: In this unit, students will use their knowledge from 3rd grade on multiplication factors to help them find factor pairs using area model/arrays. Students will use their knowledge of finding factor pairs to determine if a number is prime or composite. In addition, for the first time students will learn about prime and composite numbers in relation to rectangular arrays. Students will not be required to use the standard algorithm until 5th grade. Strategies/Skills: Students will build on their understanding of addition and subtraction by using place value strategies to make sense of the standard algorithms. They are expected to use a variety of models to support their reasoning about numbers. • Area Model/Arrays • Relationship between multiplication & division (through various properties) Video Support: Video support can be found on LearnZillion. • http://learnzillion.com o Find all the factor pairs of a number using area models https://learnzillion.com/lessons/780-find-all-the-factor-pairs-of-a-number-using-area-models o Determine multiples of a number using area models o Determine if a number is prime or composite using area models https://learnzillion.com/lessons/781-determine-multiples-of-a-number-using-area-models https://learnzillion.com/lessons/786-determine-if-a-number-is-prime-or-composite-using- area-models Adding & Subtracting Whole Numbers
9/16/2015
Adding and Subtracting Whole Numbers
Common Core State Standards: 4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place. 4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. 4.OA.3 Solve multistep 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. Essential Vocabulary: • place value vocabulary from previous unit • multiplication/multiply • division/ divide • subtraction/subtract • reasonableness • mental computation In this unit, students will apply their understanding of place value to help solve for multi-step word problems with addition and subtraction. Students will utilize estimation as part of the problem solving process. One example is students rounding to the nearest leading digit. This will help students to check their solution or answer after solving to see if it is reasonable. In addition, students will need to be fluent with numbers in order to break them apart or reconstruct them by place value. Students will build on their understanding of addition and subtraction by using place value strategies to make sense of the standard algorithms. They are expected to use a variety of models to support their reasoning about numbers. • Base Ten blocks • Show Subtotals Method • Relationship between multiplication & division Video Support can be found on The WCPSS Academics YouTube Channel. • http://tinyurl.com/WCPSSAcademicsYouTube http://www.youtube.com/watch?v=sWXsaia- Nd4&index=3&list=PLNDkuWRw1gGRpuFSgmHjf07KamFfjq8Gz Video support can be found on LearnZillion. • http://learnzillion.com o Solve multi-step word problems by rounding on a number line. o Solve multi-step word problems using front-end estimation https://learnzillion.com/student/lessons/1719-solve-multistep-word-problems-by-rounding- on-a-number-line https://learnzillion.com/student/lessons/1720-solve-multistep-word-problems-using-frontend- estimation Whole Number Place Value: Our First Unit
8/23/2015
Unit Name: Whole Number Place Value
Common Core State Standards: 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. Essential Vocabulary: · place value · greater than · less than · equal to · comparisons · compare · round · base ten · digit · ones · tens · hundreds · thousands · ten times · partial product · rectangular sections · word form · standard form · expanded form · greatest · least · expanded notation · unit Unit Overview: In this unit, students will build on their understanding of place value to the thousands place in order to expand their understanding to the millions place. This is the first time students will be exposed to the concept of the place of the digit/number to the left is 10 times larger than the place of the digit/number to the right. Students will be asked to reason about numbers using place value symbols >, <, and =. Students will also need to understand how to manipulate numbers into various expanded forms in order to flexibly add, subtract, multiply and divide. For example, the student should understand 285 = 200 + 80 + 5; or 285 = 28 tens and 5 ones; or 285 = 18 tens and 105 ones; etc. In addition, students need to understand the role of a comma and rounding techniques beyond algorithms and procedures. Strategies/Skills: Students will explore place value without the use of formal algorithms. They are expected to use a variety of models to support their reasoning about numbers. · Number lines · Hundreds board · Area models/Rectangular Sections · Relationship between multiplication & division · Expanded, word, and numerical form of numbers Video Support: Video support can be found on LearnZillion. · https://learnzillion.com/ o Understand Place Value: Multiplying by a power of 10 https://learnzillion.com/lessons/16-understand-place-value-multiplying-by-a-power-of-10 o Understand Place Value: Dividing by a power of 10 https://learnzillion.com/student/lessons/19-understand-place-value-dividing-by-a-power-of-10 o Write numbers in expanded form https://learnzillion.com/student/lessons/13-write-numbers-in-expanded-form o Write numbers in word form: using place value https://learnzillion.com/student/lessons/14-write-numbers-in-word-form-using-place-values o Find place value: using pictures https://learnzillion.com/student/lessons/12-find-place-value-using-pictures o Compare numbers: using place value https://learnzillion.com/student/lessons/15-compare-numbers-using-place-values o Locate benchmark numbers on a number line https://learnzillion.com/student/lessons/523-locate-benchmark-numbers-on-a-number-line o Round numbers to the leading digit using a number line https://learnzillion.com/student/lessons/524-round-numbers-to-the-leading-digit-using-a-number-line o Round numbers to a specified place on a number line https://learnzillion.com/student/lessons/525-round-numbers-to-a-specified-place-on-a-number-line o Round 9’s using base ten blocks https://learnzillion.com/student/lessons/526-round-9s-using-base-ten-blocks Measurement
4/13/2015
Unit Name:
Measurement Common Core State Standards: 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. 4.MD.2 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 qualities using diagrams such as number line diagrams that feature a measurement style. Essential Vocabulary: · · Convert/conversion · Liquid volume · Mass · Length · Distance Decimal · Fraction · Units · Equivalent · Measure · Metric · Customary Unit Overview: In this unit, students will apply their understanding of measurement to help them convert measurements within a single system: metric or customary for the first time. Units of measure that are introduced for the first time are: cups, pints, quarts, gallons, pounds, ounces, kilometers, millimeters, and seconds. Additional, the students will reinforce their understanding of place value by using their knowledge to convert within the metric system. Strategies/Skills: Students will build on their understanding of fractions from 3rd grade to make sense of decimals when comparing their equivalency. They are expected to use a variety of models to support their reasoning about numbers. · Conversion table · Quantity diagram · Number line diagram Video Support: Video support can be found on LearnZillion. · http://learnzillion.com o Compare and convert customary units of length https://learnzillion.com/student/lessons/2316-compare-and-convert-customary-units-of-length o Compare and convert customary units of weight https://learnzillion.com/student/lessons/2317-compare-and-convert-customary-units-of-weight o Compare and convert metric units of length https://learnzillion.com/student/lessons/2571-compare-and-convert-metric-units-of-length o Compare and convert metric units of weight https://learnzillion.com/student/lessons/2631-compare-and-convert-metric-units-of-weight o Compare and convert metric units of volume https://learnzillion.com/student/lessons/2498-compare-and-convert-metric-units-of-volume o Solve problems involving distance using diagrams https://learnzillion.com/student/lessons/2723-solve-problems-involving-distance-using-diagrams o Solve problems involving time by drawing a diagram https://learnzillion.com/student/lessons/2915-solve-problems-involving-time-by-drawing-a-diagram o Solve problems involving volume using diagrams https://learnzillion.com/student/lessons/2916-solve-problems-involving-volume-using-diagrams o Solve problems involving mass using diagrams https://learnzillion.com/student/lessons/2917-solve-problems-involving-mass-using-diagrams Decimals
3/31/2015
Unit Name:
Decimals Common Core State Standards: 4.NF.6 Use decimal notation for fractions with denominators 10 or 100 (e.g. 62/100 as .62). 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. Essential Vocabulary: · · Reason · Denominator · Numerator · Decomposing Decimal · Fraction · Unit fraction · Equivalent · Partition Unit Overview: In this unit, students will apply their understanding of fractions to help them understand decimal equivalence. Decimals are introduced for the first time in 4th grade. Students will make connections between fractions with the denominators of 10 and 100 within the place value chart. Students will use reading decimals aloud to help them understand the fractional equivalence as well. In addition, students will use their reasoning skills to compare decimals from the same whole. Strategies/Skills: Students will build on their understanding of fractions from 3rd grade to make sense of decimals when comparing their equivalency. They are expected to use a variety of models to support their reasoning about numbers. · Fraction bars and circles · Place value chart · Number line · Grid models · Ruler/meter stick Video Support: Video support can be found on LearnZillion. · http://learnzillion.com o Convert decimals to fractions to the tenths place using number line https://learnzillion.com/student/lessons/1424-convert-decimals-to-fractions-to-the-tenths-place-using-number-lines o Convert decimals to fractions to the hundredths place using visual aids https://learnzillion.com/student/lessons/1425-convert-decimals-to-fractions-to-the-hundredths-place-using-visual-aids o Convert fractions to decimals to the tenths place using visual aids and division https://learnzillion.com/student/lessons/1426-convert-fractions-to-decimals-to-the-tenths-place-using-visual-aids-and-division o Convert fractions to decimals to the hundredths place using division https://learnzillion.com/student/lessons/1427-convert-fractions-to-decimals-to-the-hundredths-place-using-division o Compare two decimals to the hundredths place using fraction models https://learnzillion.com/student/lessons/3217-compare-two-decimals-to-the-hundredths-place-using-fraction-models o Compare two decimal dollar amounts using coin values https://learnzillion.com/student/lessons/3158-compare-two-decimal-dollar-amounts-using-coin-values o Compare two decimals to the hundredths place using a number line https://learnzillion.com/student/lessons/3354-compare-two-decimals-to-the-hundredths-place-using-a-number-line o Compare two decimal lengths using a ruler https://learnzillion.com/student/lessons/3385-compare-two-decimal-lengths-using-a-ruler Multiplying Fractions by Whole Numbers
3/16/2015
Unit Name:
Multiplying Fractions by Whole Numbers Common Core State Standards: 4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. 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. c. Solve word problems involving multiplication of fraction by a whole number, e.g., by using visual models and equations to represent the problem. Essential Vocabulary: · · Reason · Denominator · Numerator · Decomposing · Whole number Operations · Fraction · Unit fraction · Multiple/multiply · Equivalent · factor Unit Overview: In this unit, students will apply their understanding of adding fractions and extend their understanding by multiplying fractions. Just as students see repeated addition as multiplication students will develop understanding that all fractions are made up of repeated unit fractions (7/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 1/5 or 7/5 = 7 x 1/5). Students are expected to use and create visual fraction models to multiply fractions by whole numbers. Strategies/Skills: Students will build on their understanding of fractions from 3rd grade to make sense of larger fractions when adding, subtracting and equivalence. They are expected to use a variety of models to support their reasoning about numbers. · Area model · Number line · Collection/set models Video Support: Video support can be found on The WCPSS Academics YouTube Channel. · http://tinyurl.com/WCPSSAcademicsYouTube o Multiply Fraction by Whole Number 1 o Multiply Fraction by Whole Number 2 Video support can be found on LearnZillion. · http://learnzillion.com o Multiply fractions by whole numbers: using repeated addition https://learnzillion.com/student/lessons/122-multiply-fractions-by-whole-numbers-using-repeated-addition o Multiply fractions by whole numbers: using models https://learnzillion.com/student/lessons/126-multiply-fractions-by-whole-numbers-using-models o Represent a fraction as the sum of unit fractions using number line https://learnzillion.com/student/lessons/2971-represent-a-fraction-as-the-sum-of-unit-fractions-using-number-line o Represent a fraction as the sum of the unit fraction using area model https://learnzillion.com/student/lessons/3026-represent-a-fraction-as-the-sum-of-unit-fractions-using-an-area-model o Estimate products in multiplication of whole numbers and fractions https://learnzillion.com/student/lessons/2927-estimate-products-in-multiplication-of-whole-numbers-and-fractions o Use a number line for multiplication of fractions and whole numbers https://learnzillion.com/student/lessons/2938-use-a-number-line-for-multiplication-of-fractions-and-whole-numbers o Use a fraction model for multiplication of fractions and whole numbers https://learnzillion.com/student/lessons/2939-use-a-fraction-model-for-multiplication-of-fractions-and-whole-numbers o Use repeated addition for multiplication of fractions and whole numbers https://learnzillion.com/student/lessons/3076-use-repeated-addition-for-multiplication-of-fractions-and-whole-numbers Comparing Fractions
2/27/2015
Comparing Fractions
Common Core State Standards: 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 results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Essential Vocabulary: · · Reason · Denominator · Numerator · Decomposing · Mixed number Operations · Greater than · Greater less · Fraction · Unit fraction · Equivalent/equal · Multiple/multiply Unit Overview: In this unit, students will apply their understanding of fractions to compare fractions by using visual models or finding common denominators or numerators. In addition, students need to use the following symbols to help compare fractions: >, =, <. *Students’ focus should be on visual models NOT on algorithms. Strategies/Skills: Students will build on their understanding of fractions from 3rd grade to make sense of larger fractions when adding, subtracting and equivalence. They are expected to use a variety of models to support their reasoning about numbers. · Fraction bars · Number Line Video Support: Video support can be found on The WCPSS Academics YouTube Channel. · http://tinyurl.com/WCPSSAcademicsYouTube o Comparing Fractions 1 o Comparing Fractions 2 Video support can be found on LearnZillion. · http://learnzillion.com o Compare fractions using the benchmark fraction 1/2 https://learnzillion.com/student/lessons/1431-compare-fractions-using-the-benchmark-fraction-1-2 o Compare fractions using the benchmark of one whole https://learnzillion.com/student/lessons/1432-compare-fractions-using-the-benchmark-of-one-whole o Compare fractions with different denominators using a number line https://learnzillion.com/student/lessons/1433-compare-fractions-with-different-denominators-using-number-lines o Compare fractions by creating common denominators https://learnzillion.com/student/lessons/1436-compare-fractions-by-creating-common-denominators o Use a number line to represent a fraction greater than one https://learnzillion.com/student/lessons/1437-use-a-number-line-to-represent-a-fraction-greater-than-one Equivalent Fractions
2/9/2015
Unit Name:
Equivalent Fractions Common Core State Standards: 4.NF.1Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the numbers 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.3 Understand a fraction a/b with a>1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions joining and separating parts referring to the same whole. 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. 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 relationship between addition and subtraction. Essential Vocabulary: · · Reason · Denominator · Numerator · Decomposing · Mixed number · Multiple/multiply Operations · Addition/joining · Subtraction/separating · Fraction · Unit fraction · Equivalent · Partition Unit Overview: In this unit, students will develop understanding of fraction equivalence and operations with fractions. Students will recognize that two different fractions can be equal (e.g. 15/9 = 5/3), and they will need to develop methods for generating and recognizing equivalent fractions. Students will apply their knowledge of fractions by joining unit fractions (e.g. 1/3, 1/2, 1/4) and separating larger fraction back into unit fractions. Mixed numbers will be introduced for the first time in 4th grade. Students will learn how to turn mixed numbers into improper fractions using fraction models/drawings. *There is NO mathematical reason why fractions must be written in simplified form, although it may be convenient to do so in some cases. Strategies/Skills: Students will build on their understanding of fractions from 3rd grade to make sense of larger fractions when adding, subtracting and equivalence. They are expected to use a variety of models to support their reasoning about numbers. · Fraction bars · Number Line Video Support: Video support can be found on The WCPSS Academics YouTube Channel. · http://tinyurl.com/WCPSSAcademicsYouTube o Finding Equivalent Fractions Video support can be found on LearnZillion. · http://learnzillion.com o Recognize equivalent fractions using number lines https://learnzillion.com/student/lessons/617 o Generate equivalent fractions using number lines https://learnzillion.com/student/lessons/619-generate-equivalent-fractions-using-number-lines o Create equivalent fractions using a number line https://learnzillion.com/student/lessons/1245 Patterns
1/30/2015
Unit Name:
Patterns Common Core State Standards: 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 a rule itself. Essential Vocabulary: · Pattern (number or shape) · Pattern rule Unit Overview: In this unit, students will apply their understanding of patterns with numbers and shapes from previous grades. In addition, this unit builds upon students’ understanding of multiples and factors in order for students to see the patterns and form a rule. Strategies/Skills: Students will build on their understanding of multiples, factors, and geometry to make sense of patterns. They are expected to use a variety of models to support their reasoning about numbers. · Function Table (vertical table/t-chart) · Number Line Video Support: Video support can be found on LearnZillion. · http://learnzillion.com o Find the rule for a function machine using a vertical table https://learnzillion.com/student/lessons/790-find-the-rule-for-a-function-machine-using-a-vertical-table o Understand repeating patterns https://learnzillion.com/student/lessons/791-understand-repeating-patterns o Find missing elements in growing patterns https://learnzillion.com/student/lessons/791-understand-repeating-patterns o Find the 9th shape for a geometric pattern using a table https://learnzillion.com/student/lessons/793-find-the-9th-shape-for-a-geometric-pattern-using-a-table o Determine the rule in patterns that decrease https://learnzillion.com/student/lessons/794-determine-the-rule-in-patterns-that-decrease o Using a table to find the rule for a geometric triangle pattern https://learnzillion.com/student/lessons/795-using-a-table-to-find-the-rule-for-a-geometric-triangle-pattern o Extend a fraction pattern using a number line https://learnzillion.com/student/lessons/796-extend-a-fraction-pattern-using-a-number-line o Generate a pattern sequence using a t-chart https://learnzillion.com/student/lessons/797-generate-a-pattern-sequence-using-a-t-chart o Find the missing inputs for a function machine using a vertical table https://learnzillion.com/student/lessons/798-find-the-missing-inputs-for-a-function-machine-using-a-vertical-table |
Mrs. Ana RhyneI teach 4th grade math and science at Weatherstone Elementary School. I graduated from Meredith College with a BA in Spanish and K-6 licensure. Archives
May 2016
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