4.1 Unit 1: Place Value
4.1-Unit 1 Whole Numbers, Place Value and Rounding in Computation
In Unit 1, students will learn to generalize place value understanding for multi-digit whole numbers and use their place value understanding and properties of operations to perform multi-digit arithmetic. In the first part of the unit, students will explore place value and the relationship among place values in multi-digit numbers as well as learning how to represent a number in standard, word and expanded form. Students will then build on their place value understanding by rounding whole numbers to any place and comparing and ordering whole numbers. Later in the unit, students move on to exploring different strategies for multi-digit addition and subtraction with the ultimate goal being mastery of the standard algorithms. They will also use estimation to determine if their solutions make sense. Finally, students will use learned strategies to be able to solve multi-step problems involving addition and subtraction of multi-digit numbers.
Students will get plenty of hands on, multi-sensory practice with these standards through our workshop model. After the whole group mini lesson, students will explore and demonstrate mastery of the standards through guided practice, partner/group work and the use of technology.
Your child will be taking notes on the standards throughout the unit in their Math Journals. Please remember that these are wonderful study tools that we encourage the students take home (as long as they remember to bring them back!) We will be teaching the students how to take very neat, detailed notes that will make awesome study tools!
4.1 Standards for Unit 1:
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.
4.NBT.4 - Fluently add and subtract multi-digit whole numbers using the standard algorithm.
4.OA.3 - 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.
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 quantities using diagrams such as number line diagrams that feature a measurement scale.
*4.MD.2 is a standard that will appear in every unit in 4th grade and will be covered more thoroughly in Unit 7
4.2 Unit 5: Decimal Fractions
Throughout this unit your child will be learning about decimal fractions and how to express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100. As we progress through the unit, students will then use decimal notation for fractions with denominators of 10 or 100. And, finally, by the end of the unit, student will be able to compare two decimals to the hundredths place by reasoning about their size, and recognize that comparisons are valid only when two decimals refer to the same whole.
We will do this using visual models and number lines. We will also practice this skill within word problems. Your child will be taking notes on the standards throughout the unit in their Math Journals. Please remember that these are wonderful study tools that we encourage the students take home (as long as they remember to bring them back!) I will be teaching the students how to take very neat, detailed notes that will make awesome study tools!
4.2 Standards for the Unit:
4.NF.5 - Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100, and use this technique to add two fractions with respective denominators 10 and 100. 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 two decimals refer to the same whole. Record the results of the comparisons with the symbols >, =, or <, and justify the conclusions (i.e. by using a visual model).
5.1 Unit 1: Order of Operations and Whole Numbers
As mentioned in the other leveled blogs, students will be practicing these skills in a multitude of ways through our Math Workshop model. Through fun games, hands on activities and manipulatives, technology, and mini lessons, students will both learn and continually practice these standards. Students will also be maintaing a detailed journal with notes, anchor charts, models, and practice problems, and are encouraged to take this wonderful study tool home :)
5.1 Standards for the Unit:
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. 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.5 - Fluently multiply multi-digit whole numbers using the standard algorithm (or other strategies demonstrating understanding of multiplication) up to a 3 digit by 2 digit factor.
5.NBT.6 - Fluently divide up to 4- digit dividends and 2-digit divisors by using at least one of the following methods: 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 or concrete models. (e.g., rectangular arrays, area models).
*Please note that using the standard algorithm (i.e. traditional long division) is not yet an expectation in 5th grade. While this is a strategy many already know, it is not included in the fifth grade standard. This becomes an expectation in 6th grade.