The focus of this week’s instruction is to deepen students’ understanding of:
- Dividing decimals,
- Mental strategies for multi-digit whole number division,
- Partial quotients, and
- Making like unit pictorially.
- Student Print Packets for each day
- End of Week Assessment
- Dry Erase Markers
- Personal White Boards
- Hundreds to thousandths place value chart (see templates)
- Place value disks (Students may choose to draw disks instead)
- Millions to thousandths place value chart (see templates)
- 2 pieces of 4 ½ " × 4 ½ " paper per student (depending on how the folding is completed before drawing the rectangular array model)
- Straightedge such as a ruler (optional; one per student)
5.NBT.A.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.B.6 Find whole-number quotients and remainders 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.B.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 operations; assess the reasonableness of answers using estimation strategies. (Limit division problems so that either the dividend or the divisor is a whole number.)
5.NF.A.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.A.2 Solve contextual problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
- Tape Diagrams: Tape diagrams are also called “bar models” and consist of a simple bar drawing that students make and adjust to fit a word or computation problem. They then use the drawing to discuss and solve the problem.
- Place Value Chart: A place value chart is a diagram that helps us to find and compare the place value of the digits in numbers.
- Standards Algorithm: A standard algorithm or method is a specific method of computation which is conventionally taught for solving mathematical problems
- Rectangular Fraction Model: a rectangle that represents the whole amount, and divide it into equal parts. Each part is a unit fraction.
Additional Terms and Symbols
- >, <, = (greater than, less than, equal to)
- Digit (any of the numbers 0 to 9; e.g., what is the value of the digit in the tens place?)
- Hundredths (as related to place value)
- Place value (the numerical value that a digit has by virtue of its position in a number)
- Tenths (as related to place value)
- Unit form (e.g., 3.21 = 3 ones 2 tenths 1 hundredth)
- Word form (e.g., one hundred thirty-five)
- Decimal (a fraction whose denominator is a power of ten and whose numerator is expressed by figures placed to the right of a decimal point)
- Divisor (the number by which another number is divided)
- Equation (a statement that the values of two mathematical expressions are equal)
- Equivalence (a state of being equal or equivalent)
- Estimate (approximation of the value of a quantity or number)
- Multiple (a number that can be divided by another number without a remainder like 15, 20, or any multiple of 5)
- Product (the result of multiplying numbers together)
- Quotient (the answer of dividing one quantity by another)
- Remainder (the number left over when one integer is divided by another)
- Renaming (decomposing or composing a number or units within a number)
- Area models (e.g., an array)
- Number bond
- Place value disks
- Benchmark fraction (e.g., 12 is a benchmark fraction when comparing 13 and 35)
- Like denominators (e.g., 18 and 58)
- Unlike denominators (e.g., 18 and 17)