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Students have to explain!
Please see the following links for more information about each individual book: These books address the standards 5th graders seem to be having the most difficult time with; decimals, fractions, and numbers and operations (place value, base 10, order of operations)
Each book comes in two versions (half page and full page): great for student study guide books, summative assessments, performance tasks, or even class books!
An answer key is not included, because the majority of each book has more than one possible answer, as much of it is rules and explanations.
Also, see the preview for a full preview (partially blocked by an oval shaped for copyright reasons) of the decimals book, so that you can see what the format is for each book.
Standards covered are:
5.OA.1 Use parentheses, brackets, or
braces in numerical expressions, and
evaluate expressions with these
5.OA.2 Write simple expressions that
record calculations with numbers, and
interpret numerical expressions without
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.
a. Read and write decimals to
thousandths using base-ten
numerals, number names, and
expanded form, e.g., 347.392 = 3 ×
100 + 4 × 10 + 7 × 1 + 3 × (1/10) +
9 x (1/100) + 2 x (1/1000)
• CCSS.Math.Content.5.NBT.A.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.
• CCSS.Math.Content.5.NBT.A.3 Read, write, and compare decimals to thousandths.
o CCSS.Math.Content.5.NBT.A.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
o CCSS.Math.Content.5.NBT.A.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
• CCSS.Math.Content.5.NBT.A.4 Use place value understanding to round decimals to any place.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
• CCSS.Math.Content.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
• CCSS.Math.Content.5.NBT.B.6 Find whole-number quotients 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.
• CCSS.Math.Content.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 addition and subtraction; relate the strategy to a written method and explain the reasoning used.
CCSS.Math.Content.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.)
CCSS.Math.Content.5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. 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 < ½
CCSS.Math.Content.5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
CCSS.Math.Content.5.NF.B.5a Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
CCSS.Math.Content.5.NF.B.4a Interpret the product (a/b) × q as a parts of a partition of qinto b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
CCSS.Math.Content.5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
CCSS.Math.Content.5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1
CCSS.Math.Content.5.NF.B.7a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
CCSS.Math.Content.5.NF.B.7b Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
CCSS.Math.Content.5.NF.B.7c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
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