The IFL offers performance-based assessments (PBAs) that assess students' learning of concepts and practices in specific Sets of Related Lessons. Sets of Related Lessons with associated PBAs are marked with an asterisk (*). Please see here for more information about the mathematics PBAs.

Grade Level

K

This lesson set provides an in-depth study of part-part-whole relationships as represented in "put together" situations and in addition equations. Students will:

- make sense of, represent, and solve "put together" addition situations;
- identify the parts and the whole in part-part-whole relationships represented by word problems and equations;
- relate counting to addition through two strategies: counting all and counting on; and
- recognize when one strategy is more appropriate than another.

Mathematical Content Standards: K.OA.A.1, K.OA.A.2

Approximately 8-15 days of instruction.

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Grade Level

1

This lesson set provides a study of "adding to" situations that explore solving for unknowns in all positions (whole, change, start). Students will:

- solve tasks with "add to" situations using a variety of strategies and part-part-whole maps;
- determine if the "unknown" in a situation represents a part of the situation or the whole amount in a situation;
- apply and discuss the commutative property of addition;
- utilize subtraction to solve unknown-addend problems; and
- use the part-part-whole map to respond to problems with situations.

Mathematical Content Standards: 1.OA.A.1, 1.OA.A.2, 1.OA.B.3, 1.OA.B.4

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

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Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

1

This lesson set provides an in-depth study of part-part-whole relationships as represented in "take from" and "take apart" situations and subtraction equations. Students will:

- solve "take from" and "take apart" situations using a variety of strategies and part-part-whole maps;
- determine if the "unknown" in a situation represents a part of the situation or the whole amount in a situation;
- interpret tables and diagrams;
- discuss subtraction as addition with an unknown-addend; and
- write and discuss related addition and subtraction equations.

Mathematical Content Standards: 1.OA.A.1, 1.OA.B.4, 1.OA.C.6, 1.OA.D.7

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

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Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

2

This lesson set provides a study of story situations that explore the part-part-whole relationship, and through it also, the relationship between subtraction and addition with an unknown addend. Students will:

- make sense of and solve "put together" situations involving an unknown addend using a variety of strategies and representations;
- determine if the unknown in "put together" situations represents a part or the whole amount in the situation;
- make sense of and solve "compare" situations with an unknown difference using a variety of strategies and representations;
- determine the unknown difference as being "how many more" or "how many fewer"; and
- understand and utilize the relationship between subtraction and addition with an unknown addend.

Mathematical Content Standards: 2.OA.A.1, 2.NBT.B.7

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

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Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

2

This set of related lessons provides students with an opportunity to develop a deep understanding of addition with two-digit numbers while providing a bridge into addition with three-digit numbers. Students will:

- solve "put together" situations using base ten blocks and/or a hundreds chart;
- determine if the unknown in a situation represents a part or a whole;
- understand that tables can be "read" and can represent part-part-whole relationships;
- apply strategies to solve addition problems; and
- use a variety of representations to respond to situations.

CCSS: 2.OA.A.1, 2.NBT.B.6, 2.NBT.B.7

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

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Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

2

This set of related lessons provides students with an opportunity to grapple with the relationship between subtraction and missing addend addition when using both operations to solve compare situations with an unknown difference. A variety of contexts provide opportunities for students to compare sets of items, heights, lengths, and distances traveled. Students will:

- solve "compare" story situations with an unknown difference involving sets of items, lengths, heights, and distance traveled and discuss attributes of "compare" story situations;
- discuss the relationship between subtraction and missing addend addition when determining a comparison situation;
- use strategies to solve compare situations: adding on to the small set to equal the larger set and subtracting by removing aligned parts to determine the difference;
- use strategies to solve subtraction equations: regrouping a ten into ones in order to subtract and making an easier number to subtract and adjusting;
- select and use tools to make sense of situations (base ten blocks, diagrams, and number lines); and
- interpret and make observations about data represented in bar graphs.

CCSS: 2.OA.A.1, 2.NBT.B.7, 2.MD.B.5

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

3

This set of related lessons provides students with a study of area measurement. Students will learn the meaning of area by tiling figures with square tiles of various sizes and solve for the unknowns in all positions (the area or the unknown length or width). Students will:

- solve area problems using a variety of strategies;
- determine that an area of a plane figure has two dimensions: length and width;
- recognize that repeated addition and multiplication can be used to determine the area of figures; and
- determine the unknown in a story situation and relate the unknowns to multiplication and division.

CCSS: 3.MD.C.5, 3.MD.C.5a, 3.MD.C.5b, 3.MD.C.6, 3.MD.C.7, 3.MD.C.7a, 3.MD.C.7b

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

3

This lesson set provides a study of the associative and distributive properties of multiplication. Students will:

- solve multiplication word problems with two and three factors;
- interpret products of whole numbers; and
- apply the properties of operation (associative or distributive) to multiply.

Mathematical Content Standards: 3.OA.A.1, 3.OA.B.5

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

3

This lesson set is designed to provide students opportunities to compare and reason about the comparison of fractions with either common denominators or common numerators. Students will:

- solve real-world situations that require a comparison of fractional amounts;
- reason about the meaning of the numerator and denominator to compare fractions;
- work with fractional amounts between 0 and 1 and fractional amounts greater than or equal to 1; and
- create and use regional and number line models to represent and compare fractions.

Mathematical Content Standards: 3.NF.A.1, 3.NF.A.2, 3.NF.A.2.A, 3.NF.A.2.B, 3.NF.A.3, 3.NF.A.3.A, 3.NF.A.3.B, 3.NF.A.3.C, and 3.NF.A.3.D

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

4

This lesson set provides a study of multiplicative comparisons, problems in which students have to solve for "how many times greater/less." Students will:

- explore the meaning of the two factors in comparison multiplication problems;;
- recognize the inverse relationship between multiplication and division, and determine that division can be used to solve comparison multiplication problems when either the group size or the scaling factor is provided; and
- use a variety of representations to respond to a problem situation, and weigh the advantages and disadvantages of such representations.

Mathematical Content Standards: 4.OA.A.1, 4.OA.A.2

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

4

This set of related lessons provides students with an introduction to addition and subtraction of fractions with like denominators in the same whole. Students will:

- represent non-unit fractions;
- understand non-unit fractions as a sum of unit fractions; and
- prove equivalency of multiplicative expressions involving one fractional factor by connecting repeated addition to multiplication.

CCSS: 4.NF.A.2, 4.NF.B.3, 4.NF.B.3a, 4.NF.B.3b, 4.NF.B.3c, 4.NF.B.3d, 4.NF.B.4, 4.NF.B.4a, 4.NF.B.4b, 4.NF.B.4c

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

4

This lesson set develops understanding of the relationship between fractions and decimals, decimal number notation and addition, as well as comparison of decimal numbers. Students will:

- express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and write fractions with denominators of 10 and 100 with decimal notation;
- combine tenths and hundredths;
- compare two decimals to hundredths and justify the comparisons using visual models; and
- compare decimals and express their relationship using the symbols, >, <, or = and explain that comparisons are valid only when the two decimals refer to the same whole.

Mathematical Content Standards: 4.NF.C.5, 4.NF.C.6, 4.NF.C.7

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

5

This lesson set provides students an introduction to fraction addition and subtraction when the denominators of fractions differ; students are given problems in which they have to consider different names for fractions relative to a same-sized whole in order to create same-sized units to combine or separate quantities. Students will:

- understand and explain the naming of units in relation to a value of one;
- understand and explain the effects of partitioning a given fraction to form an equivalent value; and
- use a variety of strategies and representations to respond to a problem situation involving addition and subtraction of fractions relative to a same-sized whole and weigh their advantages and disadvantages.

Mathematical Content Standards: 5.NF.A.1, 5.NF.A.2

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

5

This lesson set provides students with a study of multiplication when one or both factors are fractions. Students apply the meaning of factors to numbers less than 1 using visual representations. Students will:

- solve contextual situations using a variety of strategies;
- determine the fractional models that can be used to represent multiplication with fractions;
- recognize that repeated addition can be used for some fractional multiplication problems but not for others; and
- reason about why the product in fractional multiplication is less than one or both of the factors.

Mathematical Content Standards: 5.NF.B.4, 5.NF.B.4.A, 5.NF.B.4.B, 5.NF.B.5, 5.NF.B.5.B, and 5.NF.B.6

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

5

This lesson set provides an introduction to division with numbers less than one, both when the whole number amount is being divided by less than one and when the fraction is being partitioned by a whole number. Students will:

- apply understanding of division with whole numbers to division involving numbers less than one;
- understand the meaning of the dividend and the divisor and recognize what happens when a unit fraction is in either position (but not both); and
- use a variety of representations to respond to a problem situation and weigh the advantages and disadvantages of such representations.

Mathematical Content Standards: 5.NF.B.7, 5.NF.B.7a, 5.NF.B.7b, and 5.NF.B.7c

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Grade Level

5

This lesson set provides an introduction to decimal multiplication and division problems in which students have to consider how many groups of a fixed size comprise a total. Students will:

- apply understanding of division with whole numbers to division involving numbers less than one;
- recognize the meaning of the dividend and the divisor and what happens when a unit fraction is in either position (but not both); and
- use a variety of representations to respond to a problem situation and weigh the advantages and disadvantages of such representations.

Mathematical Content Standards: 5.NBT.B.5, 5.NBT.B.6, 5.NBT.B.7

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

* The IFL offers performance-based assessments (PBAs) that assess students' learning of concepts and practices in this Set of Related Lessons. PBAs come with scoring guides and annotated student work.