It is recommended that teachers review activities and read the associated directions and/or lesson plan ideas prior to using them with their students. In some cases, the activities are very open-ended and are best used in conjunction with paper/pencil activities or when students are paired and working on a single computer. If the directions and/or lesson plans are not obvious, a link is provided within the description of the resource.
It is essential that these standards be addressed in contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations.
4.1 Number and Operations: Develop an understanding of decimals, including the connections between fractions and decimals.
4.1.1
Extend the base-ten system to read, write, and represent decimal numbers (to the hundredths) between 0 and 1, between 1 and 2, etc.
Students use blocks to show place value for numbers; base and number of decimal places are adjustable. Base blocks consist of individual "units," "longs," "flats," and "blocks" (ten of each set for base 10).
4.1.2
Use models to connect and compare equivalent fractions and decimals.
Teachers can use this manipulative to show several representations for fractions (circle, rectangle, and set model) using adjustable numerators and denominators. The decimal and percent values that are equivalent to the fraction are shown.
Students explore the concept of equivalent expressions by placing expressions on each side of the balance.
Note: An initial introduction from the teacher is needed, but students will then be able to continue on their own. Students need to understand that a fraction is a division problem to be able to enter fractions.
Teachers can use this manipulative to show several representations for fractions (circle, rectangle, and set model) using adjustable numerators and denominators. The decimal and percent values that are equivalent to the fraction are shown.
Students find the difference between pairs of numbers on each side of a square to solve a puzzle. Students choose which kind of numbers to use (whole numbers, integers, fractions, decimals, or money).
Students use base ten blocks to solve addition/subtraction problems by regrouping pieces. It is a good resource to visually show regrouping.
Students are able to drag a block (e.g. 10s block) to the right to break it apart into smaller blocks (e.g. ten 1s blocks) and also combine groups of smaller place value blocks into larger place value blocks. NOTE: Need to instruct students on how to group the blocks before moving using the "lasso."
4.2 Number and Operations and Algebra: Develop fluency with multiplication facts and related division facts, and with multi-digit whole number multiplication.
4.2.1
Apply with fluency multiplication facts to 10 times 10 and related division facts.
Students must answer arithmetic questions (addition, subtraction, multiplication, division) to earn a piece to place on the board (like the game Connect Four). Parameters: time limit, difficulty level, types of questions.
Students practice their fluency of multiplication facts with a partner.
4.2.2
Apply understanding of models for multiplication (e.g., equal-sized groups, arrays, area models, equal intervals on the number line), place value, and properties of operations (commutative, associative, and distributive).
Students explore the concept of equivalent expressions. Students must place equal expressions on each side of the balance. Can be used to demonstrate and/or test properties of operations.
Note: An initial introduction from the teacher is needed, but students will then be able to continue on their own. When an equation is equal, it will show as a number sentence in a list. If the equation is not equal, the pan balance will not be level.
Students manipulate the array to create different multiplication problems. It could be used to introduce a multiplication table and how to use it. Students can also manipulate the array to make large multiplication problems, beyond 12 x 12, by clicking on the "common" button.
4.2.3
Select and use appropriate estimation strategies for multiplication (e.g., use benchmarks, overestimate, underestimate, round) to calculate mentally based on the problem situation when computing with whole numbers.
N/A
4.2.4
Develop and use accurate, efficient, and generalizable methods to multiply multi-digit whole numbers.
N/A
4.2.5
Develop fluency with efficient procedures for multiplying multi-digit whole numbers and justify why the procedures work on the basis of place value and number properties.
Students manipulate the array to create different multiplication problems. It could be used to introduce a multiplication table and how to use it. Students can also manipulate the array to make large multiplication problems, beyond 12 x 12, by clicking on the "common" button.
4.3 Measurement: Develop an understanding of area and determine the areas of two-dimensional shapes.
4.3.1
Recognize area as an attribute of two-dimensional regions.
N/A
4.3.2
Determine area by finding the total number of same-sized units of area that cover a shape without gaps or overlaps.
Students can build a shape then use additional bands to divide it into same-sized units to determine the area.
NOTE: You can use these boards to do everything you would do with a standard geoboard. It would be best used with teacher guidance first and directed student exploration after.
4.3.3
Recognize a square that is one unit on a side as the standard unit for measuring area.
Students can build a shape then use additional bands to divide it into same-sized units to determine the area.
NOTE: You can use these boards to do everything you would do with a standard geoboard. It would be best used with teacher guidance first and directed student exploration after.
4.3.4
Determine the appropriate units, strategies, and tools to solving problems that involve estimating or measuring area.
N/A
4.3.5
Connect area measure to the area model used to represent multiplication and use this to justify the formula for area of a rectangle.
Students can build a complex shape then use additional bands to divide it into rectangles to determine the area.
NOTE: You can use these boards to do everything you would do with a standard geoboard. It would be best used with teacher guidance first and directed student exploration after.
4.3.7
Solve problems involving perimeters and areas of rectangles and squares.
4.3.8
Recognize that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas.
This site allows the user to manipulate the array to create different multiplication problems. It could be used to introduce a multiplication table and how to use it. It is useful because students can manipulate to make large multiplication problems, beyond 12 x 12.
Allows students build, draw, and compare two-dimensional shapes to describe, classify, and understand relationships among types of two-dimensional objects using their defining properties.
NOTE: You can use these boards to do everything you would do with a standard geoboard. It would be best used with teacher guidance first and directed student exploration after.