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# Grade 4 Math Standards Resources

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.

### Extend the base-ten system to read, write, and represent decimal numbers (to the hundredths) between 0 and 1, between 1 and 2, etc. Base Blocks Decimals

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).

### Use models to connect and compare equivalent fractions and decimals. Equivalent Fractions Finder

Students create equivalent fractions in blue, green and red. They have a choice of using a square or a circle.

### Determine decimal equivalents or approximations of common fractions. Fraction Model I

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. Pan Balance-Numbers

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.

### Compare and order fractions and decimals.

Compare Fractions

Students practice comparing fractions getting feedback with pictures. Scroll down for instructions. Fraction Model I

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. Fraction Sorter

Students build a model of the fraction, check their work, then place the fractions in order on a number line.

Use this activity for demonstrating with the class, as well as for independent student work.

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### Represent money amounts to \$10.00 in dollars and cents, and apply to situations involving purchasing ability and making change.

Making Change

Students make change (for amounts under \$20) for customers who are buying products. Excellent way to practice how to make the least amount of change.

Diffy

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). Base Blocks Decimals

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.

### Apply with fluency multiplication facts to 10 times 10 and related division facts. Arithmetic Four

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. Product Game

Students practice their fluency of multiplication facts with a partner.

### 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). Number Line Bars

Teachers can use a number line to show addition, subtraction, multiplication and division and how they all relate.

The teacher can determine the equation; students are excited to see all the ways to show a problem such as 3 x 4 = 12. Pan Balance-Numbers

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. Rectangle Multiplication

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.

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### 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. Rectangle Multiplication

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.

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### Determine area by finding the total number of same-sized units of area that cover a shape without gaps or overlaps. Geoboards

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.

### Recognize a square that is one unit on a side as the standard unit for measuring area. Geoboards

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.

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### Connect area measure to the area model used to represent multiplication and use this to justify the formula for area of a rectangle. Rectangle Multiplication

Students manipulate the array to create different multiplication problems justifying the formula for area of a rectangle.

### Find the areas of complex shapes that can be subdivided into rectangles. Shape Explorer

Students find the areas of complex shapes that can be subdivided into rectangles.

Geoboards

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.

### Recognize that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas.

Area Explorer

Students practice calculating the area of random shapes. Perimeter can be adjusted, outline can be checked and you can compare areas and perimeters.

NOTE: This activity has a instructor section with related links, lessons and worksheets.

Perimeter Explorer

Students practice calculating the perimeter of random shapes. Area can be adjusted, outline can be checked, and you can compare areas and perimeters.

Rectangle Multiplication

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.

Geoboards

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.