## Building new foundations for lasting mathematical success.

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

Tile Farm meets all standards for mathematical practice, supporting students make sense of problems and persevere in solving them, reason abstractly and quantitatively, construct viable arguments, model with mathematics, use appropriate tools strategically, attend to precision, look for and make use of structure, and look for and express regularity in repeated reasoning.

**CCSS.MATH.CONTENT.K.MD.B.3**

Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

**CCSS.MATH.CONTENT.K.G.A.2**

Correctly name shapes regardless of their orientations or overall size.

**CCSS.MATH.CONTENT.K.G.B.6**

Compose simple shapes to form larger shapes.

**CCSS.MATH.CONTENT.1.NBT.B.2**

Understand that the two digits of a two-digit number represent amounts of tens and ones.

**CCSS.MATH.CONTENT.1.G.A.1**

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

**CCSS.MATH.CONTENT.1.G.A.2**

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

**CCSS.MATH.CONTENT.2.NBT.B.5**

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

**CCSS.MATH.CONTENT.2.NBT.B.9**

Explain why addition and subtraction strategies work, using place value and the properties of operations.^{1}

**CCSS.MATH.CONTENT.2.G.A.1**

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.** ^{1}** Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

**CCSS.MATH.CONTENT.3.G.A.1**

Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

**1** Explanations may be supported by drawings or objects.

## Sample Lesson for Early Learners

#### The House

Classify, Count, Cardinality, Compare, Add, Subtract

#### Drag & Drop: Right Triangle

Classify Triangle

Count “1 Triangle”

*Optional: Toggle ***Count*** Button to Show Cardinality at Top*

#### Connect: Right Triangle

Connect Triangle

Count “2 Triangles”

#### Save Cluster: 2 Right Triangles

Tap **Save Shape** Button

Usable *Unit of 2* is in **My Shapes**

#### Clear Canvas

Tap **Delete** Button

Confirm Clear

#### Drag, Drop, & Connect: 4 Squares

Classify Square

Count to “4 Squares”

#### Save Cluster: 4 Squares

Classify Square

Count to “4 Squares”

Compare Clusters

*Which one is greater / less than?*

#### Drag, Drop, & Add: 2 + 4 = ?

Drag 2 Triangles

Connect to 4 Squares

*How Many Shapes Are There?*

Count “6 Shapes”

#### Subtract: 6 - 4 = ?

Tap **Erase** Button

Tap & Subtract Cluster of 4 Squares

*How Many Shapes Are There?*

#### Reinforcement

Tap the **Tiles** Button

Add 4 Squares, One at a Time

Count to “6 Shapes”

Tap **Erase** Button

Tap & Subtract Cluster of 2 Triangles

6 – 2 = ?

Tap the **Tiles** Button

Add 2 Triangles, One at a Time

Count to “6 Shapes”