This lesson connects geometry to linear algebra by representing rotations and reflections about the origin as 2x2 orthogonal matrices. Students derive the specific matrix forms and verify their orthogonality conditions algebraically.
A comprehensive workshop focused on mastering rational number operations and common CCSS 7th grade math misconceptions in preparation for the NYS test.
Tier 2 reteach for standard 4.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
Tier 2 reteach for standard 4.NF.3: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Focus on like denominators and mixed numbers.
Tier 2 reteach for standard 4.NF.2: Compare two fractions with different numerators and different denominators. Focus on common denominators and benchmark fractions.
Tier 2 reteach for standard 4.NF.1: Explain why fractions are equivalent using visual fraction models. Focus on the "Splitting" and "Merging" strategies.
Tier 2 reteach for standard 4.NBT.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value.
Tier 2 reteach for standard 4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value.
A foundational lesson on multi-digit multiplication using color-coded place value strategies and the area model to support students working significantly below grade level.
Tier 2 reteach for standard 4.NBT.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Tier 2 reteach for standard 4.NBT.3: Use place value understanding to round multi-digit whole numbers to any place.
Tier 2 reteach for standard 4.NBT.2: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place.
Tier 2 reteach for standard 4.NBT.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.