Pro Tip: Searching based on the standards or the big idea can help you embed the materials in your curriculum scope and sequence.
This Rich Math Tasks volume contains a collection of learner-centered mathematical challenges for students in grades 3-12. Everything you will find in this volume was designed by Hawaiʻi teachers for Hawaiʻi students as part of the ongoing, HIDOE-led Performance Assessment Development Initiative (PADI). These tasks have been thoughtfully crafted, piloted, and revised to serve as high-quality classroom-based tools that gauge student understanding and actively enhance learning and engagement.
This booklet is designed to be easy to print, either in its entirety or by selecting the pages of PDF you'd like to use. You can also find these tasks within the math instructional guides posted with their accompanying end-of-unit tasks under the "math" tab.
If you'd like to receive a free hard copy in the mail, please email tyler.belanga@k12.hi.us with your request. Mahalo!
BIG IDEA & STANDARDS
MATERIALS AVAILABLE FOR DOWNLOAD
Applying Multiplicative Comparisons
4.OA.A.1: Interpret a multiplication equation as a comparison, e.g., interpret 35= 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
4.OA.A.2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
4.OA.A.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
K-12.MP.1-6
To download the full instructional guide (includes two instructional tasks and one end-of-unit performance task):
Applying Multi-Digit Multiplication & Division
4.OA.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
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 and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
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, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
4.MD.3: Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
K-12.MP.1-8
To download the full instructional guide (includes two instructional tasks and one end-of-unit performance task):
Applying Fractions
4.NF.A.1: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
4.NF.A.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
4.NF.B.3d: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
4.NF.B.4c: Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.
K-12.MP.1-6
To download the full instructional guide (includes two instructional tasks and one end-of-unit performance task):